A Novel Approach Based on Kano Model, Interval 2-Tuple...

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Research Article A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic Representation Model, and Prospect Theory for Apperceiving Key Customer Requirements Aijun Liu , 1,2 Qiuyun Zhu , 1 Haiyang Liu , 1 Hui Lu , 3 and Sang-Bing Tsai 4 1 School of Economics and Management, Xidian University, No. 2 Taibai South Street, Xi’an 710071, China 2 State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China 3 Tianhua College, Shanghai Normal University, Shanghai 201815, China 4 Zhongshan Institute, University of Electronic Science and Technology of China, Zhongshan 528402, China Correspondence should be addressed to Hui Lu; [email protected] and Sang-Bing Tsai; [email protected] Received 18 December 2017; Accepted 3 April 2018; Published 18 July 2018 Academic Editor: Francesco Riganti-Fulginei Copyright © 2018 Aijun Liu et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e precisely perception of key customer requirements (CRs) is critically important for customer collaborative product innovation (CCPI) design. A novel approach is proposed based on the Kano model, interval 2-tuple linguistic representation model, and prospect theory. First of all, a Kano model is constructed to preliminarily screen the relatively important product function attributes. For the uncertain and vague information of CRs, an interval 2-tuple linguistic representation model is proposed to determine the weight of CRs. en, the comprehensive prospects value is utilized for sorting the innovative programs based on the prospect theory. Finally, a numerical example is given to verify the scientific and validity of the proposed method. 1. Introduction With the increasingly fierce market competition, as well as more and more personalized and diversified CRs, it is very critical for the modern manufacturing enterprises to grasp customers’ key requirements in a relatively short time because of the complexity of decision-making problems and the fuzziness of decision-making environments (Liu and Wang [1]). What is more, integrating the CRs into the product design is very important for successful product development in CCPI, which can effectively enhance the communication between enterprises and customers and then improve the per- formance of enterprises. For example, Franke and Von Hippel [2] proposed a study to satisfy heterogeneous customer requirements via innovation toolkits, and the case of Apache security soſtware proved that collaborative innovation can bring rich profits to the company. Besides, Lilien et al. [3] compared and analyzed the CCPI process of 3M in the United States and illustrated the clear benefits of customer innovation with actual sales data. Nowadays, this method has been widely used in product design (Song et al. [4]; Dahl et al. [5]). It is well known that the key CRs is the core of CCPI; however, due to the expression of key CRs it is too subjective and vagueness to be accurately obtained. Based on this, we integrate Kano model, the interval 2-tuple linguistic representation model, and prospect theory to determine the key customer requirements. Over the past decade, the way of identifying key cus- tomer requirements including qualitative and quantitative methods was developed. About qualitative method, Chen et al. [6] proposed an ontology learning CRs representation system, the system which preprocessed customer statements by language processing tools. Wang and Tseng [7]; Wang and Tseng [8] put forward the concept of customer demand bias and employed probability analysis methods to analyze CRs. Liu et al. [9] proposed a system management approach for demand management in industrial design. Violante et al. [10] developed a user-centric approach that can meet the specific requirements of the company and help organizations effectively identify selection tools. Sheng et al. [11] took the product service system as the research object, constructed the quality house, and determined the attribute weight of the Hindawi Mathematical Problems in Engineering Volume 2018, Article ID 8192819, 23 pages https://doi.org/10.1155/2018/8192819

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Research ArticleA Novel Approach Based on Kano Model Interval 2-TupleLinguistic Representation Model and Prospect Theory forApperceiving Key Customer Requirements

Aijun Liu 12 Qiuyun Zhu 1 Haiyang Liu 1 Hui Lu 3 and Sang-Bing Tsai 4

1School of Economics and Management Xidian University No 2 Taibai South Street Xirsquoan 710071 China2State Key Laboratory for Manufacturing Systems Engineering Xirsquoan Jiaotong University Xirsquoan 710049 China3Tianhua College Shanghai Normal University Shanghai 201815 China4Zhongshan Institute University of Electronic Science and Technology of China Zhongshan 528402 China

Correspondence should be addressed to Hui Lu janetluck126com and Sang-Bing Tsai sangbinghotmailcom

Received 18 December 2017 Accepted 3 April 2018 Published 18 July 2018

Academic Editor Francesco Riganti-Fulginei

Copyright copy 2018 Aijun Liu et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The precisely perception of key customer requirements (CRs) is critically important for customer collaborative product innovation(CCPI) design A novel approach is proposed based on the Kano model interval 2-tuple linguistic representation model andprospect theory First of all a Kanomodel is constructed to preliminarily screen the relatively important product function attributesFor the uncertain and vague information of CRs an interval 2-tuple linguistic representation model is proposed to determine theweight of CRs Then the comprehensive prospects value is utilized for sorting the innovative programs based on the prospecttheory Finally a numerical example is given to verify the scientific and validity of the proposed method

1 Introduction

With the increasingly fierce market competition as well asmore and more personalized and diversified CRs it is verycritical for the modern manufacturing enterprises to graspcustomersrsquo key requirements in a relatively short time becauseof the complexity of decision-making problems and thefuzziness of decision-making environments (Liu and Wang[1]) What is more integrating the CRs into the productdesign is very important for successful product developmentin CCPI which can effectively enhance the communicationbetween enterprises and customers and then improve the per-formance of enterprises For example Franke andVonHippel[2] proposed a study to satisfy heterogeneous customerrequirements via innovation toolkits and the case of Apachesecurity software proved that collaborative innovation canbring rich profits to the company Besides Lilien et al [3]compared and analyzed the CCPI process of 3M in theUnited States and illustrated the clear benefits of customerinnovation with actual sales data Nowadays this method hasbeen widely used in product design (Song et al [4] Dahl

et al [5]) It is well known that the key CRs is the core ofCCPI however due to the expression of key CRs it is toosubjective and vagueness to be accurately obtained Based onthis we integrate Kano model the interval 2-tuple linguisticrepresentation model and prospect theory to determine thekey customer requirements

Over the past decade the way of identifying key cus-tomer requirements including qualitative and quantitativemethods was developed About qualitative method Chen etal [6] proposed an ontology learning CRs representationsystem the system which preprocessed customer statementsby language processing tools Wang and Tseng [7] Wangand Tseng [8] put forward the concept of customer demandbias and employed probability analysis methods to analyzeCRs Liu et al [9] proposed a system management approachfor demand management in industrial design Violante etal [10] developed a user-centric approach that can meet thespecific requirements of the company and help organizationseffectively identify selection tools Sheng et al [11] took theproduct service system as the research object constructedthe quality house and determined the attribute weight of the

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 8192819 23 pageshttpsdoiorg10115520188192819

2 Mathematical Problems in Engineering

Depth interviews

Choose linguistichierarchies

Initialrequirements

Customers

Customers

Customers

Questionnaire

7 Labels

3 Labels

9 Labels

5 Labels

13 Labels

Choose linguistichierarchies

Choose linguistichierarchies

Focus group

Expert

Expert

Expert

Determine thetype of indicator

Determine thetype of indicator

Determine thetype of indicator

According toexpert opinion

Design questionnaires

Analysis of thequestionnaire results

Send questionnaires

Collect questionnaires

Ranking product attributesaccording to si

Screen initial requirement based on kano model

Set the linguistic evaluationset

Obtain the key requirementof customers

Converts the linguisticcomplementary judgmentmatrix to interval 2-type

linguistic judgment matrix

e interval 2-type linguisticjudgment matrix

transformed into intervalnumber

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Determine the key requirement based on the 2-tuple linguistic information

Type oneAttribute value is

Crisp number

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Rank according to thecomposite foreground value

Obtain the best solution

Calculate the gains and lossvalues of indicators

Determine the best solution based on the 2-tuple linguistic information

Solution 1

Solution

Solution n

Figure 1 The method we proposed

product and service Carulli et al [12] proposed a methodfor capturing CRs based on virtual reality technology whichwas commonly used in the early stages of product design todeduce CRs and reduce overall cost In order to solve theproblem of inaccurate customer demand Kwong and Bai [13]

introduced the fuzzy number on the basis of traditional AHPand proposed the fuzzy AHP to determine the importanceof customer demand In the process of product collaboratedesign Halimahtun [14] used a system framework approachto conceptualize the current and future customer demand for

Mathematical Problems in Engineering 3

automotive electronics The qualitative method is simple andeasy to operate but its subjectivity is too strong to reflect theessential differences between items the results obtained aremore abstract The application effect of qualitative method isunconvincing

As for quantitative method Li et al [15] combined mini-mum deviation method the Balanced Scorecard the analytichierarchy process (AHP) the proportional method and soon and proposed a system operation method that can makebetter use of product competition and preference informa-tion Due to the ambiguity and uncertainty of the customersrsquorequirementsWang and Tseng [16] established a probability-based Bayesian classifier by using existing customer selectiondata the classifier classified CRs based on the flexibility ofcustomer demand Finally the case proved that this methodhad obvious advantages in customer demand classificationAguwa et al [17] developed a new approach to measurecustomer satisfaction by considering quantitative factors suchas quantitative data design parameters drawing outputand decision-making templates for means of measurementThis method can reduce errors and shorten the engineeringdevelopment time Liu et al [18] used language intuitionisticfuzzy number to describe the decision makerrsquos languageinformation Then comparative analysis method is used toprove the validity of the proposed method Nahm et al [19]proposed two methods of customer preference and customersatisfaction assessment the former provided a way to captureincomplete and uncertain information about the customerand the latter built a customer satisfaction model based oncompetitive benchmarking finally the effectiveness of theproposed method was proved by a door design exampleWu et al [20] integrated the gray relational theory into theQuality Function Deployment (QFD) this method takingthe uncertainty and advancement of CRs into account wasutilized to analyze dynamic CRs Liu et al [21] presented anapproach to address the dependent attribute problem leadingto a function form with design attributes as independentvariables and proved the potential to optimize the designspecification Takai and Ishii [22] analyzed and comparedtwo methods for identifying representative needs affinitydiagram (AD) and subjective clustering (SC) the CRs anal-ysis of the next generation particle accelerator was used todemonstrate the scientific nature of the proposed methodThe establishment of the key customer requirements is crucialto CCPI and the weight of key customer requirements isthe core of innovation program selectionThe fuzzy languageinformation in fuzzy decision is often expressed by fuzzynumber (Liu et al [23] Liu and Chen [24]) languagescale and interval 2-tuple linguistic representation modelAll research results suggest that constructing interval 2-tuple linguistic representation model is an effective methodto donate the information of decision-makers Based on 2-tuples and intervals Dong et al [25] proposed a linguis-tic computational model summarized the numerical scaleapproach and conducted comparative analysis to justify theeffectiveness of the interval version of the 2-tuple fuzzylinguistic representation model Herrera and Martinez [26]Herrera and Martinez [27] pointed out that the binarysemantic representation model was widely used to solve the

multiattribute decision-making problem based on languageevaluation information it had high expression accuracy Liet al [28] and Li et al [29] proposed the personalizedindividual semantics in 2-tuple linguistic model Dong et al[30] propose a connection between the linguistic hierarchymodel and the numerical scale model They also provethe equivalence of the linguistic computational models byequating the model Chen et al [31] analyzed three types offusion approaches to manage the fusion process in groupdecision-making with heterogeneous preference structuresand reviewed the different transformation functions amongutility values preference orderings numerical preferencerelations and multigranular linguistic preference relationDong et al [32] considered four formats of information iereal numbers intervals linguistic variables and triangularfuzzy numbers and proposed framework to solve complexand dynamicmultiple attribute group decision-making prob-lems As can be seen from the above literature interval2-tuple linguistic can handle the information of decision-makers well in a fuzzy environment Based on this we usethe interval 2-tuple linguistic representation model to collectand express the information of decision-makers and thendetermine the key customer requirements in CCPI In theprocess of CCPI design due to the constraints of resourcesand costs the degree of implementation of key customerrequirements can not always reach the maximumThereforeit is necessary to choose a better innovative scheme Theselection of innovative scheme is a process of MCMD Liu[33] combined the power average operator with Heronianmean operator and extended them to process interval-valuedintuitionistic fuzzy information and presented fuzzy multipleattribute group decision-making Liu and Li [34] extendedthe power Bonferroni mean operator (PBM) to processinterval-valued intuitionistic fuzzy numbers (IVIFNs) andapplied them to solve the MAGDM problems Lahdelmaand Salminen [35] proposed a new decision-making methodbased on the combination of the prospect theory and theStochastic Multicriteria Acceptability Analysis (SMAA) forstochastic multiattribute decision-making with incompletepreference information Based on the interaction operationallaws of intuitionistic fuzzy sets (IFSs) Liu et al [36] extendedthe PBM operator and the PGBM operator and then theyproposed a novel MAGDM method Grabisch et al [37]Grabisch et al [38] presented both a constructive view anda descriptive view on alternatives evaluation in the processof multicriteria decision analysis The descriptive approachwas concerned with characterizations of models of prefer-ence whereas the constructive approach aimed at buildingpreferences by questioning the decision maker The resultof quantitative methods is more intuitive concise accurateand effective than qualitative method However its operationoften has some difficulties especially some related factors aredifficult to quantify affecting the accuracy of quantification

Based on this we combine qualitative and quantitativemethods to determine the key requirements of customersThis paper integrates the Kano model the interval 2-tuplelinguistic representation model and the prospect theoryKano model as a qualitative method is proposed to identifythe initial requirements of customers It is simple and easy to

4 Mathematical Problems in Engineering

operate Because of the difference of customersrsquo knowledgestructure experience and other objective or subjective fac-tors some CRs expressionmay be uncertain linguistic prefer-enceThe interval 2-tuple linguistic representationmodel andthe prospect theory are proposed to deal with the uncertaintyThe interval 2-tuple linguistic representation model could bemore accurate in terms of vague linguistic preference and lessinformation loss in fuzzy information processing Thereforeit is appropriate to select the 2-tuple linguistic representationmodel to illustrate fuzzy linguistic preference in the processof determining CRsrsquo weight Because CRs are diversityenterprises can not meet completely based on this we usedprospect theory to evaluate the productsrsquo comprehensiveprospects value in order to achieve the maximum level ofcustomer satisfaction

The remainder of this paper is organized in the followingmanner Section 2 is CRs analysis based on the Kanomodel Section 3 is the innovative product program selectionbased on the prospect theory In Section 4 an empiricalexample is provided to demonstrate the applicability of theproposedmethod Comparative analysis is given in Section 5Finally some conclusions and future research directions aresummarized in Section 6

The article frame work we proposed is shown in Figure 1

2 Analysis of CRs Based on Kano Model

The customer can not specify the desired product attributesaccurately in a real buying scenario It is unscientific to deter-mine the true requirements of customers simply by a simplequestionnaire Therefore systematic methodological tools toclarify the real requirements of customer are necessary Kanomodel as a valid method is proposed to identify the keyCRs

21 Identification of the Initial CRs of a Product The Kanomodel as a relative accuracy expression of CRs is used torealize CRs and their effect on customer satisfaction (CS)It can classify different CRs and find attractive require-ments of products Promoting enterprises produce morepopular products which can stand out from similar prod-ucts

According to the size of the CRs impact on CSKano model divides CRs into five types requirementswhich are must-be requirements one-dimensional require-ments attractive requirements indifference requirementsand reverse requirements as shown in Figure 2

The horizontal axis is the satisfaction degree of onespecific CR and the vertical axismeans the satisfaction degreeof CS

Must-Be Requirements (M) Customers will accept if thisattribute is provided otherwise they will feel extremelydissatisfied

One-Dimensional Requirements (O) CS is a linear functionof the satisfaction degree of a certainly CR High satisfactiondegree leads to high satisfaction and low satisfaction degreeleads to low satisfaction

Attractive Requirements (A) Customers will be very satisfiedif the requirement is met if the requirement is not met theywill accept the product with satisfaction also

Indifference Requirements (I) Regardless of the fact thatrequirement is satisfied or not CS will not be impacted

Reverse Requirements (R) Customers do not want theattribute in the product and absence of this attributeincreases the degree of CS

22 Determine the Type of CRs Based on Kano ModelEstablishing the Kano model of CRs is vital for a productdesign and the common tools for determining the initial CRsare Kano questionnaire Kano assessment table and Kanosurvey results table The main steps are as follows

Step 1 Design the Kano questionnaire The Kano modelprovides a format for obtaining customer answers on eachpotential product attributeThe Kano questionnaire is shownin Table 1

From Table 1 we can know that customers have to selectone of the states out of Dislike Could understand Neutral Ofcourse and Like from the product meet the requirement sideif the requirement is met in the product Customers also haveto select one of the states from the products do not meet therequirement side

Step 2 The Kano questionnaire was issued All possiblecombinations of customer answers and the correspondingtype of product attribute are summarized in Table 2

As seen fromTable 2 besides the five types of requirementhave involved there is onemore type of requirement calledQwhere Q represents a questionable answer and the answer isinvalid It occurs when customers select like or dislike fromboth functional and dysfunctional sides

Step 3 By combining the two answers in the Kano evaluationtable (Table 2) the product criterion can be identified asattractive must-be one-dimensional indifference or rever-sal the results are shown in Table 3

In order to maximize CS we should consider the follow-ing points (Sharif Ullah and Tamaki [39])

(i) Keep must-be attributes(ii) As far as possible to meet the one-dimensional

attributes and charm attributes(iii) Avoid indifferent attributes as many as possible(iv) Avoid reverse attributes

Step 4 Calculate satisfaction coefficient and dissatisfactioncoefficient

The quantitative analysis of Kanorsquos model begins withcalculating CS and DS (Ji et al (2014)) Due to the diversi-fication of CRs CS and DS values only indicate the average

Mathematical Problems in Engineering 5

Satisfied

Dissatisfied

Attractive requirements

One-dimensional requirements

Reversal requirements

Sufficiency

Must-be requirements

Insufficiency Indifference

Figure 2 Kano model of customer satisfaction

Table 1 Kano questionnaire table

Requirement Problem Dislike Could understand Neutral Of course Like

119877119894 Products meet the requirement (select one) radicProducts do not meet the requirement (select one) radic

Table 2 Kano evaluation table

Dysfunctional questionldquoIf [the product] did not satisfied [feature x]

how do you feelrdquo

Like Of course Neutral Couldunderstand Dislike

Functional questionIf [the product]satisfied [feature x]how would you feel

Like Q A A A OOf course R I I I MNeutral R I I I MCould

understand R I I I M

Dislike R R R R Q

Table 3 Classification table of requirements

Requirements A O M I R Total number of questionnaires Kano category1198771 20 25 15 22 18 100 O1198772 15 25 15 15 30 100 Rsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdotTable 4 119862119878119894 minus 119862119863119878119894 relationship functions

Kano category A B 119891 (119910119894) 119904119894 = 119860119891 (119910119894) + 119861A

119862119878119894 minus 119863119878119894119890 minus 1 minus119862119878119894 minus 119890119863119878119894119890 minus 1 119890119910119894 119904119894 = 119862119878119894 minus 119863119878119894119890 minus 1 119890119910119894 minus 119862119878119894 minus 119890119863119878119894119890 minus 1O 119862119878119894 minus 119863119878119894 119863119878119894 119910119894 119904119894 = (119862119878119894 minus 119863119878119894) 119910119894 + 119863119878119894M

119890(119862119878119894 minus 119863119878119894)119890 minus 1 119890119862119878119894 minus 119863119878119894119890 minus 1 minus119890119910119894 119904119894 = minus119890 (119862119878119894 minus 119863119878119894)119890 minus 1 119890119910119894 + 119890119862119878119894 minus 119863119878119894119890 minus 1

