A Group Decision-Making Approach Based on DST and AHP for … · 2019. 7. 30. · ResearchArticle A...

Research ArticleA Group Decision-Making Approach Based on DST and AHP forNew Product Selection under Epistemic Uncertainty

ChongWu 1 Zijiao Zhang 2 andWei Zhong2

1School of Management Harbin Institute of Technology Harbin 150000 China2School of Economics and Management Chuzhou University Chuzhou 239000 China

Correspondence should be addressed to Zijiao Zhang zzijiaojiayou163com

Received 2 March 2019 Revised 27 April 2019 Accepted 2 June 2019 Published 19 June 2019

Guest Editor Love Ekenberg

Copyright copy 2019 Chong Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Selecting the most appropriate new product(s) is regarded as a critical decision which greatly influences the development ofmanufacturing enterprises In order to improve the accuracy of selection more experts are required to be invited to predict keyindicators for new products selection Due to limited knowledge experts use fuzzy numbersmore confidently than using numericalvalues in the prediction Therefore new product selection is a multiattribute group decision-making process under epistemicuncertaintyThe purpose of this paper is to introduce a new hybrid decision-making approach based on Analytic Hierarchy Process(AHP) and Dempster-Shafer Theory (DST) to evaluate and select a new product AHP and DST are used in weight determinationto improve the accuracy and objectivity In addition this paper proposes that DST is a proper mathematical framework to deal withthe epistemic uncertainty on the indicators of new product scheme selection In particular the initial assessments from experts aredisassembled and then combined into the evidence information By setting confidence degree reliability function and likelihoodfunction are used to evaluate and rank new products A case study in a home appliance manufacturer is provided to illustrate theproposed hybrid approach and demonstrate its applicability

1 Introduction

As the market is increasingly competitive it is more impor-tant for enterprises to choose an appropriate new productGood new products can bring hope to dying enterprises Onthe contrary bad schemes make prosperous enterprises failThere are eight phases typically in new product development(NPD) namely idea generation idea screening conceptdevelopment and testing marketing strategy developmentbusiness analysis product development market testing andcommercialization Idea screening also known as new prod-uct selection is choosing the best one from a numberof schemes which is the most important task for NPDTherefore the research on new product selection is of vitalsignificance

It is difficult to choose an optimal scheme from manydesignsThemain reasons are as follows First of all there aremany factors to be considered while making decision suchas product performance market potential project risk andcustomer demand Secondly because decision making is for

the future the impact factors are full of uncertainty That iswhy accurate number is difficult to use to represent factorsLast but not least these factors are estimated by experts onthe basis of their past experience and personal preferenceswhich leads to different evaluations by different experts Ifonly one expert is invited for evaluation the results wouldbe influenced by his own experience and preferences If morethan one expert is invited different estimations would beobtained How to deal with these differences is an importantproblem to be solved Therefore new product selection is aproblem worthy for studying

Based on the first point it is very necessary to selectseveral indicators to help the researchers make decisionsTherefore the study is a multiple criteria decision-making(MCDM) process Based on the second point fuzzy numberis advised to express indicators which are difficult to expressby accurate number And a fuzzy set should be used in thestudy of new product selection In order to eliminate theimpact of individual preferences and experience a numberof experts would be invited to estimate indicators Thus a

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 4635374 16 pageshttpsdoiorg10115520194635374

2 Mathematical Problems in Engineering

conclusion can be drawn that it is a group decision-makingproblem That is to say new product selection is a fuzzymultiattribute group decision-making model

There are three key problems to deal with in this issueThe first one is how to judge the relationship betweenthose indicators That is to say which indicators are moreimportant and which can be slightly sacrificed Thereforeweight determination is the first key point in the model Thesecond question is how to calculate and judge the attributesexpressed by fuzzy numbers so as to carry out comprehensiveevaluation The last one is how to deal with these differenceson indicators estimated by various experts and to get attributevalues more accurately In a word it is uneasy to select anoptimal scheme from multiple designs

The purpose of this paper is to present a group decision-making approach based on Dempster-Shafer Theory (DST)and Analytic Hierarchy Process (AHP) for new productselection under epistemic uncertainty Firstly many expertsare asked to grade indexes according to scale And AHP isapplied to calculate attribute weights Due to different expe-riences and preferences weights given by different experts arevarious And DST is used for the final weight to eliminate thedifference In addition DST is used as a proper mathematicalframework to dealwith the epistemic uncertainty By buildingreliability function and likelihood function comprehensiveevaluation of new scheme is carried out Finally the validityof this method is verified by a case studyThe structure of thispaper is as follows the second part is related work the thirdpart is an introduction toDempster-ShaferTheory the fourthsection is the establishment of the evaluation model and thefifth section is case study

2 Related Work

NPD is the foundation for enterprises to survive and developTherefore a key task for top management is to chooseappropriate new products When evaluating product planstop management should take many factors into considera-tion and prediction such as market trend product marketcompetitiveness product cost and technical requirementsThe work of new product evaluation is very importantand complex for enterprises It is also an important topicfor researchers Therefore many researchers have proposeddifferent tools or methods to evaluate new product schemes

(i) Risk assessment Katie et al [1] proposed a riskidentification framework from system perspectiveswhich can be used to assess risks quantitatively of newproducts Patil et al [2] predicted business risks at thebeginning of new product design and established arisk framework Fang and Marle [3] designed a wayto identify inherent risks and cross risks of projectsaccording to the direction of risk communicationMohit [4] designed a risk network corresponding todifferent functional organizations based on Bayesiannetwork method to measure risks of all new projects

(ii) Key factors Kim et al [5] summarized key factors inNPD by studying cases of developing new productsin virtual teams of SME Cooper et al [6] identified

the critical factors that set the most successful firmsapart from their competitors by benchmarking at thecompany or macro level to ensure that resources areallocated appropriately Lam et al [7] used AHP tostudy the most important 13 factors in the processof new product development from the perspectiveof conflict management Cunha [8] studied the keysuccess factors by summarizing the empirical andconceptual studies of NPD in the past 30 years

(iii) Quality function deployment (QFD) Lowe et al [9]developed a new product evaluation tool based onQFD to evaluate potential products for an innovativemetal forming process Hanumaiah et al [10] builta rapid hard tooling process selection though QFDand AHP methodology Lee [11] selected the criticalfactors though Fuzzy Delphi method and constructedhouses of quality for QFD in NPD Zhang Xuefeng[12] proposed an integrated approach based on QFDandDEA to ensure user collaboration which has beenrecognized as a critical factor in successful productdevelopment Yu L Wang L and Bao Y [13] proposeda new product evaluation approach based on QFDintegrated IVIF and CI

(iv) Artificial neural networkThieme et al [14] evaluatedand chose the new plan by constructing the neuralnetwork model HO and Tsai [15] proposed a newmethod based on structural equation model (SEM)and adaptive neural fuzzy inference system (ANFIS)to predict the effect of value process quality on theperformance of NPD

(v) AHPANP and TOPSIS Lin et al [16] constructeda method based on AHP and TOPSIS to identifycustomer requirements and design features so asto evaluate design schemes Shyur et al [17] usedANP to determine evaluation criteria and weightsand used the improved TOPSIS to arrange alter-native designs Chiuh et al [18] presented a fuzzyanalytic network process (FANP) for solving theproduct selection Akkaya et al [19] constructed anewmethod based on fuzzy AHP and fuzzyMOORAfor industrial engineering sector choosing problemJoshi and Kumar [20] held that in the process ofgroup decision-making the interaction of decisioncriteria and concept uncertainty has a great influenceon the membership function

(vi) Fuzzy set When hen solving the optimal new prod-uct plan some attributes are hard to be expressednumerically Many scholars have adopted fuzzy setsfor example Carrera Diego A et al [21] and Chen HH et al [22] On the basis of considering the favorableand unfavorable factors Lin and Yang [23] calculatedthe fuzzy attractiveness and determined portfolioselection problems Kit et al [24] proposed a for-ward selection based on fuzzy regression (FS-FR) tocorrelate engineering characteristics with consumerpreferences regarding a new product Buyukozkan G

Mathematical Problems in Engineering 3

et al [25] constructed a multicriteria group decision-making approach based on intuitionist fuzzy TOPSISfor smart phone selection Kumru et al [26] proposeda new hybrid approach for multicriteria decision-making problems through combining intuitionistfuzzy analytic hierarchy process and intuitionist fuzzymultiobjective optimization by ratio analysis

(vii) Group decision making Ren et al [27] used fuzzyinformation and group decision analysis method toconstruct an extension method of fuzzy measure-ment so as to solve the problem of evaluation andselection Ebrahimnejad S et al [28] introduceda new hierarchical multi criteria group decision-making method to solve the optimal selection ofnew product design alternatives What is more itproposed sets to evaluate and analyze new productsLo C C et al [29] and Chung et al [30] used bothgroup decision-making and fuzzy number appliedan axiomatic design method using fuzzy linguisticto make multiattribute group decision Tuzkaya [31]suggested that IFCI operators should adopt MCDMmethod take advantage of the interaction betweenfuzziness of decision environment and decision cri-teria and combine supplier evaluation processesGulcin Buyukozkan et al [32] presented a creativeapproach to evaluate the smart medical device selec-tion process in a group decision-making with intu-itionistic fuzzy set based on fuzzy choquet integralMousavi et al [33] adopted a hierarchical groupdecision-making approach to new product selectionbased on VIKOR

(viii) Other methods Sarı et al [34] used fuzzy MonteCarlo simulation to evaluate new product investmentplans so as to select the best Huanghong et al [35]adopted computational intelligence techniques forNew Product Design Wang wenpei [36] presenteda 2-tuple fuzzy linguistic computing approach todeal with heterogeneous information and informa-tion loss problems during the processes of subjectiveevaluation integration in NDP Gulcin et al [37]identified the decision points in the NPD processand the uncertainty factors affecting those points andproposed an integrated approach based on fuzzy logicto shape the decisions

Although many scholars put forward different methods fornew product scheme selection from different perspectivesthere are some external conditions which are not takeninto consideration in these methods Firstly the majority ofscholars hold the view that new product scheme selectionis a multiattribute decision-making (MADM) problem Andmany MADM methods are used for new product selectionThe MAMDmethods differ in different fields Some MADMmethods are used to solve one specific problem and theyare not suitable for other problems These MADM methodscan be divided into two categories One is compensatorymethods such as AHP TOPSIS and VIKOR The other isnoncompensatory methods such as Dominance Max-minConjunctive-Satisfying and Elimination methods When

choosing a new product some attributes considered arecross-cutting So it is more appropriate to use compen-satory MADM approach Each compensatory method hasits advantages and disadvantages Compared with TOPSISand VIKOR AHP is more suitable for determining indexweight in NPD This is found in many literatures Attributeweights is very important for the final scheme selection Itmay be inaccurate to judge the importance of each indicatoronly by personal knowledge and experience Invitingmultipleexperts to evaluate indicators weights and dealing with dif-ferent weights are seldom mentioned in previous literaturesSo in this paper an approach based on DST and AHP isproposed to solve this problem

In addition the attribute values of new products areestimated for future which makes it difficult for experts toexpress the attributes of the new scheme numerically relyingon limited knowledge and experience Experts use fuzzynumbermore confidently compared to using specific value torepresent the attributes of new schemes In order to improvethe accuracy of prediction some scholars use hesitant fuzzysets However new products from RampD to production andsales involve many links and it is difficult for an expert tograsp all the information More experts should be invited toevaluate the future performance of new products in orderto improve the accuracy of the estimations However theresearch on this aspect has hardly been mentioned in previ-ous papersThe fact that various experts would have differentknowledge leads to different results given by different expertsto the same attribute of the same design In general the bestchoice from new product plans is a fuzzy multicriteria groupdecision-making problem and an evaluation approach basedon DST is proposed

3 Dempster-Shafer Theory

DST was put forward by Professor P Dempster of HarvardUniversity Glenn Shafer a student of Professor P Dempsterhas further developed evidence theory and constructeda mathematical method for calculating uncertainty Thismethod is mainly used in information fusion expert systemintelligence analysis legal case analysis and multiattributedecision-making This method (Certa et al [38] Shafer [39]Li dawei et al [40]) is based on three different measuresnamely Basic Probability Assignment (BPA) Belief Measure(BEL) and Plausibility Measure (PL)

Definition 1 (basic probability assignment (BPA)) SupposeUis the frame of discernment BPA on frame of discernmentis a function m of 2U 997888rarr [0 1] On BPAs the followingassumptions hold

m (0) = 1 (1)sumAsubeU

m (A) = 1 (2)

m (A) gt 0 (3)

Definition 2 (belief function) Belief Function is the sum ofBPAs for all subsets of A On the frame of discernment U


reliability function based on BPA is expressed by Bel (A) andits calculation formula is as follows

Bel (A) = sumBsubeA

m (B) (4)

Definition 3 (plausibility function) Plausibility Function isthe sum of BPAs of all subsets intersecting with A On theframe of discernment U plausibility function based on BPAis expressed byPl (A) and its calculation formula is as follows

Pl (A) = sumBcapA =0

m (B) (5)

Definition 4 (trust intervals) The Trust Interval of A isdenoted as [Bel(A) Pl(A)] Bel(A) is the lower bound of theTrust Interval and Pl(A) is the upper bound For example thetrust interval of event A is (025 085) The probability that Ais true is 025 the probability that A is false is 015 and theprobability that A is uncertain is 06

Definition 5 (Dempster aggregation rule) DST can be usedto integrate evidences from multiple independent sourcesThere are a finite number of mass functions on the recog-nition framework U namely m1m2m3m4 mn Theaggregation rules are as follows(m1 oplusm2 oplus sdot sdot sdot oplusmn) (A)= 1

Ksum

A1⋂A2⋂sdotsdotsdot ⋂An=A

m1 (A1) sdotm2 (A2) sdot sdot sdotmn (An) (6)

K = sumA1⋂A2⋂sdotsdotsdot ⋂An =0

m1 (A1) sdotm2 (A2) sdot sdot sdotmn (An) (7)= 1 minus sumA1⋂A2⋂sdotsdotsdot ⋂An=0


K is called normalization factor and the value of 1-K reflectsthe degree of evidence conflict

4 A New FMCGDM Approach Model Based onAHP and DST

In order to study the complex problem in NPD this paperfocuses on the FMCGDM (fuzzy multiple criteria groupdecision-making) In this paper a new FMCGDM approachbased on DST and AHP is proposedThis method consists offour important parts Firstly an index system for new productselection is constructed and attribute weight can be analyzedby using AHP and DST Then multiple experts are askedto predict attributes performance of all new schemes and toexpress it by fuzzy number Finally DST is applied to groupdecision-making and the optimal solution is obtained Theprocess is shown in Figure 1

41 e Construction of Evaluation Index System A newdesign plan can be evaluated by scoring The principle ofscoring is that schemes which are conducive to achieve ourgoals will get higher scores and vice versa To evaluate new

Choose indicators for evaluating newproduct schemes

Invite many experts to grade indicatorimpact judgment matrixes are obtained

Use AHP to calculate different indexweights given by different experts

Calculate the final weight according theaggregation rule in DST

Invite many experts to express predictedindexed with interval numbers

Handle indicator predictions positively andnon-differently

Arrange and combine different estimatesof the new scheme

Calculate evaluations of eachcombination of new scheme

Calculate reliability and plausibilityfunction of event = １Ｃ ge １

lowastＣ

Draw reliability and curve ofevent = １Ｃ ge １

lowastＣ

Set confidence degree and calculatecomprehensive value of new scheme and

rank

plausibility

Figure 1 Conceptual framework of the proposed FMCGDMapproach based on AHP and DST for new product selection

product plans goals of developing new product should bemade clear firstly Several criteria can be selected accordingto program purposes and evaluation index system for newproduct selection is set upDifferent enterprises have differentgoals in designing and producing new products Enterprisesdesign new products in order to open a new market gain ahighermarket share contribute to the environment or obtainhigher profits

When evaluating specific product designs indicatorsmayvary according to previous research For example whena mobile phone manufacture enterprise develops a newproduct indexes may be battery life storage capacity coreprocessor efficiency screen size camera pixel development


Table 1 Scaling Method of Judgment Matrix

Scaling value Implication1 The two indicators are equally important3 The former indicator is slightly more important than the later5 The former indicator is obviously more important than the later7 The former indicator is much more important than the later9 The former indicator is extremely more important than the later2 4 6 8 The median value is between two adjacent discriminates

reciprocal If the matrix score is aij when the i-th indicator is compared with the j-ththe matrix score is 1aij when the j-th indicator is compared with the i-th

cost and product weight Therefore when selecting indica-tors decisionmakers shouldmodify indexes according to thegoals