6 Mathematical Problems in Engineering

Get the initial requirements

Focus group

Questionnaire

Depth interviews

Analysis of the questionnaire results

Send questionnaires

Collect questionnairesI and R attributes are removed according

to the rules

Ranking product attributesaccording to si

Determine the Kano category of requirements

If this property is M si = minuse (CSi minus DSi)

e minus 1eyi +

eCSi minus DSie minus 1

If this property is O si = (CSi minus DSi) yi + DSi

If this attribute is A si =CSi minus DSi

e minus 1eyi minus minus

CSi minus eDSie minus 1

Figure 3 The flow chart based on Kano model

contribution of one CR to CS which can be represented bythe number of customers who are satisfied or dissatisfiedwith a certain CR From Table 3 we can sum up the numberof attractive attributes 119873119860 one-dimensional attributes 119873119874must-be attributes 119873119872 and indifferent attributes 119873119868 andthen we can get the value of 119862119878119894 and 119862119863119878119894 by formulations(1) and (2)

119862119878119894 = 119873119860 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (1)119862119863119878119894 = minus 119873119872 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (2)

Step 5 According to Table 4 119862119878119894 minus 119862119863119878119894 relationship func-tions could be obtained (Ji et al [40])

Step 6 A rank for CRs is made according to the value of 119904119894The flow chart based on Kanomodel is shown in Figure 3

23 Weight Determination of CRs In product design it isvery difficult for product design decision-makers due to thevagueness and uncertainty of the CRs In order to solve thisdifficult Lin et al [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic

It is used for representing the linguistic assessment infor-mation by means of a 2-tuple (119904119894 120572119894) where 119904119894 is a linguisticlabel from predefined linguistic term set 119878 and 120572119894 is the valueof symbolic translation (Dong et al [42] Wei [43] Zhang[44] Zhang [45] Gangurde and Akarte [46] Liu and Chen[47] Qin and Liu [48] Wang et al [49]) See Figure 4

Definition 1 Let 119878 = 1199040 1199041 119904119892 be a linguistic termset and 120572 represents the deviation between the linguistic

information and the closest linguistic phrase in the initiallinguistic evaluation set 119878 the real number (120573 isin [0 119892]) isthe aggregation operation result of these elements of 119878 thenthe 2-tuple linguistic information is obtained by the followingfunction 119891

119891 [0 119892] 997888rarr 119878 times [minus05 05] (3)119891 (120573) = (119904119894 120572)

119904119894 119894 = 119903119900119906119899119889 (120573)120572 = 120573 minus 119894 120572 isin [minus05 05] (4)

where round is a rounding operation and 119894 isin [0 119892]Correspondingly the real number 120573 can be obtained by

the 2-tuple linguistic information according to the followingfunction 119891minus1

119891minus1 119878 times [minus05 05] 997888rarr [0 119892] (5)119891minus1 (119904119894 120572) = 119894 + 120572 = 120573 (6)

119904119894 isin 119878 997904rArr (119904119894 0) isin 119878 (7)where formula (7) represents the conversion between a

linguistic term and a 2-tuple linguistic consists in adding avalue 0 as symbolic translation

Definition 2 Let 119883 = (1199041 1205721) (1199042 1205722) (119904119899 120572119899) be a setof 2-tuples let 119908 = (1199081 1199082 119908119899)T be the weight vectorwhere 119908119894 isin [0 1] 119894 = 1 2 119899 sum119899119894=1 119908119894 = 1 and the 2-tuple weighted average (TWA) operator is defined as

TWA (119883) = 119891(1119899119899sum119895=1

119908119895998779minus1 (119903119895 120572119895)) = (1119899119899sum119895=1

119908119895120573119895) (8)

Mathematical Problems in Engineering 7

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Figure 4 Common linguistic hierarchies

As information aggregation plays a very significant role inthe process of making decision aggregation operators with2-tuple linguistic information have attracted many scholarsrsquoattention If the 2-tuples are from different linguistic termsets they cannot be aggregated directly and should beconducted tedious transformation before aggregation oper-ation to avoid complicated computation we proposed someaggregation operators with interval-valued 2-tuple linguisticinformation Besides we discuss their desired definition

Definition 3 Let the linguistic evaluation set be 119878 =1199040 1199041 119904119892 [(119904119894 1205721) (119904119895 1205722)]which is called the interval 2-tuple linguistic where 119904119894 and 119904119895 belong to the evaluation set 119878and 119894 le 119895 1205721 lt 1205722 The interval number [1205731 1205732] (1205731 1205732 isin[0 1] 1205731 le 1205732) can be obtained by the following function 119891119891 ([1205731 1205732]) = [(119904119894 1205721) (119904119895 1205722)]

119904119894 119894 = 119903119900119906119899119889 (1205731 lowast 119892)119904119895 119895 = 119903119900119906119899119889 (1205732 lowast 119892)1205721 = 1205731 minus 119894119892 1205721 isin [minus05119892 05119892 ]1205722 = 1205732 minus 119895119892 1205722 isin [minus05119892 05119892 ]

(9)

On the contrary the interval 2-tuple linguistic[(119904119894 1205721) (119904119895 1205722)] can be converted into interval numbers byfunction 119891minus1

119891minus1 [(119904119894 1205721) (119904119895 1205722)] = [ 119894119892 + 1205721 119895119892 + 1205722]= [1205731 1205732]

(10)

Particularly if 119904119894 = 119904119895 and 120572119894 = 120572119895 then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable

Definition 4 Let 119883 = [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)] be a set of 2-tuples let 119908 =(1199081 1199082 119908119899)T be the weight vector where 119908119894 isin [0 1] 119894 =1 2 119899 sum119899i=1 119908119894 = 1 and the interval 2-tuple weightedaverage (ITWA) operator is defined as

ITWA [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)]= 119891[ 119899sum

i=1119908119894119891minus1 (119904119894 120572119894) 119899sum

i=1119908119894119891minus1 (1199041015840119894 1205721015840119894)]

(11)

This approach is introduced to deal with informationassessed in different linguistic scales by using the extensionprinciple and the interval 2-tuple linguistic representationmodel It is a computing model as shown in Figure 5

In summary the process of determining theweight ofCRsis as follows

Step 1 Set the linguistic evaluation set 119878 = 1199040 1199041 119904119892Step 2 Evaluate requirement 119894 and requirement 119895 accordingto evaluator 119877(119896) and get the measure value [119906119896119894119895 V119896119894119895] where119896 = 1 2 119897 119906119896119894119895 V119896119894119895 isin 119878 119894 119895 = 1 2 119899Step 3 Obtain the linguistic complementary judgmentmatrix 119877119896 = (119906119896119894119895 V119896119894119895)119899times119899 according to the measurevalue and the weight vector of the evaluator is 119908119896 =(1199081 1199082 119908119897) where sum119897119896=1 119908119896 = 1

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Page 2: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

2 Mathematical Problems in Engineering

Depth interviews

Choose linguistichierarchies

Initialrequirements

Customers

Customers

Customers

Questionnaire

7 Labels

3 Labels

9 Labels

5 Labels

13 Labels

Choose linguistichierarchies

Choose linguistichierarchies

Focus group

Expert

Expert

Expert

Determine thetype of indicator

Determine thetype of indicator

Determine thetype of indicator

According toexpert opinion

Design questionnaires

Analysis of thequestionnaire results

Send questionnaires

Collect questionnaires

Ranking product attributesaccording to si

Screen initial requirement based on kano model

Set the linguistic evaluationset

Obtain the key requirementof customers

Converts the linguisticcomplementary judgmentmatrix to interval 2-type

linguistic judgment matrix

e interval 2-type linguisticjudgment matrix

transformed into intervalnumber

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Determine the key requirement based on the 2-tuple linguistic information

Type oneAttribute value is

Crisp number

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Rank according to thecomposite foreground value

Obtain the best solution

Calculate the gains and lossvalues of indicators

Determine the best solution based on the 2-tuple linguistic information

Solution 1

Solution

Solution n

Figure 1 The method we proposed

product and service Carulli et al [12] proposed a methodfor capturing CRs based on virtual reality technology whichwas commonly used in the early stages of product design todeduce CRs and reduce overall cost In order to solve theproblem of inaccurate customer demand Kwong and Bai [13]

introduced the fuzzy number on the basis of traditional AHPand proposed the fuzzy AHP to determine the importanceof customer demand In the process of product collaboratedesign Halimahtun [14] used a system framework approachto conceptualize the current and future customer demand for

Mathematical Problems in Engineering 3

automotive electronics The qualitative method is simple andeasy to operate but its subjectivity is too strong to reflect theessential differences between items the results obtained aremore abstract The application effect of qualitative method isunconvincing

As for quantitative method Li et al [15] combined mini-mum deviation method the Balanced Scorecard the analytichierarchy process (AHP) the proportional method and soon and proposed a system operation method that can makebetter use of product competition and preference informa-tion Due to the ambiguity and uncertainty of the customersrsquorequirementsWang and Tseng [16] established a probability-based Bayesian classifier by using existing customer selectiondata the classifier classified CRs based on the flexibility ofcustomer demand Finally the case proved that this methodhad obvious advantages in customer demand classificationAguwa et al [17] developed a new approach to measurecustomer satisfaction by considering quantitative factors suchas quantitative data design parameters drawing outputand decision-making templates for means of measurementThis method can reduce errors and shorten the engineeringdevelopment time Liu et al [18] used language intuitionisticfuzzy number to describe the decision makerrsquos languageinformation Then comparative analysis method is used toprove the validity of the proposed method Nahm et al [19]proposed two methods of customer preference and customersatisfaction assessment the former provided a way to captureincomplete and uncertain information about the customerand the latter built a customer satisfaction model based oncompetitive benchmarking finally the effectiveness of theproposed method was proved by a door design exampleWu et al [20] integrated the gray relational theory into theQuality Function Deployment (QFD) this method takingthe uncertainty and advancement of CRs into account wasutilized to analyze dynamic CRs Liu et al [21] presented anapproach to address the dependent attribute problem leadingto a function form with design attributes as independentvariables and proved the potential to optimize the designspecification Takai and Ishii [22] analyzed and comparedtwo methods for identifying representative needs affinitydiagram (AD) and subjective clustering (SC) the CRs anal-ysis of the next generation particle accelerator was used todemonstrate the scientific nature of the proposed methodThe establishment of the key customer requirements is crucialto CCPI and the weight of key customer requirements isthe core of innovation program selectionThe fuzzy languageinformation in fuzzy decision is often expressed by fuzzynumber (Liu et al [23] Liu and Chen [24]) languagescale and interval 2-tuple linguistic representation modelAll research results suggest that constructing interval 2-tuple linguistic representation model is an effective methodto donate the information of decision-makers Based on 2-tuples and intervals Dong et al [25] proposed a linguis-tic computational model summarized the numerical scaleapproach and conducted comparative analysis to justify theeffectiveness of the interval version of the 2-tuple fuzzylinguistic representation model Herrera and Martinez [26]Herrera and Martinez [27] pointed out that the binarysemantic representation model was widely used to solve the

multiattribute decision-making problem based on languageevaluation information it had high expression accuracy Liet al [28] and Li et al [29] proposed the personalizedindividual semantics in 2-tuple linguistic model Dong et al[30] propose a connection between the linguistic hierarchymodel and the numerical scale model They also provethe equivalence of the linguistic computational models byequating the model Chen et al [31] analyzed three types offusion approaches to manage the fusion process in groupdecision-making with heterogeneous preference structuresand reviewed the different transformation functions amongutility values preference orderings numerical preferencerelations and multigranular linguistic preference relationDong et al [32] considered four formats of information iereal numbers intervals linguistic variables and triangularfuzzy numbers and proposed framework to solve complexand dynamicmultiple attribute group decision-making prob-lems As can be seen from the above literature interval2-tuple linguistic can handle the information of decision-makers well in a fuzzy environment Based on this we usethe interval 2-tuple linguistic representation model to collectand express the information of decision-makers and thendetermine the key customer requirements in CCPI In theprocess of CCPI design due to the constraints of resourcesand costs the degree of implementation of key customerrequirements can not always reach the maximumThereforeit is necessary to choose a better innovative scheme Theselection of innovative scheme is a process of MCMD Liu[33] combined the power average operator with Heronianmean operator and extended them to process interval-valuedintuitionistic fuzzy information and presented fuzzy multipleattribute group decision-making Liu and Li [34] extendedthe power Bonferroni mean operator (PBM) to processinterval-valued intuitionistic fuzzy numbers (IVIFNs) andapplied them to solve the MAGDM problems Lahdelmaand Salminen [35] proposed a new decision-making methodbased on the combination of the prospect theory and theStochastic Multicriteria Acceptability Analysis (SMAA) forstochastic multiattribute decision-making with incompletepreference information Based on the interaction operationallaws of intuitionistic fuzzy sets (IFSs) Liu et al [36] extendedthe PBM operator and the PGBM operator and then theyproposed a novel MAGDM method Grabisch et al [37]Grabisch et al [38] presented both a constructive view anda descriptive view on alternatives evaluation in the processof multicriteria decision analysis The descriptive approachwas concerned with characterizations of models of prefer-ence whereas the constructive approach aimed at buildingpreferences by questioning the decision maker The resultof quantitative methods is more intuitive concise accurateand effective than qualitative method However its operationoften has some difficulties especially some related factors aredifficult to quantify affecting the accuracy of quantification

Based on this we combine qualitative and quantitativemethods to determine the key requirements of customersThis paper integrates the Kano model the interval 2-tuplelinguistic representation model and the prospect theoryKano model as a qualitative method is proposed to identifythe initial requirements of customers It is simple and easy to

4 Mathematical Problems in Engineering

operate Because of the difference of customersrsquo knowledgestructure experience and other objective or subjective fac-tors some CRs expressionmay be uncertain linguistic prefer-enceThe interval 2-tuple linguistic representationmodel andthe prospect theory are proposed to deal with the uncertaintyThe interval 2-tuple linguistic representation model could bemore accurate in terms of vague linguistic preference and lessinformation loss in fuzzy information processing Thereforeit is appropriate to select the 2-tuple linguistic representationmodel to illustrate fuzzy linguistic preference in the processof determining CRsrsquo weight Because CRs are diversityenterprises can not meet completely based on this we usedprospect theory to evaluate the productsrsquo comprehensiveprospects value in order to achieve the maximum level ofcustomer satisfaction

The remainder of this paper is organized in the followingmanner Section 2 is CRs analysis based on the Kanomodel Section 3 is the innovative product program selectionbased on the prospect theory In Section 4 an empiricalexample is provided to demonstrate the applicability of theproposedmethod Comparative analysis is given in Section 5Finally some conclusions and future research directions aresummarized in Section 6

The article frame work we proposed is shown in Figure 1

2 Analysis of CRs Based on Kano Model

The customer can not specify the desired product attributesaccurately in a real buying scenario It is unscientific to deter-mine the true requirements of customers simply by a simplequestionnaire Therefore systematic methodological tools toclarify the real requirements of customer are necessary Kanomodel as a valid method is proposed to identify the keyCRs

21 Identification of the Initial CRs of a Product The Kanomodel as a relative accuracy expression of CRs is used torealize CRs and their effect on customer satisfaction (CS)It can classify different CRs and find attractive require-ments of products Promoting enterprises produce morepopular products which can stand out from similar prod-ucts

According to the size of the CRs impact on CSKano model divides CRs into five types requirementswhich are must-be requirements one-dimensional require-ments attractive requirements indifference requirementsand reverse requirements as shown in Figure 2

The horizontal axis is the satisfaction degree of onespecific CR and the vertical axismeans the satisfaction degreeof CS

Must-Be Requirements (M) Customers will accept if thisattribute is provided otherwise they will feel extremelydissatisfied

One-Dimensional Requirements (O) CS is a linear functionof the satisfaction degree of a certainly CR High satisfactiondegree leads to high satisfaction and low satisfaction degreeleads to low satisfaction

Attractive Requirements (A) Customers will be very satisfiedif the requirement is met if the requirement is not met theywill accept the product with satisfaction also

Indifference Requirements (I) Regardless of the fact thatrequirement is satisfied or not CS will not be impacted

Reverse Requirements (R) Customers do not want theattribute in the product and absence of this attributeincreases the degree of CS

22 Determine the Type of CRs Based on Kano ModelEstablishing the Kano model of CRs is vital for a productdesign and the common tools for determining the initial CRsare Kano questionnaire Kano assessment table and Kanosurvey results table The main steps are as follows

Step 1 Design the Kano questionnaire The Kano modelprovides a format for obtaining customer answers on eachpotential product attributeThe Kano questionnaire is shownin Table 1

From Table 1 we can know that customers have to selectone of the states out of Dislike Could understand Neutral Ofcourse and Like from the product meet the requirement sideif the requirement is met in the product Customers also haveto select one of the states from the products do not meet therequirement side

Step 2 The Kano questionnaire was issued All possiblecombinations of customer answers and the correspondingtype of product attribute are summarized in Table 2

As seen fromTable 2 besides the five types of requirementhave involved there is onemore type of requirement calledQwhere Q represents a questionable answer and the answer isinvalid It occurs when customers select like or dislike fromboth functional and dysfunctional sides

Step 3 By combining the two answers in the Kano evaluationtable (Table 2) the product criterion can be identified asattractive must-be one-dimensional indifference or rever-sal the results are shown in Table 3

In order to maximize CS we should consider the follow-ing points (Sharif Ullah and Tamaki [39])

(i) Keep must-be attributes(ii) As far as possible to meet the one-dimensional

attributes and charm attributes(iii) Avoid indifferent attributes as many as possible(iv) Avoid reverse attributes

Step 4 Calculate satisfaction coefficient and dissatisfactioncoefficient

The quantitative analysis of Kanorsquos model begins withcalculating CS and DS (Ji et al (2014)) Due to the diversi-fication of CRs CS and DS values only indicate the average

Mathematical Problems in Engineering 5

Satisfied

Dissatisfied

Attractive requirements

One-dimensional requirements

Reversal requirements

Sufficiency

Must-be requirements

Insufficiency Indifference

Figure 2 Kano model of customer satisfaction

Table 1 Kano questionnaire table

Requirement Problem Dislike Could understand Neutral Of course Like

119877119894 Products meet the requirement (select one) radicProducts do not meet the requirement (select one) radic

Table 2 Kano evaluation table

Dysfunctional questionldquoIf [the product] did not satisfied [feature x]

how do you feelrdquo

Like Of course Neutral Couldunderstand Dislike

Functional questionIf [the product]satisfied [feature x]how would you feel

Like Q A A A OOf course R I I I MNeutral R I I I MCould

understand R I I I M

Dislike R R R R Q

Table 3 Classification table of requirements

Requirements A O M I R Total number of questionnaires Kano category1198771 20 25 15 22 18 100 O1198772 15 25 15 15 30 100 Rsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdotTable 4 119862119878119894 minus 119862119863119878119894 relationship functions

Kano category A B 119891 (119910119894) 119904119894 = 119860119891 (119910119894) + 119861A

119862119878119894 minus 119863119878119894119890 minus 1 minus119862119878119894 minus 119890119863119878119894119890 minus 1 119890119910119894 119904119894 = 119862119878119894 minus 119863119878119894119890 minus 1 119890119910119894 minus 119862119878119894 minus 119890119863119878119894119890 minus 1O 119862119878119894 minus 119863119878119894 119863119878119894 119910119894 119904119894 = (119862119878119894 minus 119863119878119894) 119910119894 + 119863119878119894M

119890(119862119878119894 minus 119863119878119894)119890 minus 1 119890119862119878119894 minus 119863119878119894119890 minus 1 minus119890119910119894 119904119894 = minus119890 (119862119878119894 minus 119863119878119894)119890 minus 1 119890119910119894 + 119890119862119878119894 minus 119863119878119894119890 minus 1

6 Mathematical Problems in Engineering

Get the initial requirements

Focus group

Questionnaire

Depth interviews

Analysis of the questionnaire results

Send questionnaires

Collect questionnairesI and R attributes are removed according

to the rules

Ranking product attributesaccording to si

Determine the Kano category of requirements

If this property is M si = minuse (CSi minus DSi)

e minus 1eyi +

eCSi minus DSie minus 1

If this property is O si = (CSi minus DSi) yi + DSi

If this attribute is A si =CSi minus DSi

e minus 1eyi minus minus

CSi minus eDSie minus 1

Figure 3 The flow chart based on Kano model

contribution of one CR to CS which can be represented bythe number of customers who are satisfied or dissatisfiedwith a certain CR From Table 3 we can sum up the numberof attractive attributes 119873119860 one-dimensional attributes 119873119874must-be attributes 119873119872 and indifferent attributes 119873119868 andthen we can get the value of 119862119878119894 and 119862119863119878119894 by formulations(1) and (2)

119862119878119894 = 119873119860 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (1)119862119863119878119894 = minus 119873119872 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (2)

Step 5 According to Table 4 119862119878119894 minus 119862119863119878119894 relationship func-tions could be obtained (Ji et al [40])

Step 6 A rank for CRs is made according to the value of 119904119894The flow chart based on Kanomodel is shown in Figure 3

23 Weight Determination of CRs In product design it isvery difficult for product design decision-makers due to thevagueness and uncertainty of the CRs In order to solve thisdifficult Lin et al [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic

It is used for representing the linguistic assessment infor-mation by means of a 2-tuple (119904119894 120572119894) where 119904119894 is a linguisticlabel from predefined linguistic term set 119878 and 120572119894 is the valueof symbolic translation (Dong et al [42] Wei [43] Zhang[44] Zhang [45] Gangurde and Akarte [46] Liu and Chen[47] Qin and Liu [48] Wang et al [49]) See Figure 4

Definition 1 Let 119878 = 1199040 1199041 119904119892 be a linguistic termset and 120572 represents the deviation between the linguistic

information and the closest linguistic phrase in the initiallinguistic evaluation set 119878 the real number (120573 isin [0 119892]) isthe aggregation operation result of these elements of 119878 thenthe 2-tuple linguistic information is obtained by the followingfunction 119891

119891 [0 119892] 997888rarr 119878 times [minus05 05] (3)119891 (120573) = (119904119894 120572)

119904119894 119894 = 119903119900119906119899119889 (120573)120572 = 120573 minus 119894 120572 isin [minus05 05] (4)

where round is a rounding operation and 119894 isin [0 119892]Correspondingly the real number 120573 can be obtained by

the 2-tuple linguistic information according to the followingfunction 119891minus1

119891minus1 119878 times [minus05 05] 997888rarr [0 119892] (5)119891minus1 (119904119894 120572) = 119894 + 120572 = 120573 (6)

119904119894 isin 119878 997904rArr (119904119894 0) isin 119878 (7)where formula (7) represents the conversion between a

linguistic term and a 2-tuple linguistic consists in adding avalue 0 as symbolic translation

Definition 2 Let 119883 = (1199041 1205721) (1199042 1205722) (119904119899 120572119899) be a setof 2-tuples let 119908 = (1199081 1199082 119908119899)T be the weight vectorwhere 119908119894 isin [0 1] 119894 = 1 2 119899 sum119899119894=1 119908119894 = 1 and the 2-tuple weighted average (TWA) operator is defined as

TWA (119883) = 119891(1119899119899sum119895=1

119908119895998779minus1 (119903119895 120572119895)) = (1119899119899sum119895=1

119908119895120573119895) (8)

Mathematical Problems in Engineering 7

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Figure 4 Common linguistic hierarchies

As information aggregation plays a very significant role inthe process of making decision aggregation operators with2-tuple linguistic information have attracted many scholarsrsquoattention If the 2-tuples are from different linguistic termsets they cannot be aggregated directly and should beconducted tedious transformation before aggregation oper-ation to avoid complicated computation we proposed someaggregation operators with interval-valued 2-tuple linguisticinformation Besides we discuss their desired definition

Definition 3 Let the linguistic evaluation set be 119878 =1199040 1199041 119904119892 [(119904119894 1205721) (119904119895 1205722)]which is called the interval 2-tuple linguistic where 119904119894 and 119904119895 belong to the evaluation set 119878and 119894 le 119895 1205721 lt 1205722 The interval number [1205731 1205732] (1205731 1205732 isin[0 1] 1205731 le 1205732) can be obtained by the following function 119891119891 ([1205731 1205732]) = [(119904119894 1205721) (119904119895 1205722)]

119904119894 119894 = 119903119900119906119899119889 (1205731 lowast 119892)119904119895 119895 = 119903119900119906119899119889 (1205732 lowast 119892)1205721 = 1205731 minus 119894119892 1205721 isin [minus05119892 05119892 ]1205722 = 1205732 minus 119895119892 1205722 isin [minus05119892 05119892 ]

(9)

On the contrary the interval 2-tuple linguistic[(119904119894 1205721) (119904119895 1205722)] can be converted into interval numbers byfunction 119891minus1

119891minus1 [(119904119894 1205721) (119904119895 1205722)] = [ 119894119892 + 1205721 119895119892 + 1205722]= [1205731 1205732]

(10)

Particularly if 119904119894 = 119904119895 and 120572119894 = 120572119895 then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable

Definition 4 Let 119883 = [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)] be a set of 2-tuples let 119908 =(1199081 1199082 119908119899)T be the weight vector where 119908119894 isin [0 1] 119894 =1 2 119899 sum119899i=1 119908119894 = 1 and the interval 2-tuple weightedaverage (ITWA) operator is defined as

ITWA [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)]= 119891[ 119899sum

i=1119908119894119891minus1 (119904119894 120572119894) 119899sum

i=1119908119894119891minus1 (1199041015840119894 1205721015840119894)]

(11)

This approach is introduced to deal with informationassessed in different linguistic scales by using the extensionprinciple and the interval 2-tuple linguistic representationmodel It is a computing model as shown in Figure 5

In summary the process of determining theweight ofCRsis as follows

Step 1 Set the linguistic evaluation set 119878 = 1199040 1199041 119904119892Step 2 Evaluate requirement 119894 and requirement 119895 accordingto evaluator 119877(119896) and get the measure value [119906119896119894119895 V119896119894119895] where119896 = 1 2 119897 119906119896119894119895 V119896119894119895 isin 119878 119894 119895 = 1 2 119899Step 3 Obtain the linguistic complementary judgmentmatrix 119877119896 = (119906119896119894119895 V119896119894119895)119899times119899 according to the measurevalue and the weight vector of the evaluator is 119908119896 =(1199081 1199082 119908119897) where sum119897119896=1 119908119896 = 1

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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Page 3: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 3

automotive electronics The qualitative method is simple andeasy to operate but its subjectivity is too strong to reflect theessential differences between items the results obtained aremore abstract The application effect of qualitative method isunconvincing

As for quantitative method Li et al [15] combined mini-mum deviation method the Balanced Scorecard the analytichierarchy process (AHP) the proportional method and soon and proposed a system operation method that can makebetter use of product competition and preference informa-tion Due to the ambiguity and uncertainty of the customersrsquorequirementsWang and Tseng [16] established a probability-based Bayesian classifier by using existing customer selectiondata the classifier classified CRs based on the flexibility ofcustomer demand Finally the case proved that this methodhad obvious advantages in customer demand classificationAguwa et al [17] developed a new approach to measurecustomer satisfaction by considering quantitative factors suchas quantitative data design parameters drawing outputand decision-making templates for means of measurementThis method can reduce errors and shorten the engineeringdevelopment time Liu et al [18] used language intuitionisticfuzzy number to describe the decision makerrsquos languageinformation Then comparative analysis method is used toprove the validity of the proposed method Nahm et al [19]proposed two methods of customer preference and customersatisfaction assessment the former provided a way to captureincomplete and uncertain information about the customerand the latter built a customer satisfaction model based oncompetitive benchmarking finally the effectiveness of theproposed method was proved by a door design exampleWu et al [20] integrated the gray relational theory into theQuality Function Deployment (QFD) this method takingthe uncertainty and advancement of CRs into account wasutilized to analyze dynamic CRs Liu et al [21] presented anapproach to address the dependent attribute problem leadingto a function form with design attributes as independentvariables and proved the potential to optimize the designspecification Takai and Ishii [22] analyzed and comparedtwo methods for identifying representative needs affinitydiagram (AD) and subjective clustering (SC) the CRs anal-ysis of the next generation particle accelerator was used todemonstrate the scientific nature of the proposed methodThe establishment of the key customer requirements is crucialto CCPI and the weight of key customer requirements isthe core of innovation program selectionThe fuzzy languageinformation in fuzzy decision is often expressed by fuzzynumber (Liu et al [23] Liu and Chen [24]) languagescale and interval 2-tuple linguistic representation modelAll research results suggest that constructing interval 2-tuple linguistic representation model is an effective methodto donate the information of decision-makers Based on 2-tuples and intervals Dong et al [25] proposed a linguis-tic computational model summarized the numerical scaleapproach and conducted comparative analysis to justify theeffectiveness of the interval version of the 2-tuple fuzzylinguistic representation model Herrera and Martinez [26]Herrera and Martinez [27] pointed out that the binarysemantic representation model was widely used to solve the

multiattribute decision-making problem based on languageevaluation information it had high expression accuracy Liet al [28] and Li et al [29] proposed the personalizedindividual semantics in 2-tuple linguistic model Dong et al[30] propose a connection between the linguistic hierarchymodel and the numerical scale model They also provethe equivalence of the linguistic computational models byequating the model Chen et al [31] analyzed three types offusion approaches to manage the fusion process in groupdecision-making with heterogeneous preference structuresand reviewed the different transformation functions amongutility values preference orderings numerical preferencerelations and multigranular linguistic preference relationDong et al [32] considered four formats of information iereal numbers intervals linguistic variables and triangularfuzzy numbers and proposed framework to solve complexand dynamicmultiple attribute group decision-making prob-lems As can be seen from the above literature interval2-tuple linguistic can handle the information of decision-makers well in a fuzzy environment Based on this we usethe interval 2-tuple linguistic representation model to collectand express the information of decision-makers and thendetermine the key customer requirements in CCPI In theprocess of CCPI design due to the constraints of resourcesand costs the degree of implementation of key customerrequirements can not always reach the maximumThereforeit is necessary to choose a better innovative scheme Theselection of innovative scheme is a process of MCMD Liu[33] combined the power average operator with Heronianmean operator and extended them to process interval-valuedintuitionistic fuzzy information and presented fuzzy multipleattribute group decision-making Liu and Li [34] extendedthe power Bonferroni mean operator (PBM) to processinterval-valued intuitionistic fuzzy numbers (IVIFNs) andapplied them to solve the MAGDM problems Lahdelmaand Salminen [35] proposed a new decision-making methodbased on the combination of the prospect theory and theStochastic Multicriteria Acceptability Analysis (SMAA) forstochastic multiattribute decision-making with incompletepreference information Based on the interaction operationallaws of intuitionistic fuzzy sets (IFSs) Liu et al [36] extendedthe PBM operator and the PGBM operator and then theyproposed a novel MAGDM method Grabisch et al [37]Grabisch et al [38] presented both a constructive view anda descriptive view on alternatives evaluation in the processof multicriteria decision analysis The descriptive approachwas concerned with characterizations of models of prefer-ence whereas the constructive approach aimed at buildingpreferences by questioning the decision maker The resultof quantitative methods is more intuitive concise accurateand effective than qualitative method However its operationoften has some difficulties especially some related factors aredifficult to quantify affecting the accuracy of quantification

Based on this we combine qualitative and quantitativemethods to determine the key requirements of customersThis paper integrates the Kano model the interval 2-tuplelinguistic representation model and the prospect theoryKano model as a qualitative method is proposed to identifythe initial requirements of customers It is simple and easy to

4 Mathematical Problems in Engineering

operate Because of the difference of customersrsquo knowledgestructure experience and other objective or subjective fac-tors some CRs expressionmay be uncertain linguistic prefer-enceThe interval 2-tuple linguistic representationmodel andthe prospect theory are proposed to deal with the uncertaintyThe interval 2-tuple linguistic representation model could bemore accurate in terms of vague linguistic preference and lessinformation loss in fuzzy information processing Thereforeit is appropriate to select the 2-tuple linguistic representationmodel to illustrate fuzzy linguistic preference in the processof determining CRsrsquo weight Because CRs are diversityenterprises can not meet completely based on this we usedprospect theory to evaluate the productsrsquo comprehensiveprospects value in order to achieve the maximum level ofcustomer satisfaction

The remainder of this paper is organized in the followingmanner Section 2 is CRs analysis based on the Kanomodel Section 3 is the innovative product program selectionbased on the prospect theory In Section 4 an empiricalexample is provided to demonstrate the applicability of theproposedmethod Comparative analysis is given in Section 5Finally some conclusions and future research directions aresummarized in Section 6

The article frame work we proposed is shown in Figure 1

2 Analysis of CRs Based on Kano Model

The customer can not specify the desired product attributesaccurately in a real buying scenario It is unscientific to deter-mine the true requirements of customers simply by a simplequestionnaire Therefore systematic methodological tools toclarify the real requirements of customer are necessary Kanomodel as a valid method is proposed to identify the keyCRs

21 Identification of the Initial CRs of a Product The Kanomodel as a relative accuracy expression of CRs is used torealize CRs and their effect on customer satisfaction (CS)It can classify different CRs and find attractive require-ments of products Promoting enterprises produce morepopular products which can stand out from similar prod-ucts

According to the size of the CRs impact on CSKano model divides CRs into five types requirementswhich are must-be requirements one-dimensional require-ments attractive requirements indifference requirementsand reverse requirements as shown in Figure 2

The horizontal axis is the satisfaction degree of onespecific CR and the vertical axismeans the satisfaction degreeof CS

Must-Be Requirements (M) Customers will accept if thisattribute is provided otherwise they will feel extremelydissatisfied

One-Dimensional Requirements (O) CS is a linear functionof the satisfaction degree of a certainly CR High satisfactiondegree leads to high satisfaction and low satisfaction degreeleads to low satisfaction

Attractive Requirements (A) Customers will be very satisfiedif the requirement is met if the requirement is not met theywill accept the product with satisfaction also

Indifference Requirements (I) Regardless of the fact thatrequirement is satisfied or not CS will not be impacted

Reverse Requirements (R) Customers do not want theattribute in the product and absence of this attributeincreases the degree of CS

22 Determine the Type of CRs Based on Kano ModelEstablishing the Kano model of CRs is vital for a productdesign and the common tools for determining the initial CRsare Kano questionnaire Kano assessment table and Kanosurvey results table The main steps are as follows

Step 1 Design the Kano questionnaire The Kano modelprovides a format for obtaining customer answers on eachpotential product attributeThe Kano questionnaire is shownin Table 1

From Table 1 we can know that customers have to selectone of the states out of Dislike Could understand Neutral Ofcourse and Like from the product meet the requirement sideif the requirement is met in the product Customers also haveto select one of the states from the products do not meet therequirement side

Step 2 The Kano questionnaire was issued All possiblecombinations of customer answers and the correspondingtype of product attribute are summarized in Table 2

As seen fromTable 2 besides the five types of requirementhave involved there is onemore type of requirement calledQwhere Q represents a questionable answer and the answer isinvalid It occurs when customers select like or dislike fromboth functional and dysfunctional sides

Step 3 By combining the two answers in the Kano evaluationtable (Table 2) the product criterion can be identified asattractive must-be one-dimensional indifference or rever-sal the results are shown in Table 3

In order to maximize CS we should consider the follow-ing points (Sharif Ullah and Tamaki [39])

(i) Keep must-be attributes(ii) As far as possible to meet the one-dimensional

attributes and charm attributes(iii) Avoid indifferent attributes as many as possible(iv) Avoid reverse attributes

Step 4 Calculate satisfaction coefficient and dissatisfactioncoefficient

The quantitative analysis of Kanorsquos model begins withcalculating CS and DS (Ji et al (2014)) Due to the diversi-fication of CRs CS and DS values only indicate the average

Mathematical Problems in Engineering 5

Satisfied

Dissatisfied

Attractive requirements

One-dimensional requirements

Reversal requirements

Sufficiency

Must-be requirements

Insufficiency Indifference

Figure 2 Kano model of customer satisfaction

Table 1 Kano questionnaire table

Requirement Problem Dislike Could understand Neutral Of course Like

119877119894 Products meet the requirement (select one) radicProducts do not meet the requirement (select one) radic

Table 2 Kano evaluation table

Dysfunctional questionldquoIf [the product] did not satisfied [feature x]

how do you feelrdquo

Like Of course Neutral Couldunderstand Dislike

Functional questionIf [the product]satisfied [feature x]how would you feel

Like Q A A A OOf course R I I I MNeutral R I I I MCould

understand R I I I M

Dislike R R R R Q

Table 3 Classification table of requirements

Requirements A O M I R Total number of questionnaires Kano category1198771 20 25 15 22 18 100 O1198772 15 25 15 15 30 100 Rsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdotTable 4 119862119878119894 minus 119862119863119878119894 relationship functions

Kano category A B 119891 (119910119894) 119904119894 = 119860119891 (119910119894) + 119861A

119862119878119894 minus 119863119878119894119890 minus 1 minus119862119878119894 minus 119890119863119878119894119890 minus 1 119890119910119894 119904119894 = 119862119878119894 minus 119863119878119894119890 minus 1 119890119910119894 minus 119862119878119894 minus 119890119863119878119894119890 minus 1O 119862119878119894 minus 119863119878119894 119863119878119894 119910119894 119904119894 = (119862119878119894 minus 119863119878119894) 119910119894 + 119863119878119894M

119890(119862119878119894 minus 119863119878119894)119890 minus 1 119890119862119878119894 minus 119863119878119894119890 minus 1 minus119890119910119894 119904119894 = minus119890 (119862119878119894 minus 119863119878119894)119890 minus 1 119890119910119894 + 119890119862119878119894 minus 119863119878119894119890 minus 1

6 Mathematical Problems in Engineering

Get the initial requirements

Focus group

Questionnaire

Depth interviews

Analysis of the questionnaire results

Send questionnaires

Collect questionnairesI and R attributes are removed according

to the rules

Ranking product attributesaccording to si

Determine the Kano category of requirements

If this property is M si = minuse (CSi minus DSi)

e minus 1eyi +

eCSi minus DSie minus 1

If this property is O si = (CSi minus DSi) yi + DSi

If this attribute is A si =CSi minus DSi

e minus 1eyi minus minus

CSi minus eDSie minus 1

Figure 3 The flow chart based on Kano model

contribution of one CR to CS which can be represented bythe number of customers who are satisfied or dissatisfiedwith a certain CR From Table 3 we can sum up the numberof attractive attributes 119873119860 one-dimensional attributes 119873119874must-be attributes 119873119872 and indifferent attributes 119873119868 andthen we can get the value of 119862119878119894 and 119862119863119878119894 by formulations(1) and (2)

119862119878119894 = 119873119860 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (1)119862119863119878119894 = minus 119873119872 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (2)