42 e Weights Determination Method Based on AHP andDST Through Section 41 content indicators for newproduct selection have been chosen Suppose that indexesare (U1 U2 sdot sdot sdot UN) Next we need to clarify relationshipbetween indicators that is to calculate indicator weightsWeights obtained by objectivemethods often do not conformto the reality and these obtained by subjective methods areinfluenced by expert preferences To avoid these shortcom-ings a combination of subjective and objective methods isused to calculate indexweightsThismethod is to invitemanyexperts to evaluate indicators importance and use AHP tocalculate indicator weights Because weights given by variousexperts are different so in this paper DST is used to calculatethe final weights

421 e Judgment Matrix Given by Experts Firstly manyexperts are invited to grade the impact of all indicators on thetarget Experts can give evaluating information on the impor-tance of the indicators according to their own professionalknowledge and experience This evaluating information canbe converted into scores by comparing two indicators asshown in Table 1

According to this method judgment matrix on theimportance of indexes given by all experts can be obtainedThen judgment matrix given by the m-th expert is repre-sented by Am

Am = [[[[[(am11 sdot sdot sdot am1n d

amn1 sdot sdot sdot amnn

)]]]]] (9)

422 Weight-Making by AHP In order to estimate theimpact of all indexes on the design selection AHP [41] isused to calculate index weights The calculation process is asfollows

Normalization In order to calculate eigenvalues judgmentmatrix given by every expert is normalized firstly According

to formula (10) judgment matrix is normalized and thenormalized matrix Am1015840

ij is obtained According to formula(11) the normalized matrix is summed by rows

am1015840

ij = amijsumni=1 amij

(10)

Wm = (120596m1 120596m2 sdot sdot sdot 120596m

n )= ( nsumj=1am1015840

1j

nsumj=1am1015840

2j sdot sdot sdot nsumj=1am1015840

nj ) (11)

Eigenvalues and Maximum Eigenvectors of Judgment MatrixAccording to formula (12) eigenvectors are calculated andindicator weights given by the m-th expert are obtainedAccording to formula (13) the maximum eigenvalue iscalculated


n )= ( 120596m1sumn

i=1 120596mi

120596m2sumn

i=1 120596mi

sdot sdot sdot 120596mnsumn

i=1 120596mi) (12)

120582mmax = nsumi=1

(AWm)in120596m

i(13)

Consistency Test Consistency test is to judge the credibilityof experts scores

CR = CIRI

(14)

where CR is the consistency test ratio RI is a randomconsistency index as shown in Table 2 and CI is consistencycoefficient of judgment matrix and it can be calculated as

CI = 120582max minus nn minus 1 (15)

According to formula (14) the value of CR can be calculatedIf CR lt 01 is true the inconsistency degree is withinthe acceptable range The weights given by this expert areconsidered to be valid Conversely the inconsistency degreeis unacceptable


Table 2 The table of Random Consistency Indicators RI

n 1 2 3 4 5 6 7 8 9 10 11RI 0 0 058 09 112 124 132 141 145 149 151

Table 3 Index weight given by different expert

Expert Index A Index B Index CExpert 1 04 03 03Expert 2 03 035 035

423 e Final Weight Determination Based on DST InSection 422 index weights can be calculated by usingjudgment matrixes given by all experts If the weights givenby different experts are the same with each other indexweights can be obtained However judgment matrix givenby different experts is often various due to their respectiveknowledge and experiences So these weights calculated byjudgment matrixes given by different experts are differentDST is used to synthetically analyze different weights of thesame index given by different experts and calculate the finalindex weights The aggregation rule of multiple independentinformation sources inDST can be used to solve this problem

For example three indicator weights given by two expertsare calculated through AHP method The calculation resultsare shown in Table 3

Using aggregation rule in DST the calculation process ofthe final index weights is as follows

K = 1 minusm1 (A) lowastm2 (B) +m1 (A) lowastm2 (C) +m1 (B)lowastm2 (A) +m1 (B) lowastm2 (C) +m1 (C) lowastm2 (A)+m1 (C) lowastm2 (B) = 1 minus (04 lowast 035 + 04 lowast 035+ 03 lowast 03 + 03 lowast 035 + 03 lowast 03 + 03 lowast 035)= 033Bel (A) = m1 (A) lowast m2 (A)

K= 04 lowast 03033 = 03636

Bel (B) = m1 (B) lowast m2 (B)K

= 03 lowast 035033 = 03182Bel (C) = m1 (C) lowast m2 (C)

K= 03 lowast 035033 = 03182

(16)

43 e Indicator Prediction Represented by Interval NumberMultiple experts are invited to estimate the future perfor-mance of all indicators of new product schemes Because itis a prediction for future experts use fuzzy number moreconfidently compared to using numerical values to assess thepossible future performance of every scheme

For different indicators date dimension is different Soit needs to be put in the same dimension so as to avoidmistake in the final results Index system to evaluate newschemes includes positive index and negative index In orderto facilitate calculation the negative data needs to be put

forward So there are two main steps in data processingnamely nondimensional process and positive management

431 Nondimensional Process The indicators are representedby values or interval numbers In this paper min-max ismainly used to nondimensionalize

For numerical data the nondimensional formula (17) isas follows

x1015840ij = xij minus xminj

xmaxj minus xminj(17)

where xij represents the value of the jth index of the ithscheme and x1015840ij represents the nondimensional data of the jthindex of the ith scheme xmaxj and xminj are used to representthe maximum and minimum values of the jth index datarespectively i = 1 2 sdot sdot sdot M and j = 1 2 sdot sdot sdot N M is the totalnumber of programs and N is the total number of indicators

For interval numbers the nondimensional formula is asfollows

aminus1015840ij = aminusij minusmin0leklem aminuskjmax0leklem a+kj minusmin0leklem aminuskj (18)

a+1015840ij = a+ij minusmin0leklem aminuskjmax0leklem a+kj minusmin0leklem aminuskj (19)

where [aminusij a+ij ] represents the value of the jth index ofthe ith scheme and [aminusij 1015840 a+1015840ij ] is used to represent thenondimensional data of the jth index of the ith schememin0leklemaminuskj is the minimum lower limit value of the jthindex max0leklema+kj is the maximum upper limit value ofthe jth index i = 1 2 sdot sdot sdot M j = 1 2 sdot sdot sdot N where Mrepresents the total number of programs andN represents thetotal number of indicators

432 Positive Management Indicators can be divided intopositive and negative indicators Positive indicators are theindicators that mean that the higher the values are the betterthe schemes are The negative indicators are the indicatorsthat mean that the smaller the indexes are the better theproduct is In order to make calculation more convenientnegative indicators need to be transformed into positiveindicators


For numerical data forward processing formula is asfollows

x10158401015840ij = 1 minus x1015840ij (20)

where x1015840ij stands for the nondimensional data of the jth indexof the ith scheme and x10158401015840ij stands for the forward data of thejth index of the ith scheme

For interval number forward processing formula is asfollows

a+10158401015840ij = 1 minus aminus1015840ij (21)

aminus10158401015840ij = 1 minus a+1015840ij (22)

where [aminusij 1015840 a+1015840ij ] stands for the nondimensional data of the jthindex of the ith scheme and [aminusij 10158401015840 a+10158401015840ij ] stands for the forwarddata of the jth index of the ith scheme

44 Evaluation of New Product Scheme Based on DST Itis difficult for experts to predict future data accuratelyespecially on accurate numberTherefore experts use intervalnumbers more confidently to predict future data based ontheir experience and knowledge What is more in orderto avoid the preference of individual expert and improvethe accuracy of prediction several experts were invited topredict the indicators The assumption that these expertsare equally familiar with new products is made This meansthat every expert has the same credibility In other wordsindicator values proposed by every expert appear with thesame probability For example n experts are asked to estimatethe j-th index of the i-th scheme and n estimates are obtainedThen the probability of every estimate is 1n

All experts should estimate all indicators of all newschemes Let interval number aijm characterize the estimatedvalue given by them-th expert to the j-th index attribute of thei-th scheme In order to take into account all possible futurevalues of new scheme different estimates would be arrangedand combined If there are P experts and Q indicators therewill be PQ possible combinations for every scheme Onlythrough analyzing comprehensively these combinations canevaluation results of new schemes be obtained