Step 5 According to Table 4 119862119878119894 minus 119862119863119878119894 relationship func-tions could be obtained (Ji et al [40])

Step 6 A rank for CRs is made according to the value of 119904119894The flow chart based on Kanomodel is shown in Figure 3

23 Weight Determination of CRs In product design it isvery difficult for product design decision-makers due to thevagueness and uncertainty of the CRs In order to solve thisdifficult Lin et al [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic

It is used for representing the linguistic assessment infor-mation by means of a 2-tuple (119904119894 120572119894) where 119904119894 is a linguisticlabel from predefined linguistic term set 119878 and 120572119894 is the valueof symbolic translation (Dong et al [42] Wei [43] Zhang[44] Zhang [45] Gangurde and Akarte [46] Liu and Chen[47] Qin and Liu [48] Wang et al [49]) See Figure 4

Definition 1 Let 119878 = 1199040 1199041 119904119892 be a linguistic termset and 120572 represents the deviation between the linguistic

information and the closest linguistic phrase in the initiallinguistic evaluation set 119878 the real number (120573 isin [0 119892]) isthe aggregation operation result of these elements of 119878 thenthe 2-tuple linguistic information is obtained by the followingfunction 119891

119891 [0 119892] 997888rarr 119878 times [minus05 05] (3)119891 (120573) = (119904119894 120572)

119904119894 119894 = 119903119900119906119899119889 (120573)120572 = 120573 minus 119894 120572 isin [minus05 05] (4)

where round is a rounding operation and 119894 isin [0 119892]Correspondingly the real number 120573 can be obtained by

the 2-tuple linguistic information according to the followingfunction 119891minus1

119891minus1 119878 times [minus05 05] 997888rarr [0 119892] (5)119891minus1 (119904119894 120572) = 119894 + 120572 = 120573 (6)

119904119894 isin 119878 997904rArr (119904119894 0) isin 119878 (7)where formula (7) represents the conversion between a

linguistic term and a 2-tuple linguistic consists in adding avalue 0 as symbolic translation

Definition 2 Let 119883 = (1199041 1205721) (1199042 1205722) (119904119899 120572119899) be a setof 2-tuples let 119908 = (1199081 1199082 119908119899)T be the weight vectorwhere 119908119894 isin [0 1] 119894 = 1 2 119899 sum119899119894=1 119908119894 = 1 and the 2-tuple weighted average (TWA) operator is defined as

TWA (119883) = 119891(1119899119899sum119895=1

119908119895998779minus1 (119903119895 120572119895)) = (1119899119899sum119895=1

119908119895120573119895) (8)

Mathematical Problems in Engineering 7

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Figure 4 Common linguistic hierarchies

As information aggregation plays a very significant role inthe process of making decision aggregation operators with2-tuple linguistic information have attracted many scholarsrsquoattention If the 2-tuples are from different linguistic termsets they cannot be aggregated directly and should beconducted tedious transformation before aggregation oper-ation to avoid complicated computation we proposed someaggregation operators with interval-valued 2-tuple linguisticinformation Besides we discuss their desired definition

Definition 3 Let the linguistic evaluation set be 119878 =1199040 1199041 119904119892 [(119904119894 1205721) (119904119895 1205722)]which is called the interval 2-tuple linguistic where 119904119894 and 119904119895 belong to the evaluation set 119878and 119894 le 119895 1205721 lt 1205722 The interval number [1205731 1205732] (1205731 1205732 isin[0 1] 1205731 le 1205732) can be obtained by the following function 119891119891 ([1205731 1205732]) = [(119904119894 1205721) (119904119895 1205722)]

119904119894 119894 = 119903119900119906119899119889 (1205731 lowast 119892)119904119895 119895 = 119903119900119906119899119889 (1205732 lowast 119892)1205721 = 1205731 minus 119894119892 1205721 isin [minus05119892 05119892 ]1205722 = 1205732 minus 119895119892 1205722 isin [minus05119892 05119892 ]

(9)

On the contrary the interval 2-tuple linguistic[(119904119894 1205721) (119904119895 1205722)] can be converted into interval numbers byfunction 119891minus1

119891minus1 [(119904119894 1205721) (119904119895 1205722)] = [ 119894119892 + 1205721 119895119892 + 1205722]= [1205731 1205732]

(10)

Particularly if 119904119894 = 119904119895 and 120572119894 = 120572119895 then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable

Definition 4 Let 119883 = [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)] be a set of 2-tuples let 119908 =(1199081 1199082 119908119899)T be the weight vector where 119908119894 isin [0 1] 119894 =1 2 119899 sum119899i=1 119908119894 = 1 and the interval 2-tuple weightedaverage (ITWA) operator is defined as

ITWA [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)]= 119891[ 119899sum

i=1119908119894119891minus1 (119904119894 120572119894) 119899sum

i=1119908119894119891minus1 (1199041015840119894 1205721015840119894)]

(11)

This approach is introduced to deal with informationassessed in different linguistic scales by using the extensionprinciple and the interval 2-tuple linguistic representationmodel It is a computing model as shown in Figure 5

In summary the process of determining theweight ofCRsis as follows

Step 1 Set the linguistic evaluation set 119878 = 1199040 1199041 119904119892Step 2 Evaluate requirement 119894 and requirement 119895 accordingto evaluator 119877(119896) and get the measure value [119906119896119894119895 V119896119894119895] where119896 = 1 2 119897 119906119896119894119895 V119896119894119895 isin 119878 119894 119895 = 1 2 119899Step 3 Obtain the linguistic complementary judgmentmatrix 119877119896 = (119906119896119894119895 V119896119894119895)119899times119899 according to the measurevalue and the weight vector of the evaluator is 119908119896 =(1199081 1199082 119908119897) where sum119897119896=1 119908119896 = 1

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Page 4: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

4 Mathematical Problems in Engineering

operate Because of the difference of customersrsquo knowledgestructure experience and other objective or subjective fac-tors some CRs expressionmay be uncertain linguistic prefer-enceThe interval 2-tuple linguistic representationmodel andthe prospect theory are proposed to deal with the uncertaintyThe interval 2-tuple linguistic representation model could bemore accurate in terms of vague linguistic preference and lessinformation loss in fuzzy information processing Thereforeit is appropriate to select the 2-tuple linguistic representationmodel to illustrate fuzzy linguistic preference in the processof determining CRsrsquo weight Because CRs are diversityenterprises can not meet completely based on this we usedprospect theory to evaluate the productsrsquo comprehensiveprospects value in order to achieve the maximum level ofcustomer satisfaction

The remainder of this paper is organized in the followingmanner Section 2 is CRs analysis based on the Kanomodel Section 3 is the innovative product program selectionbased on the prospect theory In Section 4 an empiricalexample is provided to demonstrate the applicability of theproposedmethod Comparative analysis is given in Section 5Finally some conclusions and future research directions aresummarized in Section 6

The article frame work we proposed is shown in Figure 1

2 Analysis of CRs Based on Kano Model

The customer can not specify the desired product attributesaccurately in a real buying scenario It is unscientific to deter-mine the true requirements of customers simply by a simplequestionnaire Therefore systematic methodological tools toclarify the real requirements of customer are necessary Kanomodel as a valid method is proposed to identify the keyCRs

21 Identification of the Initial CRs of a Product The Kanomodel as a relative accuracy expression of CRs is used torealize CRs and their effect on customer satisfaction (CS)It can classify different CRs and find attractive require-ments of products Promoting enterprises produce morepopular products which can stand out from similar prod-ucts

According to the size of the CRs impact on CSKano model divides CRs into five types requirementswhich are must-be requirements one-dimensional require-ments attractive requirements indifference requirementsand reverse requirements as shown in Figure 2

The horizontal axis is the satisfaction degree of onespecific CR and the vertical axismeans the satisfaction degreeof CS

Must-Be Requirements (M) Customers will accept if thisattribute is provided otherwise they will feel extremelydissatisfied

One-Dimensional Requirements (O) CS is a linear functionof the satisfaction degree of a certainly CR High satisfactiondegree leads to high satisfaction and low satisfaction degreeleads to low satisfaction

Attractive Requirements (A) Customers will be very satisfiedif the requirement is met if the requirement is not met theywill accept the product with satisfaction also

Indifference Requirements (I) Regardless of the fact thatrequirement is satisfied or not CS will not be impacted

Reverse Requirements (R) Customers do not want theattribute in the product and absence of this attributeincreases the degree of CS

22 Determine the Type of CRs Based on Kano ModelEstablishing the Kano model of CRs is vital for a productdesign and the common tools for determining the initial CRsare Kano questionnaire Kano assessment table and Kanosurvey results table The main steps are as follows

Step 1 Design the Kano questionnaire The Kano modelprovides a format for obtaining customer answers on eachpotential product attributeThe Kano questionnaire is shownin Table 1

From Table 1 we can know that customers have to selectone of the states out of Dislike Could understand Neutral Ofcourse and Like from the product meet the requirement sideif the requirement is met in the product Customers also haveto select one of the states from the products do not meet therequirement side

Step 2 The Kano questionnaire was issued All possiblecombinations of customer answers and the correspondingtype of product attribute are summarized in Table 2

As seen fromTable 2 besides the five types of requirementhave involved there is onemore type of requirement calledQwhere Q represents a questionable answer and the answer isinvalid It occurs when customers select like or dislike fromboth functional and dysfunctional sides

Step 3 By combining the two answers in the Kano evaluationtable (Table 2) the product criterion can be identified asattractive must-be one-dimensional indifference or rever-sal the results are shown in Table 3

In order to maximize CS we should consider the follow-ing points (Sharif Ullah and Tamaki [39])

(i) Keep must-be attributes(ii) As far as possible to meet the one-dimensional

attributes and charm attributes(iii) Avoid indifferent attributes as many as possible(iv) Avoid reverse attributes

Step 4 Calculate satisfaction coefficient and dissatisfactioncoefficient

The quantitative analysis of Kanorsquos model begins withcalculating CS and DS (Ji et al (2014)) Due to the diversi-fication of CRs CS and DS values only indicate the average

Mathematical Problems in Engineering 5

Satisfied

Dissatisfied

Attractive requirements

One-dimensional requirements

Reversal requirements

Sufficiency

Must-be requirements

Insufficiency Indifference

Figure 2 Kano model of customer satisfaction

Table 1 Kano questionnaire table

Requirement Problem Dislike Could understand Neutral Of course Like

119877119894 Products meet the requirement (select one) radicProducts do not meet the requirement (select one) radic

Table 2 Kano evaluation table

Dysfunctional questionldquoIf [the product] did not satisfied [feature x]

how do you feelrdquo

Like Of course Neutral Couldunderstand Dislike

Functional questionIf [the product]satisfied [feature x]how would you feel

Like Q A A A OOf course R I I I MNeutral R I I I MCould

understand R I I I M

Dislike R R R R Q

Table 3 Classification table of requirements

Requirements A O M I R Total number of questionnaires Kano category1198771 20 25 15 22 18 100 O1198772 15 25 15 15 30 100 Rsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdotTable 4 119862119878119894 minus 119862119863119878119894 relationship functions

Kano category A B 119891 (119910119894) 119904119894 = 119860119891 (119910119894) + 119861A

119862119878119894 minus 119863119878119894119890 minus 1 minus119862119878119894 minus 119890119863119878119894119890 minus 1 119890119910119894 119904119894 = 119862119878119894 minus 119863119878119894119890 minus 1 119890119910119894 minus 119862119878119894 minus 119890119863119878119894119890 minus 1O 119862119878119894 minus 119863119878119894 119863119878119894 119910119894 119904119894 = (119862119878119894 minus 119863119878119894) 119910119894 + 119863119878119894M

119890(119862119878119894 minus 119863119878119894)119890 minus 1 119890119862119878119894 minus 119863119878119894119890 minus 1 minus119890119910119894 119904119894 = minus119890 (119862119878119894 minus 119863119878119894)119890 minus 1 119890119910119894 + 119890119862119878119894 minus 119863119878119894119890 minus 1

6 Mathematical Problems in Engineering

Get the initial requirements

Focus group

Questionnaire

Depth interviews

Analysis of the questionnaire results

Send questionnaires

Collect questionnairesI and R attributes are removed according

to the rules

Ranking product attributesaccording to si

Determine the Kano category of requirements

If this property is M si = minuse (CSi minus DSi)

e minus 1eyi +

eCSi minus DSie minus 1

If this property is O si = (CSi minus DSi) yi + DSi

If this attribute is A si =CSi minus DSi

e minus 1eyi minus minus

CSi minus eDSie minus 1

Figure 3 The flow chart based on Kano model

contribution of one CR to CS which can be represented bythe number of customers who are satisfied or dissatisfiedwith a certain CR From Table 3 we can sum up the numberof attractive attributes 119873119860 one-dimensional attributes 119873119874must-be attributes 119873119872 and indifferent attributes 119873119868 andthen we can get the value of 119862119878119894 and 119862119863119878119894 by formulations(1) and (2)

119862119878119894 = 119873119860 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (1)119862119863119878119894 = minus 119873119872 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (2)

Step 5 According to Table 4 119862119878119894 minus 119862119863119878119894 relationship func-tions could be obtained (Ji et al [40])

Step 6 A rank for CRs is made according to the value of 119904119894The flow chart based on Kanomodel is shown in Figure 3

23 Weight Determination of CRs In product design it isvery difficult for product design decision-makers due to thevagueness and uncertainty of the CRs In order to solve thisdifficult Lin et al [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic

It is used for representing the linguistic assessment infor-mation by means of a 2-tuple (119904119894 120572119894) where 119904119894 is a linguisticlabel from predefined linguistic term set 119878 and 120572119894 is the valueof symbolic translation (Dong et al [42] Wei [43] Zhang[44] Zhang [45] Gangurde and Akarte [46] Liu and Chen[47] Qin and Liu [48] Wang et al [49]) See Figure 4

Definition 1 Let 119878 = 1199040 1199041 119904119892 be a linguistic termset and 120572 represents the deviation between the linguistic

information and the closest linguistic phrase in the initiallinguistic evaluation set 119878 the real number (120573 isin [0 119892]) isthe aggregation operation result of these elements of 119878 thenthe 2-tuple linguistic information is obtained by the followingfunction 119891

119891 [0 119892] 997888rarr 119878 times [minus05 05] (3)119891 (120573) = (119904119894 120572)

119904119894 119894 = 119903119900119906119899119889 (120573)120572 = 120573 minus 119894 120572 isin [minus05 05] (4)

where round is a rounding operation and 119894 isin [0 119892]Correspondingly the real number 120573 can be obtained by

the 2-tuple linguistic information according to the followingfunction 119891minus1

119891minus1 119878 times [minus05 05] 997888rarr [0 119892] (5)119891minus1 (119904119894 120572) = 119894 + 120572 = 120573 (6)

119904119894 isin 119878 997904rArr (119904119894 0) isin 119878 (7)where formula (7) represents the conversion between a

linguistic term and a 2-tuple linguistic consists in adding avalue 0 as symbolic translation

Definition 2 Let 119883 = (1199041 1205721) (1199042 1205722) (119904119899 120572119899) be a setof 2-tuples let 119908 = (1199081 1199082 119908119899)T be the weight vectorwhere 119908119894 isin [0 1] 119894 = 1 2 119899 sum119899119894=1 119908119894 = 1 and the 2-tuple weighted average (TWA) operator is defined as

TWA (119883) = 119891(1119899119899sum119895=1

119908119895998779minus1 (119903119895 120572119895)) = (1119899119899sum119895=1

119908119895120573119895) (8)

Mathematical Problems in Engineering 7

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Figure 4 Common linguistic hierarchies

As information aggregation plays a very significant role inthe process of making decision aggregation operators with2-tuple linguistic information have attracted many scholarsrsquoattention If the 2-tuples are from different linguistic termsets they cannot be aggregated directly and should beconducted tedious transformation before aggregation oper-ation to avoid complicated computation we proposed someaggregation operators with interval-valued 2-tuple linguisticinformation Besides we discuss their desired definition

Definition 3 Let the linguistic evaluation set be 119878 =1199040 1199041 119904119892 [(119904119894 1205721) (119904119895 1205722)]which is called the interval 2-tuple linguistic where 119904119894 and 119904119895 belong to the evaluation set 119878and 119894 le 119895 1205721 lt 1205722 The interval number [1205731 1205732] (1205731 1205732 isin[0 1] 1205731 le 1205732) can be obtained by the following function 119891119891 ([1205731 1205732]) = [(119904119894 1205721) (119904119895 1205722)]

119904119894 119894 = 119903119900119906119899119889 (1205731 lowast 119892)119904119895 119895 = 119903119900119906119899119889 (1205732 lowast 119892)1205721 = 1205731 minus 119894119892 1205721 isin [minus05119892 05119892 ]1205722 = 1205732 minus 119895119892 1205722 isin [minus05119892 05119892 ]

(9)

On the contrary the interval 2-tuple linguistic[(119904119894 1205721) (119904119895 1205722)] can be converted into interval numbers byfunction 119891minus1

119891minus1 [(119904119894 1205721) (119904119895 1205722)] = [ 119894119892 + 1205721 119895119892 + 1205722]= [1205731 1205732]

(10)

Particularly if 119904119894 = 119904119895 and 120572119894 = 120572119895 then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable

Definition 4 Let 119883 = [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)] be a set of 2-tuples let 119908 =(1199081 1199082 119908119899)T be the weight vector where 119908119894 isin [0 1] 119894 =1 2 119899 sum119899i=1 119908119894 = 1 and the interval 2-tuple weightedaverage (ITWA) operator is defined as

ITWA [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)]= 119891[ 119899sum

i=1119908119894119891minus1 (119904119894 120572119894) 119899sum

i=1119908119894119891minus1 (1199041015840119894 1205721015840119894)]

(11)

This approach is introduced to deal with informationassessed in different linguistic scales by using the extensionprinciple and the interval 2-tuple linguistic representationmodel It is a computing model as shown in Figure 5

In summary the process of determining theweight ofCRsis as follows

Step 1 Set the linguistic evaluation set 119878 = 1199040 1199041 119904119892Step 2 Evaluate requirement 119894 and requirement 119895 accordingto evaluator 119877(119896) and get the measure value [119906119896119894119895 V119896119894119895] where119896 = 1 2 119897 119906119896119894119895 V119896119894119895 isin 119878 119894 119895 = 1 2 119899Step 3 Obtain the linguistic complementary judgmentmatrix 119877119896 = (119906119896119894119895 V119896119894119895)119899times119899 according to the measurevalue and the weight vector of the evaluator is 119908119896 =(1199081 1199082 119908119897) where sum119897119896=1 119908119896 = 1

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Mathematical Problems in Engineering

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Page 5: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 5

Satisfied

Dissatisfied

Attractive requirements

One-dimensional requirements

Reversal requirements

Sufficiency

Must-be requirements

Insufficiency Indifference

Figure 2 Kano model of customer satisfaction

Table 1 Kano questionnaire table

Requirement Problem Dislike Could understand Neutral Of course Like

119877119894 Products meet the requirement (select one) radicProducts do not meet the requirement (select one) radic

Table 2 Kano evaluation table

Dysfunctional questionldquoIf [the product] did not satisfied [feature x]

how do you feelrdquo

Like Of course Neutral Couldunderstand Dislike

Functional questionIf [the product]satisfied [feature x]how would you feel

Like Q A A A OOf course R I I I MNeutral R I I I MCould

understand R I I I M

Dislike R R R R Q

Table 3 Classification table of requirements

Requirements A O M I R Total number of questionnaires Kano category1198771 20 25 15 22 18 100 O1198772 15 25 15 15 30 100 Rsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdotTable 4 119862119878119894 minus 119862119863119878119894 relationship functions

Kano category A B 119891 (119910119894) 119904119894 = 119860119891 (119910119894) + 119861A

119862119878119894 minus 119863119878119894119890 minus 1 minus119862119878119894 minus 119890119863119878119894119890 minus 1 119890119910119894 119904119894 = 119862119878119894 minus 119863119878119894119890 minus 1 119890119910119894 minus 119862119878119894 minus 119890119863119878119894119890 minus 1O 119862119878119894 minus 119863119878119894 119863119878119894 119910119894 119904119894 = (119862119878119894 minus 119863119878119894) 119910119894 + 119863119878119894M

119890(119862119878119894 minus 119863119878119894)119890 minus 1 119890119862119878119894 minus 119863119878119894119890 minus 1 minus119890119910119894 119904119894 = minus119890 (119862119878119894 minus 119863119878119894)119890 minus 1 119890119910119894 + 119890119862119878119894 minus 119863119878119894119890 minus 1

6 Mathematical Problems in Engineering

Get the initial requirements

Focus group

Questionnaire

Depth interviews

Analysis of the questionnaire results

Send questionnaires

Collect questionnairesI and R attributes are removed according

to the rules

Ranking product attributesaccording to si

Determine the Kano category of requirements

If this property is M si = minuse (CSi minus DSi)

e minus 1eyi +

eCSi minus DSie minus 1

If this property is O si = (CSi minus DSi) yi + DSi

If this attribute is A si =CSi minus DSi

e minus 1eyi minus minus

CSi minus eDSie minus 1

Figure 3 The flow chart based on Kano model

contribution of one CR to CS which can be represented bythe number of customers who are satisfied or dissatisfiedwith a certain CR From Table 3 we can sum up the numberof attractive attributes 119873119860 one-dimensional attributes 119873119874must-be attributes 119873119872 and indifferent attributes 119873119868 andthen we can get the value of 119862119878119894 and 119862119863119878119894 by formulations(1) and (2)

119862119878119894 = 119873119860 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (1)119862119863119878119894 = minus 119873119872 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (2)

Step 5 According to Table 4 119862119878119894 minus 119862119863119878119894 relationship func-tions could be obtained (Ji et al [40])

Step 6 A rank for CRs is made according to the value of 119904119894The flow chart based on Kanomodel is shown in Figure 3

23 Weight Determination of CRs In product design it isvery difficult for product design decision-makers due to thevagueness and uncertainty of the CRs In order to solve thisdifficult Lin et al [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic

It is used for representing the linguistic assessment infor-mation by means of a 2-tuple (119904119894 120572119894) where 119904119894 is a linguisticlabel from predefined linguistic term set 119878 and 120572119894 is the valueof symbolic translation (Dong et al [42] Wei [43] Zhang[44] Zhang [45] Gangurde and Akarte [46] Liu and Chen[47] Qin and Liu [48] Wang et al [49]) See Figure 4

Definition 1 Let 119878 = 1199040 1199041 119904119892 be a linguistic termset and 120572 represents the deviation between the linguistic

information and the closest linguistic phrase in the initiallinguistic evaluation set 119878 the real number (120573 isin [0 119892]) isthe aggregation operation result of these elements of 119878 thenthe 2-tuple linguistic information is obtained by the followingfunction 119891

119891 [0 119892] 997888rarr 119878 times [minus05 05] (3)119891 (120573) = (119904119894 120572)

119904119894 119894 = 119903119900119906119899119889 (120573)120572 = 120573 minus 119894 120572 isin [minus05 05] (4)

where round is a rounding operation and 119894 isin [0 119892]Correspondingly the real number 120573 can be obtained by

the 2-tuple linguistic information according to the followingfunction 119891minus1

119891minus1 119878 times [minus05 05] 997888rarr [0 119892] (5)119891minus1 (119904119894 120572) = 119894 + 120572 = 120573 (6)

119904119894 isin 119878 997904rArr (119904119894 0) isin 119878 (7)where formula (7) represents the conversion between a

linguistic term and a 2-tuple linguistic consists in adding avalue 0 as symbolic translation

Definition 2 Let 119883 = (1199041 1205721) (1199042 1205722) (119904119899 120572119899) be a setof 2-tuples let 119908 = (1199081 1199082 119908119899)T be the weight vectorwhere 119908119894 isin [0 1] 119894 = 1 2 119899 sum119899119894=1 119908119894 = 1 and the 2-tuple weighted average (TWA) operator is defined as

TWA (119883) = 119891(1119899119899sum119895=1

119908119895998779minus1 (119903119895 120572119895)) = (1119899119899sum119895=1

119908119895120573119895) (8)

Mathematical Problems in Engineering 7

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Figure 4 Common linguistic hierarchies

As information aggregation plays a very significant role inthe process of making decision aggregation operators with2-tuple linguistic information have attracted many scholarsrsquoattention If the 2-tuples are from different linguistic termsets they cannot be aggregated directly and should beconducted tedious transformation before aggregation oper-ation to avoid complicated computation we proposed someaggregation operators with interval-valued 2-tuple linguisticinformation Besides we discuss their desired definition

Definition 3 Let the linguistic evaluation set be 119878 =1199040 1199041 119904119892 [(119904119894 1205721) (119904119895 1205722)]which is called the interval 2-tuple linguistic where 119904119894 and 119904119895 belong to the evaluation set 119878and 119894 le 119895 1205721 lt 1205722 The interval number [1205731 1205732] (1205731 1205732 isin[0 1] 1205731 le 1205732) can be obtained by the following function 119891119891 ([1205731 1205732]) = [(119904119894 1205721) (119904119895 1205722)]

119904119894 119894 = 119903119900119906119899119889 (1205731 lowast 119892)119904119895 119895 = 119903119900119906119899119889 (1205732 lowast 119892)1205721 = 1205731 minus 119894119892 1205721 isin [minus05119892 05119892 ]1205722 = 1205732 minus 119895119892 1205722 isin [minus05119892 05119892 ]

(9)

On the contrary the interval 2-tuple linguistic[(119904119894 1205721) (119904119895 1205722)] can be converted into interval numbers byfunction 119891minus1

119891minus1 [(119904119894 1205721) (119904119895 1205722)] = [ 119894119892 + 1205721 119895119892 + 1205722]= [1205731 1205732]

(10)

Particularly if 119904119894 = 119904119895 and 120572119894 = 120572119895 then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable

Definition 4 Let 119883 = [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)] be a set of 2-tuples let 119908 =(1199081 1199082 119908119899)T be the weight vector where 119908119894 isin [0 1] 119894 =1 2 119899 sum119899i=1 119908119894 = 1 and the interval 2-tuple weightedaverage (ITWA) operator is defined as

ITWA [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)]= 119891[ 119899sum

i=1119908119894119891minus1 (119904119894 120572119894) 119899sum

i=1119908119894119891minus1 (1199041015840119894 1205721015840119894)]

(11)

This approach is introduced to deal with informationassessed in different linguistic scales by using the extensionprinciple and the interval 2-tuple linguistic representationmodel It is a computing model as shown in Figure 5

In summary the process of determining theweight ofCRsis as follows

Step 1 Set the linguistic evaluation set 119878 = 1199040 1199041 119904119892Step 2 Evaluate requirement 119894 and requirement 119895 accordingto evaluator 119877(119896) and get the measure value [119906119896119894119895 V119896119894119895] where119896 = 1 2 119897 119906119896119894119895 V119896119894119895 isin 119878 119894 119895 = 1 2 119899Step 3 Obtain the linguistic complementary judgmentmatrix 119877119896 = (119906119896119894119895 V119896119894119895)119899times119899 according to the measurevalue and the weight vector of the evaluator is 119908119896 =(1199081 1199082 119908119897) where sum119897119896=1 119908119896 = 1

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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Hindawiwwwhindawicom Volume 2018

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Page 6: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

6 Mathematical Problems in Engineering

Get the initial requirements

Focus group

Questionnaire

Depth interviews

Analysis of the questionnaire results

Send questionnaires

Collect questionnairesI and R attributes are removed according

to the rules

Ranking product attributesaccording to si

Determine the Kano category of requirements

If this property is M si = minuse (CSi minus DSi)

e minus 1eyi +

eCSi minus DSie minus 1

If this property is O si = (CSi minus DSi) yi + DSi

If this attribute is A si =CSi minus DSi

e minus 1eyi minus minus

CSi minus eDSie minus 1

Figure 3 The flow chart based on Kano model

contribution of one CR to CS which can be represented bythe number of customers who are satisfied or dissatisfiedwith a certain CR From Table 3 we can sum up the numberof attractive attributes 119873119860 one-dimensional attributes 119873119874must-be attributes 119873119872 and indifferent attributes 119873119868 andthen we can get the value of 119862119878119894 and 119862119863119878119894 by formulations(1) and (2)

119862119878119894 = 119873119860 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (1)119862119863119878119894 = minus 119873119872 + 119873119874119873119860 + 119873119874 + 119873119872 + 119873119868 (2)

Step 5 According to Table 4 119862119878119894 minus 119862119863119878119894 relationship func-tions could be obtained (Ji et al [40])

Step 6 A rank for CRs is made according to the value of 119904119894The flow chart based on Kanomodel is shown in Figure 3

23 Weight Determination of CRs In product design it isvery difficult for product design decision-makers due to thevagueness and uncertainty of the CRs In order to solve thisdifficult Lin et al [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic

It is used for representing the linguistic assessment infor-mation by means of a 2-tuple (119904119894 120572119894) where 119904119894 is a linguisticlabel from predefined linguistic term set 119878 and 120572119894 is the valueof symbolic translation (Dong et al [42] Wei [43] Zhang[44] Zhang [45] Gangurde and Akarte [46] Liu and Chen[47] Qin and Liu [48] Wang et al [49]) See Figure 4

Definition 1 Let 119878 = 1199040 1199041 119904119892 be a linguistic termset and 120572 represents the deviation between the linguistic

information and the closest linguistic phrase in the initiallinguistic evaluation set 119878 the real number (120573 isin [0 119892]) isthe aggregation operation result of these elements of 119878 thenthe 2-tuple linguistic information is obtained by the followingfunction 119891

119891 [0 119892] 997888rarr 119878 times [minus05 05] (3)119891 (120573) = (119904119894 120572)

119904119894 119894 = 119903119900119906119899119889 (120573)120572 = 120573 minus 119894 120572 isin [minus05 05] (4)

where round is a rounding operation and 119894 isin [0 119892]Correspondingly the real number 120573 can be obtained by

the 2-tuple linguistic information according to the followingfunction 119891minus1

119891minus1 119878 times [minus05 05] 997888rarr [0 119892] (5)119891minus1 (119904119894 120572) = 119894 + 120572 = 120573 (6)

119904119894 isin 119878 997904rArr (119904119894 0) isin 119878 (7)where formula (7) represents the conversion between a

linguistic term and a 2-tuple linguistic consists in adding avalue 0 as symbolic translation

Definition 2 Let 119883 = (1199041 1205721) (1199042 1205722) (119904119899 120572119899) be a setof 2-tuples let 119908 = (1199081 1199082 119908119899)T be the weight vectorwhere 119908119894 isin [0 1] 119894 = 1 2 119899 sum119899119894=1 119908119894 = 1 and the 2-tuple weighted average (TWA) operator is defined as

TWA (119883) = 119891(1119899119899sum119895=1

119908119895998779minus1 (119903119895 120572119895)) = (1119899119899sum119895=1

119908119895120573119895) (8)

Mathematical Problems in Engineering 7

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Figure 4 Common linguistic hierarchies

As information aggregation plays a very significant role inthe process of making decision aggregation operators with2-tuple linguistic information have attracted many scholarsrsquoattention If the 2-tuples are from different linguistic termsets they cannot be aggregated directly and should beconducted tedious transformation before aggregation oper-ation to avoid complicated computation we proposed someaggregation operators with interval-valued 2-tuple linguisticinformation Besides we discuss their desired definition

Definition 3 Let the linguistic evaluation set be 119878 =1199040 1199041 119904119892 [(119904119894 1205721) (119904119895 1205722)]which is called the interval 2-tuple linguistic where 119904119894 and 119904119895 belong to the evaluation set 119878and 119894 le 119895 1205721 lt 1205722 The interval number [1205731 1205732] (1205731 1205732 isin[0 1] 1205731 le 1205732) can be obtained by the following function 119891119891 ([1205731 1205732]) = [(119904119894 1205721) (119904119895 1205722)]

119904119894 119894 = 119903119900119906119899119889 (1205731 lowast 119892)119904119895 119895 = 119903119900119906119899119889 (1205732 lowast 119892)1205721 = 1205731 minus 119894119892 1205721 isin [minus05119892 05119892 ]1205722 = 1205732 minus 119895119892 1205722 isin [minus05119892 05119892 ]

(9)

On the contrary the interval 2-tuple linguistic[(119904119894 1205721) (119904119895 1205722)] can be converted into interval numbers byfunction 119891minus1

119891minus1 [(119904119894 1205721) (119904119895 1205722)] = [ 119894119892 + 1205721 119895119892 + 1205722]= [1205731 1205732]

(10)

Particularly if 119904119894 = 119904119895 and 120572119894 = 120572119895 then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable

Definition 4 Let 119883 = [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)] be a set of 2-tuples let 119908 =(1199081 1199082 119908119899)T be the weight vector where 119908119894 isin [0 1] 119894 =1 2 119899 sum119899i=1 119908119894 = 1 and the interval 2-tuple weightedaverage (ITWA) operator is defined as

ITWA [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)]= 119891[ 119899sum

i=1119908119894119891minus1 (119904119894 120572119894) 119899sum

i=1119908119894119891minus1 (1199041015840119894 1205721015840119894)]

(11)

This approach is introduced to deal with informationassessed in different linguistic scales by using the extensionprinciple and the interval 2-tuple linguistic representationmodel It is a computing model as shown in Figure 5

In summary the process of determining theweight ofCRsis as follows

Step 1 Set the linguistic evaluation set 119878 = 1199040 1199041 119904119892Step 2 Evaluate requirement 119894 and requirement 119895 accordingto evaluator 119877(119896) and get the measure value [119906119896119894119895 V119896119894119895] where119896 = 1 2 119897 119906119896119894119895 V119896119894119895 isin 119878 119894 119895 = 1 2 119899Step 3 Obtain the linguistic complementary judgmentmatrix 119877119896 = (119906119896119894119895 V119896119894119895)119899times119899 according to the measurevalue and the weight vector of the evaluator is 119908119896 =(1199081 1199082 119908119897) where sum119897119896=1 119908119896 = 1

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Mathematical Problems in Engineering

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Page 7: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 7

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Figure 4 Common linguistic hierarchies

As information aggregation plays a very significant role inthe process of making decision aggregation operators with2-tuple linguistic information have attracted many scholarsrsquoattention If the 2-tuples are from different linguistic termsets they cannot be aggregated directly and should beconducted tedious transformation before aggregation oper-ation to avoid complicated computation we proposed someaggregation operators with interval-valued 2-tuple linguisticinformation Besides we discuss their desired definition

Definition 3 Let the linguistic evaluation set be 119878 =1199040 1199041 119904119892 [(119904119894 1205721) (119904119895 1205722)]which is called the interval 2-tuple linguistic where 119904119894 and 119904119895 belong to the evaluation set 119878and 119894 le 119895 1205721 lt 1205722 The interval number [1205731 1205732] (1205731 1205732 isin[0 1] 1205731 le 1205732) can be obtained by the following function 119891119891 ([1205731 1205732]) = [(119904119894 1205721) (119904119895 1205722)]

119904119894 119894 = 119903119900119906119899119889 (1205731 lowast 119892)119904119895 119895 = 119903119900119906119899119889 (1205732 lowast 119892)1205721 = 1205731 minus 119894119892 1205721 isin [minus05119892 05119892 ]1205722 = 1205732 minus 119895119892 1205722 isin [minus05119892 05119892 ]

(9)

On the contrary the interval 2-tuple linguistic[(119904119894 1205721) (119904119895 1205722)] can be converted into interval numbers byfunction 119891minus1

119891minus1 [(119904119894 1205721) (119904119895 1205722)] = [ 119894119892 + 1205721 119895119892 + 1205722]= [1205731 1205732]

(10)

Particularly if 119904119894 = 119904119895 and 120572119894 = 120572119895 then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable

Definition 4 Let 119883 = [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)] be a set of 2-tuples let 119908 =(1199081 1199082 119908119899)T be the weight vector where 119908119894 isin [0 1] 119894 =1 2 119899 sum119899i=1 119908119894 = 1 and the interval 2-tuple weightedaverage (ITWA) operator is defined as

ITWA [(1199041 1205721) (11990410158401 12057210158401)] [(1199042 1205722) (11990410158402 12057210158402)] [(119904119899 120572119899) (1199041015840119899 1205721015840119899)]= 119891[ 119899sum

i=1119908119894119891minus1 (119904119894 120572119894) 119899sum

i=1119908119894119891minus1 (1199041015840119894 1205721015840119894)]

(11)

This approach is introduced to deal with informationassessed in different linguistic scales by using the extensionprinciple and the interval 2-tuple linguistic representationmodel It is a computing model as shown in Figure 5

In summary the process of determining theweight ofCRsis as follows

Step 1 Set the linguistic evaluation set 119878 = 1199040 1199041 119904119892Step 2 Evaluate requirement 119894 and requirement 119895 accordingto evaluator 119877(119896) and get the measure value [119906119896119894119895 V119896119894119895] where119896 = 1 2 119897 119906119896119894119895 V119896119894119895 isin 119878 119894 119895 = 1 2 119899Step 3 Obtain the linguistic complementary judgmentmatrix 119877119896 = (119906119896119894119895 V119896119894119895)119899times119899 according to the measurevalue and the weight vector of the evaluator is 119908119896 =(1199081 1199082 119908119897) where sum119897119896=1 119908119896 = 1

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Page 8: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

8 Mathematical Problems in Engineering

Step 4 Convert the linguistic complementary judgmentmatrix 119877119896 to the interval 2-tuple linguistic judgment matrix1198771015840119896

1198771015840119896 = ([(119906119896119894119895 0) (V119896119894119895 0)])119899times119899 (12)Step 5 The interval 2-tuple linguistic [(119906119896119894119895 0) (V119896119894119895 0)] istransformed into the corresponding interval number [119888119896119894119895 119889119896119894119895]by the inverse function 119891minus1Step 6 Aggregate the number of intervals [119888119896119894119895 119889119896119894119895] and get theinterval 2-tuple linguistic comprehensive evaluation matrix

= ([119888119894119895 119889119894119895])119899times119899 = ([sum119908119896119888119896119894119895sum119908119896119889119896119894119895])119899times119899 (13)Step 7 119877 = ([119904119894119895 1199041015840119894119895])119898times119899 is the evaluation matrix where119894 = 1 2 119898 119895 = 1 2 119899 then the comprehensive weightinterval of the evaluation object 119894 is

120579119894 = [120574119894 1205741015840119894 ] = [[(sum119899119894=1 119904119894119895)119899 (sum119899119894=1 1199041015840119894119895)119899 ]

] (14)Step 8 If the evaluation object 119894 is not inferior to theevaluation object 119896 and 120579119894 ge 120579119896 (119894 119896 = 1 2 119898) then get119901119894119896 by pairwise comparison according to the comprehensiveevaluation value from Step 7 and the formula is as follows