For clarity suppose there are three indicators and twoexperts The two experts predicted all indicators of a newscheme and the results are shown in Table 4 All possiblecombinations of the new scheme are as shown in Table 5The number of combinations is 23 = 8 The probability ofoccurrence of every combination is equal all are 18

Next comprehensive evaluation of all combination can becalculated which is equal to multiplying the attributes andthe corresponding weights and then accumulating themThecalculation process of the comprehensive value of the r-thcombination of the i-th new scheme is as follows

Qir = AW = [air1 air2 sdot sdot sdot airn] lowast [w1 w2 sdot sdot sdot wn]T= nsumj=1airj lowast wj = [ nsum

j=1aminusirj lowast wj nsum

j=1a+irj lowast wj] (23)

A project would have PQ comprehensive evaluations andthey are interval numbers This makes sorting all newschemes difficult A numerical value Qlowasti which representedthe final evaluation of the i-th scheme is needed In order tosynthesize the available information and make them usefulfor new product selection let us consider event E = Qi geQlowasti where the evaluation of the i-th new product ie Qiis compared with a generic threshold value Qlowasti To reckonQlowasti by this method is calculated from a conservative point ofview If event E = Qi ge Qlowasti occurs the actual evaluation ofnew scheme ismore thanQlowasti If the evaluation of new schemeQlowasti is acceptable the probability that the actual evaluation ofthe new scheme is greater than Qlowasti is very large So the newscheme must be acceptable The probability of occurrence ofevent E = Qi ge Qlowasti should be calculated though Dempsteraggregation rules The greater the probability of evidencesupport is the more likely the event is to occur Because it isdifficult to calculate the probability of event E = Qi ge Qlowasti directly the confidence interval of inverse event E can becalculated firstly By definition [Bel(E)Pl(E)] stands for thetrust interval of event E Bel (E) denotes the lower limit andPl (E) denotes the upper limit

(i) The reliability function of event E can be calculatedaccording to

Bel (E) = Bel (Qi le Qlowasti ) = sumQiisin[0Qlowasti ]

m (Qir) (24)

(ii) The plausibility function of event E can be calculatedaccording to

Pl (E) = Pl (Qi le Qlowasti ) = sumQicap[0Qlowasti ]=0

m (Qir) (25)

(iii) The reliability function and plausibility function ofinverse event E can be obtained by calculating thereliability function and plausibility function of eventE according to

Bel (E) = Bel (Qi ge Qlowasti ) = 1 minus Pl (Qi le Qlowasti ) (26)

Pl (E) = Pl (Qi ge Qlowasti ) = 1 minus Bel (Qi le Qlowasti ) (27)

It is more reasonable to determine the Qlowasti from the curvedepicted by the last equation since the greater the com-prehensive evaluation is the better the scheme is Set aconfidence degree g As long as plausibility function ofinverse event E = Qi ge Qlowasti is greater than the confidencedegree g the value of Qlowasti is reasonable The value of Qlowasti is theabscissa of the intersection point of line y = g (parallel to x-axis) and plausibility function curve In this way Qlowasti can beused to rank the new schemes to get the optimal one

Here there is still a problem that is the Qlowasti of more thanone schemes obtained by plausibility function may be equalIn order to rank the schemes with same Qlowasti reliability valuer of event E = Qi ge Qlowasti is solved for sorting The r is thelongitudinal coordinate of the intersection point of line x=


Table 4 Experts Predictions to Indicators

Expert Indicator 1 Indicator 2 Indicator 3Expert A [05 06] [03 04] [09 1]Expert B [03 04] [02 03] [08 09]

Table 5 All possible combinations

combination Indicator 1 Indicator 2 Indicator 31 [05 06] [03 04] [09 1]2 [05 06] [03 04] [08 09]3 [05 06] [02 03] [09 1]4 [05 06] [02 03] [08 09]5 [03 04] [03 04] [09 1]6 [03 04] [03 04] [08 09]7 [03 04] [02 03] [09 1]8 [03 04] [02 03] [08 09]Qlowasti and reliability function curve If the r is equal changeconfidence degree g and then solveQlowasti Repeat the above stepsuntil a comparison can be made

The calculation process is as follows

(i) Set a confidence level g Draw a line y = g parallel tothe X axis and the intersection point of this line andplausibility function curve is (Qlowasti g) so as to obtainQlowasti

(ii) By comparing Qlowasti new schemes are sorted(iii) If there are no two or more schemes with equal Qlowasti

the calculation process is over(iv) If there is more than one scheme with equalQlowasti the

reliability value r of event E = Qi ge Qlowasti shouldbe calculated Draw a line x = Qlowasti parallel to Y axisand the intersection point of this line and reliabilityfunction curve is (Qlowasti r) By this way the r can beobtained

(v) By comparing r scheme with equal Qlowasti are sorted(vi) If the reliability value r of new schemes with equal Qlowasti

are not equal the calculation process is over(vii) If there are more than one scheme with equal Qlowasti and

r a new confidence level g1015840 is set to rank schemes withequal r and Qlowasti and g1015840 = g Repeat steps (i)-(v) untilall schemes are sorted completely The calculationprocess can be shown in Figure 2

5 Case Study

In order to prove the application of this method in newproduct selection a case study of a household appliancesmanufacturing enterprise would be introduced in this sec-tion This household appliances manufacturer is located inQingdao China Regarding product innovation and userrsquosneeds as key factors for its development this company has

invested a lot of money in product development and marketresearchThis also enables this enterprise to obtainmany newproduct schemes How to choose the right products is animportant problem The names and technical characteristicsof new schemes are not provided in this study since theseare confidential contents to this corporation The name ofnew schemes is replaced by Arabic numerals and estimationsare given by experts directly without discussing the featureinformation

51 Decision Attributes for NPD The goal of choosing newproducts to this enterprise is for the better developmentHow to select appropriate attributes frommany factors whichaffect enterprise growth is the first problem to be solved Thecorrectness of enterprise decision-making is influenced bythe quality and quantity of attributes In order to constructappropriate indicator system the company leaders invitedseveral departmental representatives to set up a new productcommittee These departmental representatives are frommarketing finance RampD and product department Throughanalyzing and screening all factors the five indicators areselected in the final namely Technical Difficulty (C1) Prod-uct Performance (C2) Market Potential (C3) Project Risk(C4) and Project Cost (C5) Technical Difficulty (C1) isproduct complexities which highlight physical possibility ofproduct realization Product Performance (C2) is superiorquality and new product features Market Potential (C3)reflects the market demand Project Risk (C4) is about allthings that might prevent successful completion ProjectCost (C5) depicts the consumption of resources The specificcontents of the indicators are shown in Table 6

52 A Weight Determination Method Based on AHP and DSTfor NPD The indicators for evaluating new product schemesare selected though Section 51 and the next important thingis to determine these indicator weights In this paper fourexperts involved from different departments in the company


Draw reliability function curve and plausibilityfunction curve of

Set a confidence level g

Draw a line y = g parallel to the X axis and the intersection point of this line and plausibilityfunction curve is ( g) so as to obtain

By comparing new schemes are sorted

Are there two or more schemes with equal AAAre there two or more

schemes with equal

Draw a line x = parallel to the Y axis and theintersection point of this line and reliability function curve is ( r) So r is obtained

By comparing r scheme with equal are sorted

Are there more than one scheme with equal and r

AAAArerere hththere more than one schememewith equal and r

Reset a new confidence level g to rank schemes with equal r and and g ne g

EndEnd

NO

NO

parallYES

fid

YES

= １Ｃ ge １lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

Figure 2 Flow diagram of the prioritization procedure for new product selection

were invited to score the importance of the indicators Theyare from marketing finance RampD and product departmentand have been working in this company for more than fiveyears The four managers scored the indicator importanceaccording to the scoring scale of Table 1 Four judgmentmatrices are obtained as follows

A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)

According to each expertrsquos score on each index the weight ofeach index is calculated through AHP as shown in Table 7Because of various work experience and knowledge multipleexperts assigned different weights to the same indicators Inorder to obtainmore reliable weights the aggregation rules inDST are used to calculate the final weight It is mainly based


on that the greater the evidence is the greater the probabilityof events is According to formula (6) and (8) in Section 3 thefinal index weights are obtained The result of empowermentis as follows

w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)