119901119894119896 = 119901 (120579119894 ge 120579119896)= max1 minusmax 1205741015840119896 minus 120574119894(1205741015840119894 minus 120574119894) + (1205741015840

119896minus 120574119896) 0 0 (15)

Then obtain the following probability matrix 119875

119875 = (119875119894119896)119898times119899 =[[[[[[[

11987511 11987512 sdot sdot sdot 119875111989811987521 11987522 sdot sdot sdot 1198752119898 1198751198981 1198751198982 sdot sdot sdot 119875119898119898

]]]]]]]

(16)

Among them the rank vector of possible degree matrix isobtained

120593119894 = sum119898119896=1 119875119894119896 + 1198982 minus 1119898 (119898 minus 1) (17)Step 9 We obtain the ranking vector 120593119894 of the probabilitymatrix 119875 According to the size of 120593119894 obtain the weights ofdifferent CRs

The flow chart based on the interval 2-tuple linguisticinformation is shown in Figure 5

3 Selection of Innovative Schemes Based onProspect Theory

Due to restrictions on resources such as technology cost andequipment the innovation efficiency is not obvious in CCPI

design process Therefore the prospects theory is proposedin the case of customer demand which has been identifiedwhich considers the companyrsquos technology cost advancedequipment and the conflict between the demand and theimpact of psychological factors of the customers Accordingto the customer satisfaction and the expected value of eachattribute of the product we can calculate the comprehensiveprospect value and determine the optimal product scheme byusing the prospect theory

31 Gains and Loss Value of Product Attributes Firstlywe regard aspiration-levels as reference points Then gainsand losses of alternatives are obtained by the correspond-ing formulas Since attribute values are represented in thethree types crisp number interval number and intuitivetrapezoidal fuzzy number there are three possible types forcomparing an attribute value with an aspiration level (seeFigure 6)

In Figure 6 type one represents the situation that attributevalue is crisp numbers type two represents the situation thatattribute values are interval numbers type three representsthe situation that attribute values are intuitive trapezoidalfuzzy number

Assuming that aspiration level is clear number theattribute value has three types clear number interval num-ber and intuitive trapezoidal fuzzy number For the threetypes of attribute values the specific description is as followswhere 119909119894119897 is representing the value of attribute 119897 of supplier 119894(see Tables 5 and 6)(1) If 119868119897 isin 119868119862 let 119909119894119897 = 1199091015840119894119897 where 1199091015840119894119897 is clear number and119894 isin 119872 119897 isin 119873119870(2) If 119868119897 isin 119868119876 let 119909119894119897 = 119909119894119897 where 119909119894119897 is an intervalnumber 119909119894119897 = [1199091119894119897 1199092119894119897] Assuming that the attribute values arerandomly obtained in the interval [1199091119894119897 1199092119894119897] and are uniformlydistributed the probability density function is 119891119894119897(119909)

119891119894119897 (119909) = 11199092119894119897minus 1199091119894119897

1199091119894119897 le 119909 le 11990921198941198970 other 119894 isin 119872 119897 isin 119873 (18)

(3) If 119868119895 isin 119868119865 let 119909119894119897 = 119909119894119897 where 119909119894119897is intuitive trapezoidal fuzzy number 119909119894119897 =⟨([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909) ([1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] 120591119909)⟩ and 0 le 120601119909 le 10 le 120591119909 le 1 120601119909 + 120591119909 le 1 119886119894119897 119887119894119897 119888119894119897 119889119894119897 1198861198941198971 1198891198941198971 isin 119877 and themembership function 120601119894119897(119909) is as shown

120601119894119897 (119909) =

119909 minus 119886119894119897119887119894119897 minus 119886119894119897 119886119894119897 le 119909 le 119887119894119897120601119894119897 119887119894119897 le 119909 le 119888119894119897119889119894119897 minus 119909119889119894119897 minus 119888119894119897 119888119894119897 le 119909 le 1198891198941198970 others

119894 isin 119872 119897 isin 119873 (19)

If [119886119894119897 119887119894119897 119888119894119897 119889119894119897] = [1198861198941198971 119887119894119897 119888119894119897 1198891198941198971] the intuitionistictrapezoidal fuzzy number 119909119894119897 = ([119886119894119897 119887119894119897 119888119894119897 119889119894119897] 120601119909 120591119894119897)32 Calculating the Gains and Losses Value Let the expectvalue 119890 = (1198901 1198902 119890119897) of customers as the reference point in

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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Page 9: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 9

Set the linguistic evaluation set

7 Labels

3 Labels 9 Labels

5 Labels

13 Labels

Obtain the key requirement of customers

Converts the linguistic complementary judgment matrix to

the interval 2-type linguisticjudgment matrix

e interval 2-type linguisticjudgment matrix

transformed into interval number

e interval 2-type linguisticinformation comprehensive

evaluation matrix

Get the ranking vector

Figure 5 The flow chart based on the interval 2-tuple linguistic information

Type oneAttribute value is

Crisp number

The typeof attribute value

Type threeIntuitive trapezoidal

fuzzy number

Type twoAttribute value isinterval number

Figure 6 The types of attribute value

Table 5 Possible cases of position relationships between attribute value and aspiration level

Type Cases Position relationships between attribution value and aspiration level

Type one Case one (a) 119909119894119897 ge 119890119897 el xil

Case one (b) 119909119894119897 lt 119890119897 elxil

Type two

Case two (a) 1199091119894119897 gt 119890119897 el x1il x2il

Case two (b) 1199091119894119897 le 119890119897 le 1199092119894119897 elx1il x2il

Case two (c) 1199092119894119897 lt 119890119897 elx1il x2il

Type three

Case three (a) 119890119897 lt 119886119894119897 el ail dil

Case three (b) 119886119894119897 le 119890119897 le 119889119894119897 elail dil

Case three (c) 119889119894119897 lt 119890119897 elail dil

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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Page 10: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

10 Mathematical Problems in Engineering

Table 6 Variable symbol description

Variable Meaning119878 = 1198781 1198782 119878119894 119878119898 A set ofm alternative products119868 = 1198681 1198682 119868119894 119868119897 The set of product attributes119864 = (1198901 1198902 119890119899) Expectation vector of requirements119868119862 Attribute sets whose attribute values are distinct numbers119868119876 Attribute sets whose attribute values are interval numbers119868119865 Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers119873 = 1 2 119899 Product attribute sets119872 = 1 2 119898 Scheme numbers

Table 7 Calculation formula when the attribute value is a clear number

Attributetype

The relationship between attribute valueand the reference point

Calculation of gain (119866119894119897) and loss value(119871 119894119897)

119868119897 isin 119868119870 1199091015840119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (20)119871 119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (21)1199091015840119894119897 ge 119890119897 119866119894119897 = 1199091015840119894119897 minus 119890119894119897 119894 isin 119872 119897 isin 119873 (22)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (23)

this paperThen calculate the gains and loss of each attributevalue relative to the reference point When the attribute valueis a clear number we obtain the gains and losses value ofproduct attribute according to the calculation formula shownin Table 7

When the attribute value is the number of intervalsaccording to the attribute value and the position of thereference point the formula of each attribute value of theinnovation scheme is shown in Table 8

When the attribute value is intuitionistic trapezoidalfuzzy number according to the relative position of theattribute value and the reference point the formula of eachattribute value of the innovation scheme is shown in Table 9

33 Calculating the Prospect Values and Ranking For the gainmatrix 119866119905 = [119866119894119897]119898lowast119899 and the loss matrix 119871 119905 = [119871 119894119897]119898lowast119899 ofeach scheme calculate the prospective value of the candidateproduct Based on prospect theory the value of gain matrix119866119894119897 is

V(+)119894119897 = (119866119894119897)119886 119894 isin 119872 119897 isin 119873 (36)The value 119881(minus)

119894119897of loss is

V(minus)119894119897 = minus120582 (minus119871 119894119897)119887 119894 isin 119872 119897 isin 119873 (37)where 119886 and 119887 represent the degree of concavity and

convexity of the loss region and gain region of the valuefunction 0 lt 119886 lt 1 0 lt 119887 lt 1 and 120582 indicates the lossdegree of the decision maker (120582 gt 1) Among them 119886 and 119887greater decision-makers incline to risk more and 120582 greaterthe ability of decision-makers to avoid losses is greater

Due to the difference in the dimension of the productattribute value is so large that we use the range transformation

method to reduce the dimension the new gain and loss valuesof each innovation scheme are obtained by formulas (38)-(39)

119881(+)119894119897 = V(+)119894119897

minusmin V(+)119894119897

max V(+)119894119897

minusmin V(+)119894119897

(38)119881(minus)119894119897 = V(minus)

119894119897minusmin V(minus)

119894119897

max V(minus)119894119897

minusmin V(minus)119894119897

(39)119881119894119897 = 119881(+)119894119897 minus 119881(minus)119894119897 119894 isin 119872 119897 isin 119873 (40)

According to formula (40) the prospect decision matrixcan be obtained

The flow chart based on prospect theory is shown inFigure 7

4 Case Study

In order to enhance market competitiveness an ElectronicManufacturing Enterprise in Xirsquoan has designed five inno-vation schemes for mobile phones Moreover this enterpriseuses the proposed method to determine the optimal schemeAccording to the mobile phone function it has identified 35types of CRs (Appendix A1) and a market survey of whetheror not to provide the demand item based on the Kano modelis conducted to screen out ten relatively important require-ments towards customer satisfaction (Appendix A3) Fiveexperts 119877119896 (119896 = 1 2 3 4 5) are invited to participate in theevaluation of the importance of CRs that affected customersatisfaction As such experts 1198771 and 1198772 use nine elements ofthe linguistic evaluation set 119878 = 1199040 1199041 1199042 1199043 1199044 1199045 1199046 1199047 1199048experts 1198773 and 1198774 employ even elements of the linguisticevaluation set 119883 = 1199090 1199091 1199092 1199093 1199094 1199095 1199096 and last

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Page 11: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 11

Table 8 The calculation formula when the attribute value is the interval number

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)1199092119894119897 lt 119890119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (24)

119871 119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (25)

119868119897 isin 119868119868 1199091119894119897 le 119890119897 le 1199092119894119897 119866119894119897 = int1199092119894119897119890119897(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (26)

119871 119894119897 = int1198901198971199091119894119897

(119909 minus 119890119897) 119891119894119897 (119909) 119889119909 119894 isin 119872 119897 isin 119873 (27)

1199091119894119897 gt 119890119897 119866119894119897 = int11990921198941198971199091119894119897

(119909 minus 119890119897)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (28)

119871 119894119897 = int11990921198941198971199091119894119897

(119890119897 minus 119909)119891119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (29)

Table 9 Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers

Attribute type The relationship between attribute value and the reference point Calculation of gain (119866119894119897) and loss value (119871 119894119897)119890119897 le 119886119894119897 119866119894119897 = int119889119894119895

119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (30)119871 119894119897 = 0 119894 isin 119872 119897 isin 119873 (31)

119868119897 isin 119868119865 119886119894119897 le 119890119897 le 119889119894119897 119866119894119897 = int119889119894119897119890119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (32)

119871 119894119897 = int119890119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (33)

119890119897 ge 119889119894119897 119866119894119897 = 0 119894 isin 119872 119897 isin 119873 (34)119871 119894119897 = int119889119894119897119886119894119897(119909 minus 119890119897)120601119894119897(119909)119889119909 119894 isin 119872 119897 isin 119873 (35)

Output gains and loss

values of index

Outputgains andloss values

of index

YesYes

No No

i = i + 1

Output gainsand loss

values of index

Output gainsand loss values

of index

Output gainsand loss

values of index

l = l + 1

Output index

Yes

No No

Output gains andloss values of

index

Rank according tothe composite

foreground value

No No

Yes Yes Output gains

and loss values of index

Output gains and loss values

of index

Output gains and loss values of

index

Yes

Yes Yes

Yes

No

No

No

l = 1

i = 1

When the attribute value is intuitionistic fuzzy number

When the

attribute value is clear number

When the attributevalue is interval

number

Output the bestsolution

Il isin IK

x998400til lt etl

Il isin II

xt1il ge etlxt2il le etl

etl le atil etl ge dtil

l lt n

i lt s

Figure 7 The flow chart based on prospect theory

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Mathematical Problems in Engineering

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Page 12: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

12 Mathematical Problems in Engineering

Table10Th

eexp

ertsrsquo

evaluatio

nresults

basedon

prospecttheory

attribute

Inno

vatio

nschemes

Custom

erexpe

ctativev

alues

S1S2

S3S4

S5I1

minus40

00

minus48

I2(156

01750)

(150018

00)(150

01800)

(150016

80)(150

01800)

1680

I3([5

689]0

703)

([678

9]050

4)([6

789]0

802)

([467

9]080

1)([5

789]0

603)

8I4

([578

9]070

2)([4

568]0

604)

([678

9]050

4)([5

789]0

603)

([568

9]060

4)7

I5([6

789]0

802)

([568

9]070

3)([5

789]0

802)

([567

9]070

3)([5

689]0

703)

6

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Mathematical Problems in Engineering

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Page 13: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 13

Table 11 The gain value of the innovation schemes

Attribute The gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0 0 0 0 0 8I2 24519 24 24 0 24 1680I3 2110 16 1330 112 16 8I4 6160 112 1112 2930 2930 7I5 2710 7730 16760 5120 7730 6

Table 12 The loss value of the innovation schemes

Attribute The loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus4 0 0 0 minus4 8I2 minus72019 minus54 minus54 minus90 minus54 1680I3 minus92 minus1112 minus43 minus25760 minus5930 8I4 minus23 minus14960 minus16 minus23 minus23 7I5 0 minus16 minus112 0 minus16 6

experts 1198775 adopt five elements of the linguistic evaluationset 119884 = 1199100 1199101 1199102 1199103 1199104 Expertsrsquo opinions are shownin Appendix B1 The weight vector corresponding to theexpertsrsquo opinions is 119908 = (025 025 02 02 01) andfinally five key attributes are determined as being the mostimportant product attributes in the five innovative evaluationschemes (see Table 10)These key attributes are the followingoperating system (I1) CPU core count (I2) antitheft tracking(I3) fingerprint sensor (I4) and battery capacity (I5) Basedon the prospect theory the customerrsquos expectation value ofa product attribute is taken as the reference point and theproposed method is used to determine the optimal schemeThe calculation steps are discussed in the following

Step 1 Obtain the five expertsrsquo linguistic evaluation valueswith respect to the five attributes of the above-mentioned fiveinnovation schemes (Appendix B1)

Step 2 Determine the gain and loss values of each innovationscheme based on formula (19)ndash(36) and the results areshown in Tables 11 and 12

Step 3 Determine the new gain and loss values of eachinnovation scheme when the influence of the dimension iseliminated according to the formula ((37) and (38)) theresults are shown in Tables 13 and 14

Step 4 Obtain the prospect value of each attribute value asshown in Table 15

Step 5 Calculate the weights of the CRs and rank

It can be observed from the weight of the indicators120593 = (0114 0112 0110 0105 0104) (Appendix B5) thatthe standardization of the weight of the indicators was 120596 =(02092 02055 02018 01927 01908)

According to the formula (40) the comprehensiveprospect of each scheme is 119906 = (minus06910 minus06203 minus06118minus07153 minus05989) so the merits of the innovative programare 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784

The proposed hybrid method provides a systemic ana-lytical model for apperceiving the key customer require-ments and obtaining the optimal innovation schemesAccording to the Kano model ten relatively importantrequirements towards customer satisfaction are screened out(Appendix A3) combined with expertsrsquo opinion five indica-tors ie operating system (I1) CPU core count (I2) antithefttracking (I3) fingerprint sensor (I4) and battery capacity(I5) are determined as the most important indicators Andthen with the help of interval 2-tuple linguistic we easilyobtain the weights of these indicators Finally based onthe prospect theory the comprehensive prospect value ofeach scheme is calculated it is suggested that the optimalinnovative scheme is 11987855 Comparative Analysis

In order to verify the validity of the developed methodthe Technique for Order of Preference by Similarity to anIdeal Solution (TOPSIS) (Gangurde et al 2013) and theVlse Kriterjumska Optimizacija I Kompromisno Resenje(VIKOR) (Qin et al 2015) were compared with the methodsproposed in this paper (see Tables 16ndash18)

From Table 16 it is obvious that 1198765 ≻ 1198761 ≻ 1198763 ≻ 1198764 ≻1198762 but for the fact that 018 minus 0062 lt 1(5 minus 1) and by theformula 018minus0062 lt 1(119898minus1) we can know that S1 S2 S3S4 and S5 are all close to the ideal scheme

From Table 18 we can see that the sorted results are quitedifferent the result of the proposed MCDMmodel based onprospect theory is 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784 the TOPSISmethod obtains result as 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782 and the

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Page 14: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

14 Mathematical Problems in Engineering

Table 13 The new gain value of the innovation schemes after eliminated influence of dimension

Attribute The new gain value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0000 0000 0000 0112 0000 8I2 0579 1000 1000 0000 1000 1680I3 0117 0013 0029 0007 0013 8I4 0062 0007 0057 0059 0059 7I5 0146 0140 0150 0139 0140 6

Table 14 The new loss value of the innovation schemes after eliminated influence of dimension

Attribute The new loss value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 0935 1000 1000 1000 0935 8I2 0533 0362 0362 0000 0362 1680I3 0928 0982 0975 0931 0965 8I4 0987 0958 0996 0987 0987 7I5 1000 0996 0998 1000 0996 6

Table 15 The prospect values of the innovation schemes

Attribute The prospect value of the innovation schemes Customer expectative valuesS1 S2 S3 S4 S5

I1 minus0935 minus1000 minus1000 minus0888 minus0935 8I2 0046 0638 0638 0000 0638 1680I3 minus0811 minus0970 minus0946 minus0925 minus0953 8I4 minus0925 minus0951 minus0940 minus0927 minus0927 7I5 minus0854 minus0856 minus0848 minus0861 minus0856 6

Table 16 The result of TOPSIS method

TOPSISScheme The ideal solution The negative solution Similarity degreeS1 0126 0125 0499S2 0051 0003 005S3 004 0013 0248S4 0131 0139 0514S5 0017 0041 0707

Table 17 The result of VIKOR method

VIKORScheme 119880119894 119877119894 119876119894S1 0367 0191 018S2 0726 0209 1S3 0491 0209 0672S4 0561 0206 0706S5 0411 018 0062

Table 18 The results of the three methods

Method Evaluation resultsProspect theory 1198785 ≻ 1198783 ≻ 1198782 ≻ 1198781 ≻ 1198784TOPSIS 1198785 ≻ 1198784 ≻ 1198781 ≻ 1198783 ≻ 1198782VIKOR 1198785 asymp 1198781 asymp 1198783 asymp 1198784 asymp 1198782

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Page 15: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 15

Table 19

1 Camera 2 Shell color 3 E-mail 4 Theoretical talk time 5 Screen material6 Battery capacity 7 Theoretical standby time 8 CPU count 9 Operating system 10 Key shape11 Screen size 12 GPS 13 Shell material 14 Internet 15 Screen color16 HDMI interface 17 Radio 18 Electronic dictionary 19 Alarm clock 20 No USB connected to the computer21 USB 22 Calendar 23 Video 24 Word 25 Sound recorder26 E-book 27 Pinyin input 28 Calculator 29 Music 30 Typewriting31 Bluetooth 32 Antitheft tracking 33 Flashlight 34 Fingerprint sensor 35 Quick boot