53 Data Collection and Preprocessing for NPD In Sections51 and 52 the indicators and their weights for evaluating newproduct are determined The next thing to do is to predictthe future performance of all indicators of new schemesThrough the active efforts of all staff ten new products arecollected Two experts who are very familiar with these newproducts took the initiative to participate in the estimation ofall indicators One expert (A) is the manager of RampD and theother (B) is the manager of marketing departmentThey havebeen working for more than five years and are very familiarwithmarket and enterpriseThey gave respectively a suitablescore which is between 1 and 10 points for all indicatorsBecause it is a prediction experts use interval numbers moreconfidently than using numerical values to assess the possiblefuture performance of each indicator The estimated valuesare shown in Table 8

According to the data processing formula in Section 43the estimated values are handled positively and nondiffer-ently And the results are shown in Table 9

54 Evaluation and Ranking of New Product Schemes Based onDST In Section 53 two experts estimated the future perfor-mance of all indicators of the ten new schemes Because theyare very familiar with these new products the probability ofoccurrence of the indicator value given by the two experts isequal namely 12 Following the decomposition andmergingapproach given in Section 44 the five indicators given by thetwo experts are combinedThe number of combinations is 25namely 32

Every combinationwould get a comprehensive evaluationaccording to formula (23) and the occurrence probabilityof every comprehensive value is 132 According to thecalculation process in Section 44 plausibility curve andbelief curve of event E = Qi ge Qlowasti are drawn Set confidencelevel g as 09 and draw a line y = g parallel to the X axis Theintersection point of this line and plausibility function curveis (Qlowasti g) so as to obtain Qlowasti Due to the limitation of spaceit is impossible to list all the schemes However in order toillustrate thismethod the new product scheme 2 is illustratedas an example Table 10 shows 32 combinations of scheme 2and their comprehensive values Figure 3 shows the Belief andPlausibility curves of event E = Q2 ge Qlowast2 and Qlowast2 is 05

According to the same method the evaluation results Qlowastiof these ten new products are obtainedThe new products are

010203040506

0807

091

(0509)

y=09

045 05 055 060403503

Bel１Ｃ ge １lowastＣ

Pl１Ｃ ge １lowastＣ

Figure 3 Belief and plausibility curves of new product Scheme 2

sorted according to Qlowasti and the ranking results are shown inTable 11

Among them the evaluation results Qlowasti of new productschemes 4 and 5 are both 059They are equally ranked in thethird position of Table 11 For the sake of clarity the reliabilityvalue of event E = Qi ge 059 is solved for sorting Draw aline x = 059 parallel to the Y axis and the intersection pointof this line and reliability function curve leads to Bel(Q4 ge059) = 0 and Bel(Q5 ge 059) = 0 Therefore it isstill impossible to rank the two schemes Aiming at betterdiscriminating their actual criticality we reset confidencelevel g as 08 And draw a line y = 08 parallel to the X axisTheintersection point of this line and plausibility function curveleads to Qlowastlowast4 = 061 whereas Qlowastlowast5 = 059 as shown in Figures4 and 5 The new product scheme 4 results are more criticalthan scheme 5 As a consequence the new product scheme4 still remains in the third position of the final rankingwhereas scheme 5 shifts to the forth The final ranking ofnew product schemes is shown in Table 12 In this schemeselection scheme 6 is the best choice

In real life the top manager in this enterprise finallyadopted scheme 8 and scheme 3 through many seminarsand repeated evaluations After successful RampD and puttingscheme 8 and scheme 3 into the market it is found that theactual situation is the same as the result of the evaluationin this paper New product 8 has achieved good economicreturns and new scheme 3 has achieved lower economicreturns which is the same as our final evaluation

6 Conclusions

The evaluation and selection of new product schemes is aprediction and decision-making process for future problemswhich has many risks and uncertainties It is one of the keyevents which influences the future development of enter-prises Therefore it is imperative to take a reliable approachto assess new products In this paper a new method basedon AHP and DST is proposed to make the best decisions in


Table 6 The specific contents of the indicators

Indicator The specific contentsTechnical Difficulty Technological difficulty in Research Development and ProductionProduct Performance The new properties costs and physical characteristics

Market Potential Market capacity demand trend profit potential competitive ability marketcompetition

Project Risk Financial risks managerial risks envisioning risks design risks and execution risksProject Cost Financial consumption human consumption and material consumption

Table 7 Weights assigned by different expert

Indictor Expert A Expert B Expert C Expert DTechnical Difficulty 01103 03276 01568 00975Product Performance 02097 01103 02945 01568Market Potential 03276 02422 00975 01568Project Risk 02422 01103 02945 02945Project Cost 01103 02097 01568 02945

Table 8 Table of Expertsrsquo Prediction for New Products

Indictor C1 C2 C3 C4 C5Expert A B A B A B A B A BScheme 1 [7 8] [6 7] [8 9] 9 [7 8] 8 [89]89 8 9 9Scheme 2 [7 8] [5 6] [4 5] 4 [3 4] 4 [5 6] 5 [8 9] 8Scheme 3 [4 5] 4 [1 2] 2 [2 3] 2 [3 4] 3 [4 5] 4Scheme 4 [8 9] [7 8] [4 5] [5 6] [4 5] 5 [7 8] [6 7] 8 [7 8]Scheme 5 [8 9] [8 9] 7 [7 8] 8 [7 8] [7 8] [7 8] 4 5Scheme 6 [2 3] 3 [2 3] [2 3] [9 10] 9 [8 9] [7 8] 9 [8 9]Scheme 7 [4 5] [5 6] [2 3] 3 [4 5] [3 4] [5 6] [4 5] [4 5] [3 4]Scheme 8 [7 8] [8 9] [4 5] [3 4] 2 [2 3] [4 5] [5 6] [2 3] [1 2]Scheme 9 [2 3] [3 4] [4 5] [5 6] [4 5] [4 5] [2 3] 2 [4 5] [5 6]Scheme 10 [4 5] [3 4] 2 [2 3] [1 2] [2 3] [1 2] 1 [5 6] [5 6]

y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)




a fuzzy environment There are four stages in this methodThe first stage is attributes selection for evaluation which

y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)




is the first stage for all decision-making problems At thisstage we need to make clear what indicators influence new


Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]


Table 10 The combinations of new product scheme 2

combination C1 C2 C3 C4 C5 evaluation1 [071 086] [05 062] [067 078] [05 063] [0 012] [047 059]2 [071 086] [05 062] [067 078] [05 063] 012 [049 059]3 [071 086] [05 062] [067 078] 05 [0 012] [044 057]4 [071 086] [05 062] [067 078] 05 012 [046 057]5 [071 086] [05 062] 067 [05 063] [0 012] [047 054]6 [071 086] [05 062] 067 [05 063] 012 [049 054]7 [071 086] [05 062] 067 05 [0 012] [044 052]8 [071 086] [05 062] 067 05 012 [046 052]9 [071 086] 062 [067 078] [05 063] [0 012] [049 059]10 [071 086] 062 [067 078] [05 063] 012 [051 059]11 [071 086] 062 [067 078] 05 [0 012] [046 057]12 [071 086] 062 [067 078] 05 012 [048 057]13 [071 086] 062 067 [05 063] [0 012] [049 054]14 [071 086] 062 067 [05 063] 012 [051 054]15 [071 086] 062 067 05 [0 012] [046 052]16 [071 086] 062 067 05 012 [048 052]17 [043 057] [05 062] [067 078] [05 063] [0 012] [047 057]18 [043 057] [05 062] [067 078] [05 063] 012 [049 057]19 [043 057] [05 062] [067 078] 05 [0 012] [044 054]20 [043 057] [05 062] [067 078] 05 012 [046 054]21 [043 057] [05 062] 067 [05 063] [0 012] [047 052]22 [043 057] [05 062] 067 [05 063] 012 [049 052]23 [043 057] [05 062] 067 05 [0 012] [044 05]24 [043 057] [05 062] 067 05 012 [046 05]25 [043 057] 062 [067 078] [05 063] [0 012] [049 057]26 [043 057] 062 [067 078] [05 063] 012 [051 057]27 [043 057] 062 [067 078] 05 [0 012] [046 054]28 [043 057] 062 [067 078] 05 012 [048 054]29 [043 057] 062 067 [05 063] [0 012] [049 052]30 [043 057] 062 067 [05 063] 012 [051 052]31 [043 057] 062 067 05 [0 012] [046 05]32 [043 057] 062 067 05 012 [048 05]Table 11 New products ranking on the basis of Plausibility curves

Scheme Qlowasti RankingScheme 1 045 8Scheme 2 05 7Scheme 3 055 5Scheme 4 059 3Scheme 5 059 3Scheme 6 051 6Scheme 7 062 2Scheme 8 071 1Scheme 9 038 10Scheme 10 044 9

product selection and build an index system The secondstage is to determine the indicator weights through AHPand DST Several experts score the indicators according to

scoring criteriaThen the indicator weights given by differentexperts are calculated through AHP Then the final weightsare calculated through Dempster aggregation rule In thethird stage all indexes of new schemes are predicted andpreprocessed This problem is forecasted by experts based onthe fact that they are familiar with the market enterprisesand each new scheme at the same time Even so experts useinterval numbersmore confidently to represent the indicatorscompared to numerical values In order to facilitate futureevaluation we need to handle the interval values positivelyand nondifferently The fourth stage is the evaluation ofnew schemes based on DST By analyzing the belief andplausibility function of event E = Qi ge Qlowasti we can getthe critical value Qlowasti with given confidence level The criticalvalue is used to express the evaluation of new products and torank them In order to prove how the proposed fuzzy hybridmethodworks a newproducts evaluation inQingdao is takenas an example to make an empirical study through which thefollowing conclusions can be drawn


Table 12 Final ranking

Scheme confidence level q=09 confidence level q=08 RankingQlowasti Pl (Qir ge Qlowasti ) Qlowasti

Scheme 8 071 ndash ndash 1Scheme 7 062 ndash ndash 2Scheme 4 059 0 061 3Scheme 5 059 0 059 4Scheme 3 055 ndash ndash 5Scheme 6 051 ndash ndash 6Scheme 2 05 ndash ndash 7Scheme 1 045 ndash ndash 8Scheme 10 044 ndash ndash 9Scheme 9 038 ndash ndash 10

These indicators were selected by the research teambased on years of work experience The members of theresearch group are middle-level managers who have morethan five yearsrsquo working experience in the enterprise andhave a lot of practical experience of NPD These attributesare as follows Technical Difficulty (C1) is the product andmethods complexity which highlights the physical possibilityof product realization Product Performance (C2) is thesuperior quality and new product features which reflects theproduct substantial competitive advantage Market Potential(C3) reflects market demand growth and size which showsan increase in demand for a particular product over timeProject Risk (C4) is about any feature that might poten-tially interferewith successful completion including financialrisks managerial risks envisioning risks design risks andexecution risks Project Cost (C5) depicts the consumptionof resources The attributes for NPD which are put forwardin this case can be used for a reference to other enterprises

What is more the evaluation of new products is aprediction for future problems which has many risks anduncertainties Because it is a prediction for future experts usefuzzy numbermore confidently compared to using numericalvalues to assess the possible future performance of everyscheme And a number of experts are invited to predict thefuture performance of the new schemes which can improvethe prediction accuracy Therefore there would be multiplefuzzy numbers for the same index of the same scheme Thisadds to the difficulty of the evaluation and ranking of newproducts A new product evaluation and ranking methodbased on DST is proposed in this paper Dempster-ShaferTheory (DST) is suggested as a proper mathematical frame-work to deal with the epistemic uncertainty This methodallows experts to use interval numbers to express indicatorsand obtain all possible combinations as evidence throughdecomposition and merging approach Through analyzingthe Belief and Plausibility curve of event E = Qir ge Qlowasti the critical value Qlowasti is obtained and used as the evaluationresults of the scheme and sorted

Finally the method based on AHP and DST proposedin this paper has higher reliability of index weights Weightdetermination is a key content for MADM problem Sub-jective or objective methods were used to determine weight

However the weight obtained by objective method oftendoes not accord with the actual situation and the weightobtained by subjective valuation method is often influencedby experts The method based on DST and AHP is acomprehensive index weighting method which combinessubjective and objectivemethods If only one expert evaluatesthe importance of the index it is difficult to ensure thatthe index weight is not affected by the expertrsquos personalpreferences Therefore many experts are often invited toevaluate the indicator weight to improve the accuracy of theevaluationThemethod based on AHP and DST proposed inthis paper is used to deal with the difference of index weight

Data Availability

The data used to support the findings of this study areincluded within the article No additional data are available

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is financially supported by National Natural Sci-ence Foundation of China under Grant No 71771066 and71531013 and The Key Program in the Youth Elite SupportPlan in Universities of Anhui Province (GXYQZD2017084)

References

[1] K G Lough R Stone and I Y Tumer ldquoThe risk in early designmethodrdquo Journal of Engineering Design vol 20 no 2 pp 155ndash173 2009

[2] R Patil K Grantham and D Steele ldquoBusiness risk in earlydesign a business risk assessment approachrdquo EMJ - EngineeringManagement Journal vol 24 no 1 pp 35ndash46 2012

[3] C Fang and F Marle ldquoDealing with project complexity bymatrix-based propagation modelling for project risk analysisrdquoJournal of Engineering Design vol 24 no 4 pp 239ndash256 2013

[4] M Goswami and M K Tiwari ldquoA predictive risk evaluationframework for modular product concept selection in new


product design environmentrdquo Journal of Engineering Designvol 25 no 1-3 pp 150ndash171 2014

[5] B Kim and J Kim ldquoStructural factors of NPD (new productdevelopment) team for manufacturabilityrdquo International Jour-nal of Project Management vol 27 no 7 pp 690ndash702 2009

[6] R G Cooper and E J Kleinschmidt ldquoBenchmarking thefirmrsquos critical success factors in new product developmentrdquoeJournal of Product Innovation Management vol 12 no 5 pp374ndash391 1995

[7] P-K Lam and K-S Chin ldquoIdentifying and prioritizing criticalsuccess factors for conflict management in collaborative newproduct developmentrdquo Industrial Marketing Management vol34 no 8 pp 761ndash772 2005

[8] H Ernst ldquoSuccess factors of new product development Areview of the empirical literaturerdquo International Journal ofManagement Reviews vol 4 no 1 pp 1ndash40 2002

[9] A Lowe K Ridgway and H Atkinson ldquoQFD in new produc-tion technology evaluationrdquo International Journal of ProductionEconomics vol 67 no 2 pp 103ndash112 2000

[10] N Hanumaiah B Ravi and N P Mukherjee ldquoRapid hard tool-ing process selection using QFD-AHPmethodologyrdquo Journal ofManufacturing Technology Management vol 17 no 3 pp 332ndash350 2006

[11] A H I Lee and C-Y Lin ldquoAn integrated fuzzy QFD frameworkfor new product developmentrdquo Flexible Services and Manufac-turing Journal vol 23 no 1 pp 26ndash47 2011

[12] X Zhang ldquoldquoUser selection for collaboration in product devel-opment based onQFDandDEAapproachrdquo Journal of IntelligentManufacturing vol 30 no 5 pp 2231ndash2243 2019

[13] L Yu LWang and Y Bao ldquoTechnical attributes ratings in fuzzyQFD by integrating interval-valued intuitionistic fuzzy sets andChoquet integralrdquo So Computing vol 22 no 6 pp 2015ndash20242018

[14] R JThiemeM Song andR J Calantone ldquoArtificial neural net-work decision support systems for new product developmentproject selectionrdquo Journal of Marketing Research vol 37 no 4pp 499ndash507 2000

[15] Y-C Ho and C-T Tsai ldquoComparing ANFIS and SEM inlinear and nonlinear forecasting of new product developmentperformancerdquo Expert Systems with Applications vol 38 no 6pp 6498ndash6507 2011

[16] M-C Lin C-C Wang M-S Chen and C A Chang ldquoUsingAHP and TOPSIS approaches in customer-driven productdesign processrdquo Computers in Industry vol 59 no 1 pp 17ndash312008

[17] H J Shyur ldquoCOTS evaluation using modified TOPSIS andANPrdquo Applied Mathematics and Computation vol 177 no 1 pp251ndash259 2006

[18] C-C Chyu and Y-C Fang ldquoA hybrid fuzzy analytic networkprocess approach to the new product development selectionproblemrdquo Mathematical Problems in Engineering vol 2014Article ID 485016 13 pages 2014

[19] G Akkaya B Turanoglu and S Oztas ldquoAn integrated fuzzyAHP and fuzzy MOORA approach to the problem of industrialengineering sector choosingrdquo Expert Systems with Applicationsvol 42 no 24 pp 9565ndash9573 2015

[20] D Joshi and S Kumar ldquoInterval-valued intuitionistic hesitantfuzzy Choquet integral based TOPSISmethod formulti-criteriagroup decision makingrdquo European Journal of OperationalResearch vol 248 no 1 pp 183ndash191 2016

[21] D A Carrera and R V Mayorga ldquoSupply chain management amodular fuzzy inference system approach in supplier selectionfor new product developmentrdquo Journal of Intelligent Manufac-turing vol 19 no 1 pp 1ndash12 2008

[22] H H Chen A HI Lee and Y Tong ldquoAnalysis of new productmix selection at TFT-LCD technological conglomerate networkunder uncertaintyrdquo Technovation vol 26 no 11 pp 1210ndash12212006

[23] C-T Lin and Y-S Yang ldquoA linguistic approach to measuringthe attractiveness of new products in portfolio selectionrdquoGroupDecision and Negotiation vol 24 no 1 pp 145ndash169 2015

[24] K Y Chan and S H Ling ldquoA forward selection based fuzzyregression for new product development that correlates engi-neering characteristics with consumer preferencesrdquo Journal ofIntelligent amp Fuzzy Systems Applications in Engineering andTechnology vol 30 no 3 pp 1869ndash1880 2016

[25] G Buyukozkan and S Guleryuz ldquoMulti criteria group decisionmaking approach for smart phone selection using intuitionisticfuzzy TOPSISrdquo International Journal of Computational Intelli-gence Systems vol 9 no 4 pp 709ndash725 2016

[26] K D Atalay and G F Can ldquoA new hybrid intuitionisticapproach for new product selectionrdquo So Computing vol 22no 8 pp 2633ndash2640 2018

[27] Z Ren Z Xu and H Wang ldquoDual hesitant fuzzy VIKORmethod for multi-criteria group decision making based onfuzzy measure and new comparison methodrdquo InformationSciences vol 388-389 pp 1ndash16 2017

[28] S Ebrahimnejad S M Mousavi R Tavakkoli-Moghaddam HHashemi and B Vahdani ldquoA novel two-phase group decisionmaking approach for construction project selection in a fuzzyenvironmentrdquo Applied Mathematical Modelling Simulation andComputation for Engineering and Environmental Systems vol36 no 9 pp 4197ndash4217 2012

[29] C-C Lo P Wang and K-M Chao ldquoA fuzzy group-preferencesanalysis method for new-product developmentrdquo Expert Systemswith Applications vol 31 no 4 pp 826ndash834 2006

[30] C-H Yeh andY-H Chang ldquoModeling subjective evaluation forfuzzy groupmulticriteria decisionmakingrdquo European Journal ofOperational Research vol 194 no 2 pp 464ndash473 2009

[31] G Tuzkaya ldquoAn intuitionistic fuzzy choquet integral operatorbased methodology for environmental criteria integrated sup-plier evaluation processrdquo International Journal of EnvironmentalScience and Technology vol 10 no 3 pp 423ndash432 2013

[32] G Buyukozkan and F Gocer ldquoSmart medical device selectionbased on intuitionistic fuzzy Choquet integralrdquo So Computingpp 1ndash19 2018

[33] S M Mousavi S A Torabi and R Tavakkoli-Moghaddam ldquoAhierarchical group decision-making approach for new productselection in a fuzzy environmentrdquo Arabian Journal for Scienceand Engineering vol 38 no 11 pp 3233ndash3248 2013

[34] I Sarı and C Kahraman ldquoNew product selection using fuzzylinear programming and fuzzy montecarlo simulationrdquo Com-munications in Computer amp Information Science vol 300 no 3pp 441ndash448 2012

[35] H-ZHuang Y Liu Y Li L Xue andZWang ldquoNew evaluationmethods for conceptual design selection using computationalintelligence techniquesrdquo Journal of Mechanical Science andTechnology vol 27 no 3 pp 733ndash746 2013

[36] W-P Wang ldquoEvaluating new product development perfor-mance by fuzzy linguistic computingrdquo Expert Systems withApplications vol 36 no 6 pp 9759ndash9766 2009


[37] G Buyukozkan and O Feyzioglu ldquoA fuzzy-logic-baseddecision-making approach for new product developmentrdquoInternational Journal of Production Economics vol 90 no 1pp 27ndash45 2004

[38] A Certa M Enea G M Galante and C M La Fata ldquoAmultistep methodology for the evaluation of human resourcesusing the evidence theoryrdquo International Journal of IntelligentSystems vol 28 no 11 pp 1072ndash1088 2013

[39] G Shafer ldquoDempsterrsquos rule of combinationrdquo InternationalJournal of Approximate Reasoning vol 79 pp 26ndash40 2016

[40] D Li H Tang S Xue and Y Su ldquoAdaptive sub-intervalperturbation-based computational strategy for epistemicuncertainty in structural dynamics with evidence theoryrdquoProbabilistic Engineering Mechanics vol 53 pp 75ndash86 2018

[41] C-H Goh Y-C A Tung and C-H Cheng ldquoA revisedweighted sum decision model for robot selectionrdquo Computersamp Industrial Engineering vol 30 no 2 pp 193ndash199 1996

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


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


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


conclusion can be drawn that it is a group decision-makingproblem That is to say new product selection is a fuzzymultiattribute group decision-making model

There are three key problems to deal with in this issueThe first one is how to judge the relationship betweenthose indicators That is to say which indicators are moreimportant and which can be slightly sacrificed Thereforeweight determination is the first key point in the model Thesecond question is how to calculate and judge the attributesexpressed by fuzzy numbers so as to carry out comprehensiveevaluation The last one is how to deal with these differenceson indicators estimated by various experts and to get attributevalues more accurately In a word it is uneasy to select anoptimal scheme from multiple designs

The purpose of this paper is to present a group decision-making approach based on Dempster-Shafer Theory (DST)and Analytic Hierarchy Process (AHP) for new productselection under epistemic uncertainty Firstly many expertsare asked to grade indexes according to scale And AHP isapplied to calculate attribute weights Due to different expe-riences and preferences weights given by different experts arevarious And DST is used for the final weight to eliminate thedifference In addition DST is used as a proper mathematicalframework to dealwith the epistemic uncertainty By buildingreliability function and likelihood function comprehensiveevaluation of new scheme is carried out Finally the validityof this method is verified by a case studyThe structure of thispaper is as follows the second part is related work the thirdpart is an introduction toDempster-ShaferTheory the fourthsection is the establishment of the evaluation model and thefifth section is case study

2 Related Work

NPD is the foundation for enterprises to survive and developTherefore a key task for top management is to chooseappropriate new products When evaluating product planstop management should take many factors into considera-tion and prediction such as market trend product marketcompetitiveness product cost and technical requirementsThe work of new product evaluation is very importantand complex for enterprises It is also an important topicfor researchers Therefore many researchers have proposeddifferent tools or methods to evaluate new product schemes

(i) Risk assessment Katie et al [1] proposed a riskidentification framework from system perspectiveswhich can be used to assess risks quantitatively of newproducts Patil et al [2] predicted business risks at thebeginning of new product design and established arisk framework Fang and Marle [3] designed a wayto identify inherent risks and cross risks of projectsaccording to the direction of risk communicationMohit [4] designed a risk network corresponding todifferent functional organizations based on Bayesiannetwork method to measure risks of all new projects

(ii) Key factors Kim et al [5] summarized key factors inNPD by studying cases of developing new productsin virtual teams of SME Cooper et al [6] identified

the critical factors that set the most successful firmsapart from their competitors by benchmarking at thecompany or macro level to ensure that resources areallocated appropriately Lam et al [7] used AHP tostudy the most important 13 factors in the processof new product development from the perspectiveof conflict management Cunha [8] studied the keysuccess factors by summarizing the empirical andconceptual studies of NPD in the past 30 years

(iii) Quality function deployment (QFD) Lowe et al [9]developed a new product evaluation tool based onQFD to evaluate potential products for an innovativemetal forming process Hanumaiah et al [10] builta rapid hard tooling process selection though QFDand AHP methodology Lee [11] selected the criticalfactors though Fuzzy Delphi method and constructedhouses of quality for QFD in NPD Zhang Xuefeng[12] proposed an integrated approach based on QFDandDEA to ensure user collaboration which has beenrecognized as a critical factor in successful productdevelopment Yu L Wang L and Bao Y [13] proposeda new product evaluation approach based on QFDintegrated IVIF and CI