Table 20

Numbering Initial customer requirements A O M I R Belongs to the Kano category1 Camera 0 0236 05281 0236 0 M2 Shell color 05236 03213 00112 01438 0 A3 E-mail 0 04202 00876 04921 0 I4 Theoretical talk time 0 0218 01753 06067 0 I5 Screen material 0 01326 0009 08584 0 I6 Battery capacity 02517 06371 00112 01 0 O7 Theoretical standby time 0 0618 01101 02719 0 O8 CPU count 05124 03371 01326 0018 0 O9 Operating system 06584 02135 0 01281 0 A10 Key shape 05461 03371 01169 0 0 A11 Screen size 0 08944 00225 00831 0 O12 GPS 0 01416 05281 03303 0 M13 Shell material 0 02629 00225 07146 0 I14 Internet 0 02494 04607 02899 0 M15 Screen color 0 03191 05348 01461 0 M16 HDMI interface 0 01708 00337 07888 00067 I17 Radio 0 01438 08292 00202 00067 M18 Electronic dictionary 0 0036 07618 01753 0027 M19 Alarm clock 0 0164 04449 03843 00067 M20 No USB connected to the computer 0 0173 0 08045 00225 I21 USB 0 00831 07775 01258 00135 M22 Calendar 0 01303 07258 01371 00067 M23 Video 0 00697 07124 01775 00404 M24 Word 0 04494 00449 05056 0 I25 Sound recorder 0 00944 04854 04135 00067 M26 E-book 0 00876 0 08989 00135 I27 Pinyin input 0 0391 04652 01371 00067 M28 Calculator 0 01573 04449 03978 0 M29 Music 0 03034 05393 01573 0 M30 Typewriting 0 04315 00315 05371 0 I31 Bluetooth 0 02563 05486 01951 0 M32 Anti-theft tracking 06025 03 00028 00695 0 A33 Flashlight 0 03546 04369 02085 0 M34 Fingerprint sensor 047 02586 01089 01625 0 A35 Quick boot 0 04863 03957 0118 0 O

Table 21

1 Key shape 2 Shell color 3 Operating system4 Screen size 5 Theoretical standby time 6 CPU count7 Fingerprint sensor 8 Battery capacity 9 Antitheft tracking10 Quick boot

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Mathematical Problems in Engineering

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Page 16: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

16 Mathematical Problems in Engineering

Table22

Expert

Theo

pinion

ofexperts

R 1

[s4s 4]

[s4s 6]

[s6s 7]

[s3s 5]

[s4s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s1s 2]

[s4s 6]

[s3s 4]

[s4s 4]

[s4s 4]

[s2s 3]

[s6s 7]

[s4s 4]

[s5s 6]

[s2s 4]

[s3s 4]

[s4s 6]

[s 4s4]

[s5s 6]

[s4s 4]

[s6s 7]

[s6s 7]

[s5s 6]

[s6s 7]

[s6s 7]

[s4s 4]

[s2s 3]

[s2s 3]

[s4s 4]

[s2s 4]

[s4s 4]

[s2s 3]

[s4s 6]

[s5s 7]

[s3s 4]

[s6s 6]

[s6s 7]

[s5s 6]

[s4s 6]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 7]

[s1s 2]

[s4s 6]

[s1s 3]

[s2s 2]

[s6s 7]

[s4s 6]

[s1s 3]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s6s 7]

[s5s 6]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 6]

[s3s 4]

[s3s 3]

[s4s 4]

[s2s 3]

[s4s 4]

[s3s 4]

[s6s 7]

[s5s 7]

[s6s 6]

[s5s 7]

[s2s 3]

[s6s 6]

[s5s 7]

[s4s 4]

[s4s 4]

[s4s 6]

[s4s 6]

[s2s 3]

[s3s 4]

[s1s 2]

[s3s 4]

[s5s 6]

[s4s 6]

[s4s 4]

[s4s 4]

[s4s 4]

[s4s 6]

[s2s 3]

[s5s 6]

[s1s 2]

[s4s 6]

[s2s 2]

[s6s 7]

[s4s 6]

[s3s 5]

[s4s 4]

R 2

[s4s 4]

[s5s 6]

[s5s 6]

[s5s 5]

[s0s 1]

[s4s 5]

[s3s 5]

[s3s 3]

[s3s 5]

[s3s 3]

[s3s 3]

[s4s 4]

[s5s 6]

[s4s 4]

[s2s 4]

[s6s 6]

[s1s 2]

[s7s 8]

[s5s 7]

[s3s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s2s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s1s 2]

[s5s 6]

[s4s 5]

[s4s 6]

[s4s 5]

[s7s 8]

[s4s 4]

[s3s 5]

[s5s 6]

[s1s 2]

[s5s 5]

[s2s 4]

[s1s 2]

[s3s 5]

[s3s 5]

[s4s 6]

[s5s 5]

[s4s 4]

[s5s 6]

[s4s 4]

[s4s 5]

[s5s 6]

[s0s 1]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s4s 4]

[s4s 4]

[s5s 6]

[s0s 1]

[s4s 4]

[s7s 8]

[s1s 2]

[s4s 5]

[s4s 5]

[s4s 6]

[s0s 1]

[s2s 4]

[s4s 4]

[s5s 6]

[s5s 6]

[s4s 5]

[s5s 6]

[s1s 2]

[s4s 4]

[s1s 2]

[s3s 4]

[s4s 5]

[s6s 7]

[s4s 4]

[s3s 5]

[s0s 1]

[s7s 8]

[s7s 8]

[s4s 5]

[s3s 5]

[s5s 6]

[s0s 1]

[s3s 5]

[s7s 8]

[s4s 4]

[s5s 6]

[s5s 6]

[s0s 1]

[s3s 5]

[s0s 1]

[s0s 1]

[s3s 5]

[s4s 5]

[s2s 4]

[s1s 2]

[s4s 4]

R 3

[x3x3]

[x4x

5][x1x2]

[x4x5]

[x1x2]

[x3x4]

[x0x1]

[x1x2]

[x2x4]

[x2x4]

[x4x5]

[x3x3]

[x3x3]

[x1x2]

[x4x5]

[x0x1]

[x0x1]

[x0x1]

[x4x5]

[x1x2]

[x4x5]

[x2x4]

[x3x3]

[x3x4]

[x0x1]

[x3x4]

[x4x5]

[x1x2]

[x1x2]

[x3x3]

[x2x4]

[x3x4]

[x1x2]

[x3x3]

[x2x4]

[x0x1]

[x2x4]

[x1x3]

[x1x2]

[x2x4]

[x3x3]

[x0x1]

[x2x4]

[x1x3]

[x3x3]

[x4x5]

[x4x5]

[x1x2]

[x2x4]

[x1x3]

[x4x5]

[x3x4]

[x2x3]

[x2x4]

[x1x3]

[x3x3]

[x5x5]

[x2x4]

[x2x4]

[x2x4]

[x4x5]

[x2x4]

[x2x4]

[x2x4]

[x2x3]

[x3x4]

[x3x3]

[x3x4]

[x4x5]

[x3x4]

[x2x4]

[x4x5]

[x4x5]

[x4x5]

[x2x4]

[x3x4]

[x0x1]

[x3x3]

[x3x4]

[x0x1]

[x0x1]

[x3x3]

[x2x4]

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x4x5]

[x3x3]

[x1x2]

[x2x4]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x0x1]

[x2x4]

[x2x4]

[x1x2]

[x3x3]

Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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Mathematical Problems in Engineering 17

Table22C

ontin

ued

Expert

Theo

pinion

ofexperts

R 4

[x3x3]

[x1x2]

[x4x5]

[x2x4]

[x3x5]

[x2x3]

[x3x3]

[x3x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x2x4]

[x3x3]

[x3x3]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x4]

[x4x5]

[x4x5]

[x5x5]

[x3x4]

[x3x3]

[x3x4]

[x3x3]

[x2x3]

[x3x4]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x4x5]

[x2x3]

[x3x3]

[x3x3]

[x2x3]

[x2x3]

[x4x5]

[x3x4]

[x4x5]

[x2x4]

[x2x3]

[x2x3]

[x2x3]

[x3x3]

[x3x3]

[x3x3]

[x3x4]

[x2x3]

[x2x4]

[x3x3]

[x4x5]

[x2x3]

[x3x4]

[x2x3]

[x3x3]

[x5x5]

[x4x5]

[x3x5]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x2x3]

[x2x3]

[x3x5]

[x3x3]

[x2x4]

[x3x3]

[x2x3]

[x2x4]

[x5x5]

[x4x5]

[x2x3]

[x5x5]

[x4x5]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x3]

[x3x3]

[x2x4]

[x3x5]

[x3x3]

[x3x3]

[x3x3]

[x2x3]

[x3x3]

R 5

[y2y 2

][y2y 4

][y2y 3

][y2y 3

][y2y 3

][y0y 2

][y0y 1

][y2y 3

][y1y 3

][y2y 4

][y1y 1

][y2y 2

][y0y 1

][y2y 4

][y3y 4

][y1y 3

][y0y 2

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y0y 2

][y2y 3

][y4y 4

][y2y 4

][y2y 3

][y2y 4

][y0y 1

][y2y 4

][y2y 4

][y3y 4

][y2y 2

][y0y 1

][y2y 3

][y2y 3

][y0y 1

][y3y 4

][y2y 3

][y1y 3

][y2y 3

][y1y 3

][y1y 3

][y2y 2

][y3y 4

][y4y 4

][y2y 3

][y1y 3

][y2y 4

][y2y 4

][y2y 4

][y0y 2

][y0y 2

][y2y 3

][y2y 2

][y2y 3

][y0y 1

][y2y 4

][y2y 3

][y0y 2

][y2y 4

][y2y 4

][y2y 4

][y1y 3

][y0y 2

][y2y 2

][y0y 2

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y2y 3

][y2y 3

][y1y 3

][y2y 2

][y4y 4

][y0y 1

][y2y 3

][y1y 3

][y3y 4

][y2y 4

][y2y 4

][y2y 3

][y1y 3

][y0y 2

][y2y 2

][y1y 3

][y3y 4

][y2y 3

][y0y 2

][y3y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 4

][y2y 3

][y2y 2

]

18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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18 Mathematical Problems in Engineering

VIKOR method proves that there is no obvious differencebetween these innovative schemes However the optimalsolution is always scheme 1198785 From our results we can seethat the VIKOR method has a low degree of discriminationand because the TOPSISmethod relies solely on the data itselfand is prone to reverse the phenomenon so it is appropriateto evaluate the innovation schemes with the prospect theoryThe prospect theory takes full account of decision-makersrsquopsychological factors and behavioral science It weighs bothgains and losses making the evaluation more comprehensiveand objective The decision result is closer to the actualsituation and can better guide the production activities ofenterprises

6 Conclusion

Customer requirement is the initial information source andbasis for product collaborative design and is key to the successof CCPI Based on the fuzzy characteristics as well as thedynamicity diversity and individuation of CRs a Kanomodelwas constructed to identify and filter the initial requirementsof customers in this paper secondly the weights of CRswere determined by the proposed interval 2-tuple linguisticrepresentationmodel finally a comprehensive evaluation forthe innovation schemes was given based on the prospecttheory In this process some practical results have beenobtained(1)TheKanomodel focuses on the analysis of factors thataffect customer satisfaction Through this model we are ableto capture the product attributes which can greatly improvecustomer satisfaction(2) Interval 2-tuple linguistic representation model ismore accurate when expressing the vague language ofcustomers and experts In addition it is a great advantage to

accurately convert the decision-makersrsquo linguistic informa-tion due to little information loss(3) This paper introduces the prospect theory into theprocess of CCPI from the perspective of product designoptions and considers the subjective attitude of decision-makers fully The scheme chosen based on the prospecttheory is more scientific and makes the actual process ofdecision-making more efficient

Appendix

A Customer Requirements Based onKano Model

A1 Initial Customer Requirements See Table 19

A2 Kano Category for Initial Customer Requirements SeeTable 20

A3 Reserved Customer Requirements See Table 21

B Determination of the Weight of CustomerRequirements Based on Interval 2-TupleLinguistic Representation Model

B1 Expert Language Complementary Judgment Matrix SeeTable 22

B2 Interval 2-Tuple Linguistic Judgment Matrix

1198771 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)][(1199043 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199042 0) (1199044 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)][(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199046 0) (1199047 0)][(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199047 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)][(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199041 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199046 0) (1199047 0)] [(1199045 0) (1199046 0)][(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199044 0)] [(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199044 0)][(1199046 0) (1199047 0)] [(1199045 0) (1199047 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199042 0) (1199043 0)] [(1199046 0) (1199046 0)] [(1199045 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199046 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199043 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)][(1199044 0) (1199046 0)] [(1199042 0) (1199043 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199046 0)] [(1199042 0) (1199042 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199046 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

1198772 =

[[[[[[[[[[[[[[[[[[[[[[[[[[

[(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)] [(1199043 0) (1199045 0)] [(1199043 0) (1199043 0)][(1199043 0) (1199043 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199046 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199047 0) (1199048 0)] [(1199045 0) (1199047 0)] [(1199043 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199044 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199045 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)][(1199043 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199045 0) (1199045 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)][(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199044 0) (1199044 0)] [(1199047 0) (1199048 0)][(1199041 0) (1199042 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199044 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199042 0) (1199044 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)] [(1199045 0) (1199046 0)] [(1199044 0) (1199045 0)][(1199045 0) (1199046 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199043 0) (1199044 0)] [(1199044 0) (1199045 0)] [(1199046 0) (1199047 0)] [(1199044 0) (1199044 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)][(1199047 0) (1199048 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199045 0)] [(1199043 0) (1199045 0)] [(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199047 0) (1199048 0)] [(1199044 0) (1199044 0)] [(1199045 0) (1199046 0)][(1199045 0) (1199046 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199040 0) (1199041 0)] [(1199040 0) (1199041 0)] [(1199043 0) (1199045 0)] [(1199044 0) (1199045 0)] [(1199042 0) (1199044 0)] [(1199041 0) (1199042 0)] [(1199044 0) (1199044 0)]

]]]]]]]]]]]]]]]]]]]]]]]]]]

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

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Page 19: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 19

1198773

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199090 0) (1199091 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)][(1199093 0) (1199093 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199091 0) (1199092 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)][(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199090 0) (1199091 0)][(1199090 0) (1199091 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)][(1199092 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199090 0) (1199091 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199091 0) (1199092 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198774

=

[[[[[[[[[[[[[[[[[[[[

[(1199093 0) (1199093 0)] [(1199091 0) (1199092 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)][(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199094 0) (1199095 0)][(1199094 0) (1199095 0)] [(1199095 0) (1199095 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199094 0)][(1199094 0) (1199095 0)] [(1199092 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)][(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199094 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199093 0) (1199095 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199093 0)][(1199092 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199095 0) (1199095 0)] [(1199094 0) (1199095 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)][(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199094 0)] [(1199093 0) (1199095 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199093 0) (1199093 0)] [(1199092 0) (1199093 0)] [(1199093 0) (1199093 0)]

]]]]]]]]]]]]]]]]]]]]

1198775

=

[[[[[[[[[[[[[[[[[[[[

[(1199102 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199100 0) (1199101 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199104 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199100 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199101 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)][(1199100 0) (1199102 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199100 0) (1199102 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)][(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199102 0) (1199102 0)] [(1199104 0) (1199104 0)] [(1199100 0) (1199101 0)][(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199101 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199102 0) (1199102 0)] [(1199101 0) (1199103 0)][(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199100 0) (1199102 0)] [(1199103 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199104 0)] [(1199102 0) (1199103 0)] [(1199102 0) (1199102 0)]

]]]]]]]]]]]]]]]]]]]](B1)

B3 Interval Matrix

11987711015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 0750] [0750 0875] [0375 0625] [0500 0500] [0500 0500] [0500 0500] [0250 0375] [0125 0250] [0500 0750][0375 0500] [0500 0500] [0500 0500] [0250 0375] [0750 0875] [0500 0500] [0625 0750] [0250 0500] [0375 0500] [0500 0750][0500 0500] [0625 0750] [0500 0500] [0750 0875] [0750 0875] [0625 0750] [0750 0875] [0750 0875] [0500 0500] [0250 0375][0250 0375] [0500 0500] [0250 0500] [0500 0500] [0250 0375] [0500 0750] [0625 0875] [0375 0500] [0750 0750] [0750 0875][0625 0750] [0500 0750] [0500 0500] [0625 0750] [0500 0500] [0500 0500] [0625 0875] [0125 0250] [0500 0750] [0125 0375][0250 0250] [0750 0875] [0500 0750] [0125 0375] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0750 0875] [0625 0750][0750 0750] [0625 0875] [0500 0500] [0500 0750] [0375 0500] [0375 0375] [0500 0500] [0250 0375] [0500 0500] [0375 0500][0750 0875] [0625 0875] [0750 0750] [0625 0875] [0250 0375] [0750 0750] [0625 0875] [0500 0500] [0500 0500] [0500 0750][0500 0750] [0250 0375] [0375 0500] [0125 0250] [0375 0500] [0625 0750] [0500 0750] [0500 0500] [0500 0500] [0500 0500][0500 0750] [0250 0375] [0625 0750] [0125 0250] [0500 0750] [0250 0250] [0750 0875] [0500 0750] [0375 0625] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

11987721015840

=

[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0625 0750] [0625 0750] [0625 0625] [0000 0125] [0500 0625] [0375 0625] [0375 0375] [0375 0625] [0375 0375][0375 0375] [0500 0500] [0625 0750] [0500 0500] [0250 0500] [0750 0750] [0125 0250] [0875 1000] [0625 0875] [0375 0625][0625 0750] [0125 0250] [0500 0500] [0250 0500] [0500 0500] [0625 0750] [0000 0125] [0125 0250] [0625 0750] [0500 0625][0500 0750] [0500 0625] [0875 1000] [0500 0500] [0375 0625] [0625 0750] [0125 0250] [0625 0625] [0250 0500] [0125 0250][0375 0625] [0375 0625] [0500 0750] [0625 0625] [0500 0500] [0625 0750] [0500 0500] [0500 0625] [0625 0750] [0000 0125][0625 0750] [0625 0750] [0500 0625] [0625 0750] [0500 0500] [0500 0500] [0625 0750] [0000 0125] [0500 0500] [0875 1000][0125 0250] [0500 0625] [0500 0625] [0500 0750] [0000 0125] [0250 0500] [0500 0500] [0625 0750] [0625 0750] [0500 0625][0625 0750] [0125 0250] [0500 0500] [0125 0250] [0375 0500] [0500 0625] [0750 0875] [0500 0500] [0375 0625] [0000 0125][0875 1000] [0875 1000] [0500 0625] [0375 0625] [0625 0750] [0000 0125] [0375 0625] [0875 1000] [0500 0500] [0625 0750][0625 0750] [0000 0125] [0375 0625] [0000 0125] [0000 0125] [0375 0625] [0500 0625] [0250 0500] [0125 0250] [0500 0500]

]]]]]]]]]]]]]]]]]]]]

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 20: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