(iv) Artificial neural networkThieme et al [14] evaluatedand chose the new plan by constructing the neuralnetwork model HO and Tsai [15] proposed a newmethod based on structural equation model (SEM)and adaptive neural fuzzy inference system (ANFIS)to predict the effect of value process quality on theperformance of NPD

(v) AHPANP and TOPSIS Lin et al [16] constructeda method based on AHP and TOPSIS to identifycustomer requirements and design features so asto evaluate design schemes Shyur et al [17] usedANP to determine evaluation criteria and weightsand used the improved TOPSIS to arrange alter-native designs Chiuh et al [18] presented a fuzzyanalytic network process (FANP) for solving theproduct selection Akkaya et al [19] constructed anewmethod based on fuzzy AHP and fuzzyMOORAfor industrial engineering sector choosing problemJoshi and Kumar [20] held that in the process ofgroup decision-making the interaction of decisioncriteria and concept uncertainty has a great influenceon the membership function

(vi) Fuzzy set When hen solving the optimal new prod-uct plan some attributes are hard to be expressednumerically Many scholars have adopted fuzzy setsfor example Carrera Diego A et al [21] and Chen HH et al [22] On the basis of considering the favorableand unfavorable factors Lin and Yang [23] calculatedthe fuzzy attractiveness and determined portfolioselection problems Kit et al [24] proposed a for-ward selection based on fuzzy regression (FS-FR) tocorrelate engineering characteristics with consumerpreferences regarding a new product Buyukozkan G












m (A) = 1 (2)

m (A) gt 0 (3)




Bel (A) = sumBsubeA

m (B) (4)



m (B) (5)



Ksum



















lowastＣ


lowastＣ


rank

plausibility














)]]]]] (9)





am1015840


(10)


n )= ( nsumj=1am1015840

1j

nsumj=1am1015840


nj ) (11)



n )= ( 120596m1sumn

i=1 120596mi

120596m2sumn

i=1 120596mi


i=1 120596mi) (12)


(AWm)in120596m

i(13)


CR = CIRI

(14)






n 1 2 3 4 5 6 7 8 9 10 11RI 0 0 058 09 112 124 132 141 145 149 151







K= 04 lowast 03033 = 03636



K= 03 lowast 035033 = 03182

(16)
















x10158401015840ij = 1 minus x1015840ij (20)
















m (Qir) (24)



m (Qir) (25)



















5 Case Study











schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018



















m (A) = 1 (2)

m (A) gt 0 (3)




Bel (A) = sumBsubeA

m (B) (4)



m (B) (5)



Ksum



















lowastＣ


lowastＣ


rank

plausibility














)]]]]] (9)





am1015840


(10)


n )= ( nsumj=1am1015840

1j

nsumj=1am1015840


nj ) (11)



n )= ( 120596m1sumn

i=1 120596mi

120596m2sumn

i=1 120596mi


i=1 120596mi) (12)


(AWm)in120596m

i(13)


CR = CIRI

(14)






n 1 2 3 4 5 6 7 8 9 10 11RI 0 0 058 09 112 124 132 141 145 149 151







K= 04 lowast 03033 = 03636



K= 03 lowast 035033 = 03182

(16)
















x10158401015840ij = 1 minus x1015840ij (20)
















m (Qir) (24)



m (Qir) (25)



















5 Case Study











schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018










Bel (A) = sumBsubeA

m (B) (4)



m (B) (5)



Ksum



















lowastＣ


lowastＣ


rank

plausibility














)]]]]] (9)





am1015840


(10)


n )= ( nsumj=1am1015840

1j

nsumj=1am1015840


nj ) (11)



n )= ( 120596m1sumn

i=1 120596mi

120596m2sumn

i=1 120596mi


i=1 120596mi) (12)


(AWm)in120596m

i(13)


CR = CIRI

(14)






n 1 2 3 4 5 6 7 8 9 10 11RI 0 0 058 09 112 124 132 141 145 149 151







K= 04 lowast 03033 = 03636



K= 03 lowast 035033 = 03182

(16)
















x10158401015840ij = 1 minus x1015840ij (20)
















m (Qir) (24)



m (Qir) (25)



















5 Case Study











schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018


















)]]]]] (9)





am1015840


(10)


n )= ( nsumj=1am1015840

1j

nsumj=1am1015840


nj ) (11)



n )= ( 120596m1sumn

i=1 120596mi

120596m2sumn

i=1 120596mi


i=1 120596mi) (12)


(AWm)in120596m

i(13)


CR = CIRI

(14)






n 1 2 3 4 5 6 7 8 9 10 11RI 0 0 058 09 112 124 132 141 145 149 151







K= 04 lowast 03033 = 03636



K= 03 lowast 035033 = 03182

(16)
















x10158401015840ij = 1 minus x1015840ij (20)
















m (Qir) (24)



m (Qir) (25)



















5 Case Study











schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018










n 1 2 3 4 5 6 7 8 9 10 11RI 0 0 058 09 112 124 132 141 145 149 151







K= 04 lowast 03033 = 03636



K= 03 lowast 035033 = 03182

(16)
















x10158401015840ij = 1 minus x1015840ij (20)
















m (Qir) (24)



m (Qir) (25)



















5 Case Study











schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018










x10158401015840ij = 1 minus x1015840ij (20)
















m (Qir) (24)



m (Qir) (25)



















5 Case Study











schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018





















5 Case Study











schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018














schemes with equal






EndEnd

NO

NO

parallYES

fid

YES


１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ

１lowastＣ



A1 =((((((((

1 12 13 12 12 1 12 1 23 2 1 1 32 1 1 1 21 12 13 12 1))))))))

A2 =(((((((

1 3 1 3 213 1 12 1 121 2 1 2 113 1 12 1 1212 2 1 2 1)))))))

A3 =((((((((

1 12 2 12 12 1 3 1 212 13 1 12 122 1 2 1 21 12 2 12 1))))))))

A4 =((((((((

1 12 12 13 122 1 1 12 122 1 1 12 123 2 2 1 13 2 2 1 1))))))))

(28)




w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018










w1 = 009w2 = 017w3 = 020w4 = 037w5 = 017

(29)






010203040506

0807

091

(0509)

y=09

045 05 055 060403503







6 Conclusions











y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018

















y=09X=059y=08

010203040506

0807

091

045 05 055 06 065 0704

(05909)

(05908)





y=09X=059y=08

045 05 055 06 065 0704

010203040506

0807

091

(05909)

(06108)






Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018









Table9Pre-processin

gresulttable

Indictor

C 1C 2

C 3C 4

C 5Ex

pert

AB

AB

AB

AB

AB

Scheme1

[071086]

[057071]

[0012]

[00][0220

33]022

[0881]

0880

0Scheme2

[071086]

[043057]

[05062]

062[0670

78]067

[05063]

05[0012

]012

Scheme3

[029043]

[029029]

[08701]

[087087]

[078089]

089[0250

38]025

[05062]

062Scheme4

[0861]

[071086]

[05062]

[03705]

[056067]

[067078]

[075088]

[063075]

012[0120

25]Scheme5

[0861]

[0861]

025[0120

25]022

[022033]

[075088]

[075088]

06205

Scheme6

[0014]

[014014]

[075087]

[075087]

[0011]

011[0881

][0750

88]0

[0012]

Scheme7

[029043]

[043057]

[075087]

[075075]

[056067]

[067078]

[05063]

[03805]

[05062]

[062075]

Scheme8

[071086]

[0861]

[05062]

[062075]

089[0780

89][0380

5][0506

3][0750

87][0871

]Scheme9

[0014]

[014029]

[05062]

[03705]

[056067]

[056067]

[013025]

013[0506

2][0370

5]Scheme10

[029043]

[014029]

087[0750

87][0891

][0780

89][0013

]0

[03705]

[03705]















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018






















Data Availability




Acknowledgments


References




















































Journal of












Journal of







Volume 2018






Volume 2018























































Journal of












Journal of







Volume 2018






Volume 2018








A Group Decision-Making Approach Based on DST and AHP for … · 2019. 7. 30. · ResearchArticle A...

Documents

Transcript of A Group Decision-Making Approach Based on DST and AHP for … · 2019. 7. 30. · ResearchArticle A...