20 Mathematical Problems in Engineering

11987731015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0667 0833] [0167 0333] [0667 0833] [0167 0333] [0500 0667] [0000 0167] [0167 0333] [0333 0667] [0333 0667][0667 0833] [0500 0500] [0500 0500] [0167 0333] [0667 0833] [0000 0167] [0000 0167] [0000 0167] [0667 0833] [0167 0333][0667 0833] [0333 0667] [0500 0500] [0500 0667] [0000 0167] [0500 0667] [0667 0833] [0167 0333] [0167 0333] [0500 0500][0333 0667] [0500 0667] [0167 0333] [0500 0500] [0333 0667] [0000 0167] [0333 0667] [0167 0500] [0167 0333] [0333 0667][0500 0500] [0000 0167] [0333 0667] [0167 0500] [0500 0500] [0667 0833] [0667 0833] [0167 0333] [0333 0667] [0167 0500][0667 0833] [0500 0667] [0333 0500] [0333 0667] [0167 0500] [0500 0500] [0833 0833] [0333 0667] [0333 0667] [0333 0667][0667 0833] [0333 0667] [0333 0667] [0333 0667] [0333 0500] [0500 0667] [0500 0500] [0500 0667] [0667 0833] [0500 0667][0333 0667] [0667 0833] [0667 0833] [0667 0833] [0333 0667] [0500 0667] [0000 0167] [0500 0500] [0500 0667] [0000 0167][0000 0167] [0500 0500] [0333 0667] [0500 0500] [0167 0333] [0667 0833] [0333 0667] [0667 0833] [0500 0500] [0167 0333][0333 0667] [0667 0833] [0500 0667] [0667 0833] [0333 0667] [0000 0167] [0333 0667] [0333 0667] [0167 0333] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987741015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0167 0333] [0667 0833] [0333 0667] [0500 0833] [0333 0500] [0500 0500] [0500 0833] [0667 0833] [0833 0833][0500 0667] [0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0667] [0333 0500] [0333 0500] [0333 0500][0333 0667] [0500 0500] [0500 0500] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0667] [0667 0833][0667 0833] [0833 0833] [0500 0667] [0500 0500] [0500 0667] [0500 0500] [0333 0500] [0500 0667] [0333 0667] [0333 0500][0333 0500] [0333 0500] [0667 0833] [0333 0500] [0500 0500] [0500 0500] [0333 0500] [0333 0500] [0667 0833] [0500 0667][0667 0833] [0333 0667] [0333 0500] [0333 0500] [0333 0500] [0500 0500] [0500 0500] [0500 0500] [0500 0667] [0333 0500][0333 0667] [0500 0500] [0667 0833] [0333 0500] [0500 0667] [0333 0500] [0500 0500] [0833 0833] [0667 0833] [0500 0833][0500 0500] [0333 0500] [0500 0500] [0333 0500] [0333 0500] [0333 0500] [0500 0833] [0500 0500] [0333 0667] [0500 0500][0333 0500] [0333 0667] [0833 0833] [0667 0833] [0333 0500] [0833 0833] [0667 0833] [0333 0500] [0500 0500] [0333 0500][0500 0500] [0333 0500] [0500 0500] [0333 0667] [0500 0833] [0500 0500] [0500 0500] [0500 0500] [0333 0500] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]]

11987751015840

=

[[[[[[[[[[[[[[[[[[[[[[[

[0500 0500] [0500 1000] [0500 0750] [0500 0750] [0500 0750] [0000 0500] [0000 0250] [0500 0750] [0250 0750] [0500 1000][0250 0250] [0500 0500] [0000 0250] [0500 1000] [0750 1000] [0250 0750] [0000 0500] [0250 0750] [0500 0750] [0500 0750][0250 0750] [0250 0750] [0500 0500] [0000 0500] [0500 0750] [1000 1000] [0500 1000] [0500 0750] [0500 1000] [0000 0250][0500 1000] [0500 1000] [0750 1000] [0500 0500] [0000 0250] [0500 0750] [0500 0750] [0000 0250] [0750 1000] [0500 0750][0250 0750] [0500 0750] [0250 0750] [0250 0750] [0500 0500] [0750 1000] [1000 1000] [0500 0750] [0250 0750] [0500 1000][0500 1000] [0500 1000] [0000 0500] [0000 0500] [0500 0750] [0500 0500] [0500 0750] [0000 0250] [0500 1000] [0500 0750][0000 0500] [0500 1000] [0500 1000] [0500 1000] [0250 0750] [0000 0500] [0500 0500] [0000 0500] [0250 0750] [0750 1000][0500 1000] [0500 1000] [0500 0750] [0250 0750] [0500 0750] [0500 0750] [0250 0750] [0500 0500] [1000 1000] [0000 0250][0500 0750] [0250 0750] [0750 1000] [0500 1000] [0500 1000] [0500 0750] [0250 0750] [0000 0500] [0500 0500] [0250 0750][0750 1000] [0500 0750] [0000 0500] [0750 1000] [0500 0750] [0500 1000] [0500 0750] [0500 1000] [0500 0750] [0500 0500]

]]]]]]]]]]]]]]]]]]]]]]](B2)

B4 Interval 2-Tuple Linguistic ComprehensiveEvaluation Matrix

=

[[[[[[[[[[[[[[[[[[[[[[[

(0500 0500) (0498 0708) (0561 0714) (0500 0688) (0308 0464) (0417 0565) (0319 0440) (0340 0496) (0350 0594) (0502 0681)(0500 0544) (0500 0500) (0448 0538) (0371 0485) (0525 0710) (0404 0521) (0254 0469) (0373 0583) (0500 0685) (0369 0585)(0500 0688) (0379 0558) (0500 0500) (0483 0694) (0429 0552) (0679 0775) (0504 0683) (0369 0523) (0465 0613) (0421 0542)(0500 0681) (0567 0681) (0490 0675) (0500 0500) (0323 0542) (0431 0583) (0371 0590) (0383 0540) (0425 0613) (0402 0590)(0500 0619) (0335 0552) (0475 0688) (0438 0619) (0500 0500) (0590 0679) (0581 0710) (0306 0460) (0506 0750) (0215 0458)(0500 0683) (0560 0773) (0383 0594) (0321 0565) (0431 0588) (0500 0500) (0598 0654) (0323 0477) (0529 0711) (0558 0746)(0500 0600) (0498 0708) (0500 0681) (0433 0708) (0285 0465) (0323 0502) (0500 0500) (0485 0631) (0573 0721) (0494 0681)(0500 0740) (0436 0648) (0596 0654) (0413 0623) (0339 0527) (0529 0652) (0469 0713) (0500 0500) (0485 0648) (0225 0377)(0500 0646) (0473 0652) (0527 0681) (0408 0585) (0400 0579) (0506 0627) (0444 0719) (0544 0692) (0500 0500) (0406 0554)(0500 0708) (0313 0467) (0450 0627) (0307 0494) (0342 0594) (0306 0452) (0529 0683) (0404 0646) (0275 0460) (0500 0500)

]]]]]]]]]]]]]]]]]]]]]]]

(B3)

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 21: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 21

B5 Weight Dependence and Possibility Matrix and CustomerDemand Weights Based on Interval 2-Tuple Linguistic ofImportance Evaluation Value 120579

119894

120579119894= [(0430 0554) (0419 0535) (0474 0600) (0427 0559) (0439 0582) (0474 0592) (0451 0584) (0455 0584) (0467 0590) (0395 0520)]

119875 =

[[[[[[[[[[[[[[[[[[[[[[[

0500 0563 0320 0496 0431 0331 0401 0414 0352 06390438 0500 0252 0436 0371 0261 0337 0353 0285 05810680 0748 0500 0671 0599 0516 0575 0585 0534 08170504 0565 0330 0500 0436 0340 0408 0421 0361 06380569 0629 0402 0564 0500 0414 0475 0486 0432 06980669 0739 0484 0660 0586 0500 0562 0572 0519 08110599 0663 0425 0593 0525 0438 0500 0511 0457 07330586 0647 0415 0579 0514 0428 0489 0500 0447 07160648 0716 0466 0639 0568 0481 0543 0553 0500 07860361 0419 0183 0362 0302 0189 0267 0284 0214 0500

]]]]]]]]]]]]]]]]]]]]]]]

120593 = (0094 0087 0114 0095 0102 0112 0105 0104 0110 0079)

(B4)

Data Availability

All relevant data are within the paper

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The study was supported by ldquoResearch Fund from KeyLaboratory of Computer Integrated Manufacturing inGuangdong Provincerdquo (CIMSOF2016002) ldquoState KeyLaboratory for Manufacturing Systems Engineering (XirsquoanJiaotong University)rdquo (sklms2017005) ldquoCentral UniversityScience Research Foundation of Chinardquo (JB170609)ldquoChina Postdoctoral Science Foundation Funded Projectrdquo(2016M590929) and ldquoShaanxi Natural Science FoundationProjectrdquo (2017JM7004)

References

[1] P Liu andPWang ldquoSomeq-RungOrthopair FuzzyAggregationOperators and their Applications to Multiple-Attribute Deci-sion Makingrdquo International Journal of Intelligent Systems vol33 no 2 pp 259ndash280 2018

[2] N Franke and E Von Hippel ldquoSatisfying heterogeneous userneeds via innovation toolkits the case of Apache securitysoftwarerdquo Research Policy vol 32 no 7 pp 1199ndash1215 2003

[3] G L Lilien P D Morrison K Searls M Sonnack and EVon Hippel ldquoPerformance assessment of the lead user idea-generation process for newproduct developmentrdquoManagementScience vol 48 no 8 pp 1042ndash1059 2002

[4] W Song XMing Y Han and ZWu ldquoA rough set approach forevaluating vague customer requirement of industrial product-service systemrdquo International Journal of Production Researchvol 51 no 22 pp 6681ndash6701 2013

[5] D W Dahl C Fuchs and M Schreier ldquoWhy and whenconsumers prefer products of user-driven firms A socialidentification accountrdquo Management Science vol 61 no 8 pp1978ndash1988 2015

[6] X Chen C-H Chen K F Leong and X Jiang ldquoAn ontologylearning system for customer needs representation in productdevelopmentrdquoThe International Journal of Advanced Manufac-turing Technology vol 67 no 1-4 pp 441ndash453 2013

[7] Y Wang and M M Tseng ldquoIntegrating comprehensive cus-tomer requirements into product designrdquo CIRP Annals - Man-ufacturing Technology vol 60 no 1 pp 175ndash178 2011

[8] Y Wang andM Tseng ldquoIncorporating tolerances of customersrsquorequirements for customized productsrdquo CIRP Annals - Manu-facturing Technology vol 63 no 1 pp 129ndash132 2014

[9] Z L Liu Z Zhang andYChen ldquoA scenario-based approach forrequirements management in engineering designrdquo ConcurrentEngineering Research Applications vol 20 no 2 pp 99ndash1092012

[10] M G Violante E Vezzetti and M Alemanni ldquoAn integratedapproach to support the Requirement Management (RM)tool customization for a collaborative scenariordquo InternationalJournal on Interactive Design and Manufacturing vol 11 no 2pp 191ndash204 2017

[11] Z Sheng Y Wang J Song and H Xie ldquoCustomer require-ment modeling and mapping of numerical control machinerdquoAdvances inMechanical Engineering vol 7 no 10 pp 1ndash11 2015

[12] M Carulli M Bordegoni and U Cugini ldquoAn approach for cap-turing the Voice of the Customer based onVirtual PrototypingrdquoJournal of Intelligent Manufacturing vol 24 no 5 pp 887ndash9032013

[13] C K Kwong and H Bai ldquoA fuzzy AHP approach to thedetermination of importanceweights of customer requirements

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 22: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

22 Mathematical Problems in Engineering

in quality function deploymentrdquo Journal of Intelligent Manufac-turing vol 13 no 5 pp 367ndash377 2002

[14] H M Khalid and M G Helander ldquoA framework for affec-tive customer needs in product designrdquo Theoretical Issues inErgonomics Science vol 5 no 1 pp 27ndash42 2004

[15] Y-L Li K-S Chin and X-G Luo ldquoDetermining the finalpriority ratings of customer requirements in product planningby MDBM and BSCrdquo Expert Systems with Applications vol 39no 1 pp 1243ndash1255 2012

[16] Y Wang and M M Tseng ldquoA Naıve Bayes approach tomap customer requirements to product variantsrdquo Journal ofIntelligent Manufacturing vol 26 no 3 pp 501ndash509 2015

[17] C C Aguwa L Monplaisir and O Turgut ldquoVoice of thecustomer Customer satisfaction ratio based analysisrdquo ExpertSystems with Applications vol 39 no 11 pp 10112ndash10119 2012

[18] P Liu J Liu and J M Merigo ldquoPartitioned Heronian meansbased on linguistic intuitionistic fuzzy numbers for dealingwithmulti-attribute group decision makingrdquo Applied Soft Comput-ing vol 62 pp 395ndash422 2018

[19] Y-E Nahm H Ishikawa and M Inoue ldquoNew rating methodsto prioritize customer requirements in QFD with incompletecustomer preferencesrdquo The International Journal of AdvancedManufacturing Technology vol 65 no 9ndash12 pp 1587ndash16042013

[20] H-H Wu A Y H Liao and P-C Wang ldquoUsing grey theoryin quality function deployment to analyse dynamic customerrequirementsrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 11-12 pp 1241ndash1247 2005

[21] X Liu W J Zhang Y L Tu and R Jiang ldquoAn analyti-cal approach to customer requirement satisfaction in designspecification developmentrdquo IEEE Transactions on EngineeringManagement vol 55 no 1 pp 94ndash102 2008

[22] S Takai and K Ishii ldquoA use of subjective clustering to supportaffinity diagram results in customer needs analysisrdquo ConcurrentEngineering Research and Applications vol 18 no 2 pp 101ndash1092010

[23] P Liu J Liu and S-M Chen ldquoSome intuitionistic fuzzy DombiBonferroni mean operators and their application to multi-attribute group decision makingrdquo Journal of the OperationalResearch Society 2017

[24] P Liu and S-MChen ldquoGroupDecisionMakingBased onHero-nian Aggregation Operators of Intuitionistic Fuzzy NumbersrdquoIEEE Transactions on Cybernetics 2016

[25] Y Dong G Zhang W-C Hong and S Yu ldquoLinguisticcomputational model based on 2-tuples and intervalsrdquo IEEETransactions on Fuzzy Systems vol 21 no 6 pp 1006ndash1018 2013

[26] F Herrera and LMartınez ldquoA 2-tuple fuzzy linguistic represen-tation model for computing with wordsrdquo IEEE Transactions onFuzzy Systems vol 8 no 6 pp 746ndash752 2000

[27] F Herrera and L Martınez ldquoA model based on linguistic 2-tuples for dealing with multigranular hierarchical linguisticcontexts in multi-expert decision-makingrdquo IEEE Transactionson Systems Man and Cybernetics Part B Cybernetics vol 31no 2 pp 227ndash234 2001

[28] C-C Li Y Dong F Herrera E Herrera-Viedma and LMartınez ldquoPersonalized individual semantics in computingwithwords for supporting linguistic group decisionmaking Anapplication on consensus reachingrdquo Information Fusion vol 33pp 29ndash40 2017

[29] C Li R M Rodrıguez L Martınez Y Dong and F HerreraldquoPersonalized individual semantics based on consistency in

hesitant linguistic group decision making with comparativelinguistic expressionsrdquo Knowledge-Based Systems vol 145 pp156ndash165 2018

[30] Y Dong C-C Li and F Herrera ldquoConnecting the linguistichierarchy and the numerical scale for the 2-tuple linguisticmodel and its use to deal with hesitant unbalanced linguisticinformationrdquo Information Sciences vol 367-368 pp 259ndash2782016

[31] X Chen H Zhang and Y Dong ldquoThe fusion process withheterogeneous preference structures in group decision makinga surveyrdquo Information Fusion vol 24 pp 72ndash83 2015

[32] Y Dong H Zhang and E Herrera-Viedma ldquoConsensus reach-ing model in the complex and dynamic MAGDM problemrdquoKnowledge-Based Systems vol 106 pp 206ndash219 2016

[33] P D Liu ldquoMultiple attribute group decision making methodbased on interval-valued intuitionistic fuzzy power heronianaggregation operatorsrdquo Computers amp Industrial Engineeringvol 108 pp 199ndash212 2017

[34] P Liu and H Li ldquoInterval-Valued Intuitionistic Fuzzy PowerBonferroni Aggregation Operators and Their Application toGroupDecisionMakingrdquoCognitive Computation pp 1ndash19 2017

[35] R Lahdelma and P Salminen ldquoSMAA-2 stochastic multicrite-ria acceptability analysis for groupdecisionmakingrdquoOperationsResearch vol 49 no 3 pp 444ndash454 2001

[36] P Liu S-M Chen and J Liu ldquoMultiple attribute group decisionmaking based on intuitionistic fuzzy interaction partitionedBonferroni mean operatorsrdquo Information Sciences vol 411 pp98ndash121 2017

[37] M Grabisch C Labreuche and J-C Vansnick ldquoOn theextension of pseudo-Boolean functions for the aggregation ofinteracting criteriardquo European Journal of Operational Researchvol 148 no 1 pp 28ndash47 2003

[38] M Grabisch S Greco and M Pirlot ldquoBipolar and bivari-ate models in multicriteria decision analysis Descriptive andconstructive approachesrdquo International Journal of IntelligentSystems vol 23 no 9 pp 930ndash969 2008

[39] A M M Sharif Ullah and J Tamaki ldquoAnalysis of Kano-model-based customer needs for product developmentrdquo Systems Engi-neering vol 14 no 2 pp 154ndash172 2011

[40] P Ji J Jin T Wang and Y Chen ldquoQuantification and integra-tion of Kanorsquos model into QFD for optimising product designrdquoInternational Journal of Production Research vol 52 no 21 pp6335ndash6348 2014

[41] J Lin J-B Lan and Y-H Lin ldquoA method of multi-attributegroup decision-making based on the aggregation operatorsfor interval two-tuple linguistic informationrdquo Jilin NormalUniversity Journal(Natural Science Edition) vol 1 pp 5ndash9 2009

[42] Y CDong Y F XuH Y Li andB Feng ldquoTheOWA-based con-sensus operator under linguistic representation models usingposition indexesrdquo European Journal of Operational Researchvol 203 no 2 pp 455ndash463 2010

[43] GWei ldquoAmethod formultiple attribute group decisionmakingbased on the ET-WG and ET-OWG operators with 2-tuplelinguistic informationrdquoExpert SystemswithApplications vol 37no 12 pp 7895ndash7900 2010

[44] H Zhang ldquoThe multiattribute group decision making methodbased on aggregation operators with interval-valued 2-tuplelinguistic informationrdquoMathematical and Computer Modellingvol 56 no 1-2 pp 27ndash35 2012

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 23: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Mathematical Problems in Engineering 23

[45] H Zhang ldquoSome interval-valued 2-tuple linguistic aggregationoperators and application inmultiattribute groupdecisionmak-ingrdquo Applied Mathematical Modelling Simulation and Compu-tation for Engineering and Environmental Systems vol 37 no 6pp 4269ndash4282 2013

[46] S R Gangurde and M M Akarte ldquoCustomer preference ori-ented product design using AHP-modified TOPSIS approachrdquoBenchmarking vol 20 no 4 pp 549ndash564 2013

[47] P Liu and S-M Chen ldquoMultiattribute group decision makingbased on intuitionistic 2-tuple linguistic informationrdquo Informa-tion Sciences vol 430431 pp 599ndash619 2018

[48] J D Qin X W Liu and W Pedrycz ldquoAn extended VIKORmethod based on prospect theory formultiple attribute decisionmaking under interval type-2 fuzzy environmentrdquo Knowledge-Based Systems vol 86 pp 116ndash130 2015

[49] Y M Wang Y Luo and Z Hua ldquoOn the extent analysismethod for fuzzy AHP and its applicationsrdquo European Journalof Operational Research vol 186 no 2 pp 735ndash747 2008

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 24: A Novel Approach Based on Kano Model, Interval 2-Tuple ...downloads.hindawi.com/journals/mpe/2018/8192819.pdf · A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom