Knowledge-Based Systems 66 (2014) 210–220

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Knowledge-Based Systems

journal homepage: www.elsevier .com/locate /knosys

An investment evaluation of supply chain RFID technologies: A groupdecision-making model with multiple information sources

http://dx.doi.org/10.1016/j.knosys.2014.05.0120950-7051/� 2014 Elsevier B.V. All rights reserved.

⇑ Tel.: +886 3 4361070x5616; fax: +886 3 4373959.E-mail address: sjchuu@tiit.edu.tw

Shian-Jong Chuu ⇑Department of Business Administration, Taoyuan Innovation Institute of Technology, 414, Sec. 3, Chung-Shang E. Rd., Chungli, Taoyuan 320, Taiwan

a r t i c l e i n f o a b s t r a c t

Article history:Received 24 September 2013Received in revised form 4 May 2014Accepted 7 May 2014Available online 14 May 2014

Keywords:Radio frequency identificationSupply chain managementGroup decision-making2-Tuple linguistic representationMaximum entropy ordered weightedaveraging

Selection of radio frequency identification (RFID) technology is important to improving supply chaincompetitiveness. The objective of this paper is to develop a group decision-making model using fuzzymultiple attributes analysis to evaluate the suitability of supply chain RFID technology. Since numerousattributes have been considered in evaluating the RFID technology suitability, most information availablein this stage exhibits imprecise, subjective and vague. Fuzzy set theory appears as an essential tool to pro-vide a decision framework for modeling imprecision and vagueness inherent in the RFID technologyselection process. In this paper, a fuzzy multiple attributes group decision-making algorithm using theprinciples of fusion of fuzzy information, 2-tuple linguistic representation model, and maximum entropyordered weighted averaging operator is developed. The proposed method is apt to manage evaluationinformation assessed using both linguistic and numerical scales in group decision making problem withmultiple information sources. The aggregation process is based on the unification of fuzzy information bymeans of fuzzy sets on a basic linguistic term set. Then, the unified information is transformed into lin-guistic 2-tuple in a way to rectify the problem of loss information of other fuzzy linguistic approaches.The proposed method can facilitate the complex RFID technology selection process and consolidateefforts to enhance group decision-making process. Additionally, this study presents an example usinga case study to illustrate the availability of the proposed method and its advantages.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

As competition intensifies and markets become global, organi-zations have begun to realize that improving efficiencies withinan organization is insufficient, and their whole supply chain mustbe made competitive [30,40]. Generally, a supply chain is a net-work of suppliers, manufacturers, distributors, and retailersinvolved in creating a product/service and then moving it the con-sumer, and involves the complex flow of materials, products, ser-vices, information, and money across multiple functional areaswithin and among the complex hierarchies of the participatingenterprises. Radio frequency identification (RFID) is an emergingtechnology that is increasingly being used in supply chain manage-ment [62]. RFID technology is the most cutting edge technology forsupply chain integrity and traceability [26]. RFID technology showsgreat potential for process improvement and cost reduction relatedto supply chain management [28]. Supply chain RFID technology isan emerging application that has attracted a lot of attention fromresearchers and practitioners in the US, Europe, and Asia [28,45].

Selecting a suitable RFID technology is important for supply chainswhen making capital investment decisions to improve theirperformance.

RFID has been identified as one of the ten greatest contributorytechnologies of the 21st century [5]. RFID is a wireless automaticidentification, data collection and storage technology which ismainly consists of three components: tags, readers, and middle-ware that bridges RFID hardware and enterprise applications. AnRFID tag consists of an integrated circuit chip that stores identifica-tion data of the item to which it is attach, connected with anantenna to transmit this data via radio waves. RFID tags can beactive (with batteries) or passive (without batteries). An RFIDreader is a device that emits radio signals and collects data aboutthe item from the compatible tag. The reader then converts theradio waves returned from the tag into digital data and forwardsthem to a computer system [46]. A reader can scan an area forany tags that are tuned to the same frequency as the reader.Through radio waves, RFID technologies provide a real-time com-munication with numerous objects at the same time at a distance,without contact or direct line of sight [14,42]. These advancedidentification and communication characteristics of RFID can sup-port real-time control of goods in the supply chain including raw

S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220 211

materials, work in process, and finished goods, thus enhancingsupply chain visibility. The enhanced supply chain visibility leadsto reduced stock-out, lower labor costs, reduced transaction costs,and improved inventory management in their supply chains [48].The contribution of RFID to supply chain is not only in increasingthe efficiency of systems but also in supporting the reorganizationof the systems that become more efficient [42].

Despite the promising applications of RFID in supply chainmanagement, a number of challenges have hampered the adoptionof RFID: technology challenges, standard challenges, patent chal-lenges, cost challenges, infrastructure challenges, return on invest-ment challenges, and barcode to RFID migration challenges [55]. Inpractice, while some organizations that adopt these technologiesreport reaping considerable benefits, others have been less suc-cessful, which indicates that RFID investment remains promisingbut high risky [42]. Costs remain the largest impediment for thewidespread adoption of RFID [55]. Furthermore, the rapid growthof the RFID industry is now creating problems. There are alsonumerous different RFID systems obtained by combining differenttypes and number of tags, frequencies and readers, tagging levels,open/closed loops, environment sensors. The costs and potentialbenefits of these technologies vary in a wide range [42]. Prospec-tive firms now face the situation of having to decide among severalRFID technologies, all of which are capable of performing a specifictask. The development of appropriate assessment approaches iscrucial to ensuring that each RFID project is assessed from the per-spective of all benefits and costs. Many reviews have revealed dif-ficulties in justification of the RFID investment using traditionaleconomic technology [28,29], and a few existing methodologieshave provided satisfactory solutions [28,50].

Since RFID technology has recently received an emerging atten-tion, there is a growing literature on RFID technology. Manyreviews have considered RFID technology, management issues inRFID applications, functionality of RFID, major application of RFID,privacy and security, challenges to RFID adoption, RFID technolo-gies in supply chains [5,31,35,42,55,62]. However, the literatureon RFID applications in supply chains is limited, and most of theexisting studies were published in the last few years [42]. Rela-tively new to the field, numerous precision-based methods of RFIDtechnology evaluation have recently been developed. These justifi-cation techniques are classified into analytical models, simulationmodels, cases studies and experiments [42]. The challenge forthese methods is that the treatment of qualitative effects beingbased on crisp evaluation, i.e., the evaluation values must be pre-cise. However, in real life, the assessments of performance ratingsfor subjective attributes (or the importance grades of all attributes)are generally expressed via fuzzy linguistic assessment [59]. There-fore, the primary problem of the above methods is that they arebased on accurate measurement and crisp evaluation.

Classical methods of solving supply chain RFID technologyselection problems cannot effectively handle problems involvingimprecise, subjective and vague information. In fact, most deci-sion-makers (or experts) view performance ratings for subjectiveattributes as linguistic labels, such as high, middle, and low. SinceZadeh [58] introduced fuzzy sets theory to deal with vaguenessproblems, linguistic terms have been used in approximate reason-ing within the fuzzy framework to handle imprecise data andvague linguistic expression. Several researchers have utilized fuzzysets theory for supply chain RFID investment evaluation problems.Kim et al. [23] proposed a genetic algorithm based on fuzzy cogni-tive map weight learning method. The proposed method used toimplement forward analysis (what–if analysis) and backward anal-ysis (cause analysis) in a simulated RFID-enabled supply chainenvironment. Lin [32] identified the key factors of RFID technologydevelopment in the logistics and supply chain management. Thefuzzy Delphi and fuzzy analysis hierarchy process methods are

adopted in this research. Lee and Lee [28] proposed a normativeinvestment evaluation model for supply chain RFID technologies,which capture intangible benefits and integrate them into theobjective function. Trappey et al. [47] proposed a hybrid qualitativeand quantitative approach to model and evaluate the performanceof RFID-enabled reverse logistic operations. The proposed methodapplied fuzzy cognitive maps and genetic algorithm to construct areverse logistics network decision model and assign weights,respectively. Ustundag et al. [50] proposed a systematic frameworkof the economic analysis for RFID investment. In this method, fuzzyrule-based system and Monte-Carlo simulation method are used todetermine the revenue increase and expected net present value ofan RFID investment, respectively. Moreover, Lee and Lee [29] pre-sented the fuzzy real option model to evaluate RFID adoption in thesupply chain, in which the present values of expected cash flowsand expected costs are estimated by trapezoidal fuzzy numbers.Qu et al. [41] proposed a Markov chain model for quantifying thevalue of RFID in hospital equipment tracking, which estimatesthe benefit of RFID at item level. However, these methods allowthe group decision-making scenario to be ignored, which determanagement from using fuzzy multiple attributes analysis. Ideally,groups should be able to achieve better decisions than individualsbecause of having greater collective knowledge. Therefore, thispaper proposed a group decision-making model for resolving sup-ply chain RFID investment evaluation problems.

The remainder of this paper is organized as follows. In Section 2we provide a methodological perspective focused on methods usedin supply chain RFID technology selection, and introduce somebasic definitions notations of fuzzy numbers, linguistic assess-ments, 2-tuple linguistic representation and operation, respec-tively. Section 3 then presents a fuzzy fusion method. A fuzzymultiple attribute group decision-making model for evaluatingan appropriate RFID is proposed in Section 4. The process aggre-gates each parameter assessed by an individual, and aggregatesthe results to determine the final ranking order. In Section 5, anexample using a case of Taiwanese bicycle manufacturers is usedto illustrate the computational process of the proposed method.Finally, the last section concludes this research.

2. Preliminaries

This section presents a methodology of supply chain RFID tech-nology selection, some basic definitions and concepts of fuzzynumbers, linguistic assessments, and 2-tuple fuzzy linguistic rep-resentation and operation, respectively. These definitions and con-cepts will be used throughout the paper, unless stated otherwise.

2.1. Supply chain RFID technology selection methodology

From a methodological perspective, the supply chain RFID tech-nology selection problem is a fuzzy multiple attribute and groupdecision-making problem involving the consideration of fuzzyassessments and the opinions of multiple decision makers (orexperts). In the supply chain RFID selection decision problem,numerous effects (attributes) must be considered in justifying aparticular supply chain RFID technology [24,32]. Using RFID as anexemplar technology, Bunduchi et al. [4] presented that the magni-tude of benefits and costs associated with technological processinnovation adoption within different industries varies as technol-ogy diffuses beyond early adopters to the early majority. These fac-tors are classified into subjective and objective attributes, also seenin Kim and Garrison [24], Lee and Lee [28], Lin [32], Ustundag et al.[50]. Objective attributes are defined by using appropriate numer-ical terms, such as investment cost and cost reduction, used forassessing the quantitative effects of RFID technology. Since precise

212 S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220

quantitative information may not be available or computationalcosts may be excessively high, these expert identified performanceratings can be ‘approximate numerical values’, which can beexpressed by sentences such as ‘approximately equal to’, ‘at least’,or ‘approximately between’ [50]. Subjective attributes have qualita-tive definitions, e.g. process visibility, product traceability, etc.,used for assessing the qualitative effects of RFID technology, whichmay be unquantifiable due to the nature of such technology. Expertopinions can be represented linguistically, using terms such as‘high’, ‘middle’, or ‘low’. Consequently, with respect to multipleattribute analysis, appropriate RFID technology selection is difficultto synthesize. To improve the quality of decisions in fuzzy environ-ments, contemporary organizations prefer group decision-making.Group decision-making is a typical decision-making activity whereseveral experts are utilized alleviate some of the decision-makingdifficulties due to the problem’s complexity and uncertainty [60].

Obviously much real world knowledge is fuzzy rather than pre-cise. In RFID technology selection problems, assessment dataemployed in multiple attributes analysis are generally fuzzy lin-guistic, numerical, or some mixture of thereof. Hence, a usefuldecision-making model is to provide the ability to handle multiplefuzzy assessments, that is, by aggregating the opinions of multipleexperts. This study attempts to establish a useful group decision-making model by using fuzzy multiple attributes analysis toimprove the supply chain RFID technology selection process. Inorder to effectively avoid the loss and distortion of fuzzy informa-tion, we propose a group decision-making algorithm based onfusion method of fuzzy information, 2-tuple fuzzy linguistic repre-sentation model, and maximum entropy ordered weighted averag-ing (MEOWA) operators.

Fusion method of fuzzy information is proposed by Herreraet al. [16]. The method is used to manage information assessedusing different linguistic scales in a decision making problem withmultiple information sources. Chuu [7] has developed a fusionmethod of fuzzy information assessed using both linguistic andnumerical scales. Dursun and Karsak [10] also proposed an aggre-gation process based on the unification of information by means offuzzy sets on a basic linguistic term set. Then, the unified informa-tion is transformed into linguistic 2-tuples in a way to manageinformation assessed using both linguistic and numerical scalesin a decision making problem with multiple information sources.More recently, Dursun and Karsak [11] presented a fuzzy weightedaverage method for the fusion of imprecise and subjective informa-tion expressed as linguistic variables or fuzzy numbers.

The 2-tuple fuzzy linguistic representation model that was pro-posed by Herrera and Martinez [17] is based on the concept ofsymbolic translation. It is used for representing the linguisticassessment information by means of a 2-tuples, which are com-posed of a linguistic term and a numerical value. The main advan-tage of this representation is to be continuous in its domain.Therefore, it can express any counting of information in the uni-verse of the discourse. In recent past, several studies have usedthe 2-tuple linguistic representation model. Fan et al. [12] pro-posed a fuzzy linguistic approach based on 2-tuple linguistic repre-sentation model to evaluate the knowledge managementcapability in a fuzzy environment. Dursun and Karsak [10] devel-oped a fuzzy multi-criteria decision making algorithm using theprinciples of fusion of fuzzy information, 2-tuple linguistic repre-sentation model, and technique for order preference by similarityto ideal solution (TOPSIS) for personal selection. Wang [51] hasproposed a fuzzy linguistic computing approach based on 2-tuplefuzzy linguistic information to evaluate the supplier performance.Lately, Ju et al. [19] proposed a hybrid fuzzy method consistingfuzzy analytical hierarchy process (AHP) and 2-tuple fuzzy linguis-tic approach to evaluate emergency response capacity. Wei andZhao [53] developed some dependent 2-tuple linguistic aggrega-

tion operators, in which the associated weights only depend onthe aggregated 2-tuple linguistic arguments, and then apply themto develop some approaches for multiple attribute group decisionmaking. Ko [25] developed an failure modes and effects analysisbased on 2-tuple linguistic representation approach to treat theassessments of the three risk indices: severity, occurrence, anddetectability. Park et al. [39] developed some 2-tuple linguisticharmonic operators, which can be utilized to aggregate preferenceinformation taking the form of linguistic variables, and their appli-cations in multiple attribute group decision making. Doukas et al.[8] also proposed a fuzzy method consisting TOPSIS and 2-tuplefuzzy linguistic approach for assessing companies’ energy andenvironmental policies.

The ordered weighting averaging (OWA) operators introducedby Yager [56] provide a family of aggregation operators lyingbetween the ‘and’ requiring all the criteria to be satisfied, and the‘or’ requiring at least one of the criteria to be satisfied. With respectto the OWA operator weights, Yager [56] also provided two mea-sures, namely ‘orness’ and ‘dispersion (or entropy)’. The orness is avalue that lies in [0,1], and measures the degree to which theaggregation resembles an ‘or’ operation, and can be considered agauge of decision-maker optimism. The more closely the ornessof an OWA operator approaches the ‘or’ operator, the more theoptimistic decision-maker is about obtaining the best solution.The dispersion measures the degree to which all the aggregatesare equally used. In the framework of multiple attribute groupdecision-making under uncertainty, the OWA operators can beprovided for aggregating the attributes (or experts) associated withsome fuzzy linguistic quantifiers [20], such as ‘as many as possible’,‘most’, ‘average’, ‘almost all’ and ‘at least half’, used to determine theweights. To determine OWA operator weights, O’Hagan [36] devel-oped a maximum entropy approach, which formulates the problemas a constraint nonlinear optimization model with a predefineddegree of orness as its constraint and the entropy as its objectivefunction. The resultant weights and OWA operators are termedthe maximum entropy weights and MEOWA operators, respec-tively. Filev and Yager [13] examined the analytical properties ofMEOWA operators and proposed a two-step process for obtainingthe maximum entropy weights that generate some prescribedorness without having to solve the constraint nonlinear optimiza-tion problem. In practice, Chuu [6] proposed a fuzzy multi-attri-bute decision-making model based on MEOWA operators forevaluating manufacturing flexibility. Mitchell and Estrakh [34] pre-sented an application of MEOWA operators to lossless image com-pression, and found maximum entropy weights to be effective.

2.2. Fuzzy numbers

Fuzzy numbers are very useful in improving information repre-sentation and processing in a fuzzy environment. The most com-monly used fuzzy numbers are triangular and trapezoidal fuzzynumbers. Trapezoidal (or triangular) fuzzy numbers have beenused to characterize linguistic terms (or approximate numericalvalues) used in approximate reasoning. It is obvious that triangularfuzzy numbers are special cases of trapezoidal fuzzy numbers [15].In this paper, trapezoidal fuzzy numbers are chosen for applicationconsidering their intuitive representation, ease in computation,and good enough to capture the vagueness of fuzzy assessment[21,29,37,50]. A real fuzzy number A be a special fuzzy subset ofreal number R with membership function lA(x), which is a contin-uous mapping from R to the closed interval [0,1], and has the fol-lowing properties with �1 < n1 6 n2 6 n3 6 n4 <1 where n1, n2,n3 and n4 are real numbers [9]:

1. lA (x) = 0, for all x 2 (�1, n1] and [n4, 1).2. lA (x) is strictly increasing on [n1, n2].

S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220 213

3. lA (x) = 1, for all x 2 [n2, n3].4. lA (x) is strictly decreasing on [n3, n4].

In this paper, it is assumes that A is convex, normal andbounded, i.e. n1 > �1, n4 <1 and a trapezoidal fuzzy numberA = (n1, n2, n3, n4) is represented by the membership function lA

(x) given below, where n1, n2, n3 and n4 are real numbers [3]

lAðxÞ ¼

ðx� n1Þ=ðn2 � n1Þ; n1 6 x 6 n2;

1; n2 6 x 6 n3;

ðx� n4Þ=ðn3 � n4Þ; n3 6 x 6 n4;

0; otherwise:

8>>><>>>:

ð1Þ

with 0 6 n1 6 n2 6 n3 6 n4. The x in interval [n2, n3] yields the max-imal grade of lA (x), i.e., lA(x) = 1, which is the most likely value ofthe evaluation data. Meanwhile, the n1 and n4 comprise the lowerand upper limits of the available area for the evaluation data,respectively, which are used to reflect the fuzziness of the assess-ment data.

Some basic arithmetic operations on positive trapezoidal fuzzynumber A1 = (a1, b1, c1, d1), where 0 6 a1 6 b1 6 c1 6 d1, andA2 = (a2, b2, c2, d2), where 0 6 a2 6 b2 6 c2 6 d2, can be shown as fol-lows [22]:

1. Addition:

A1 � A2 ¼ ða1 þ a2; b1 þ b2; c1 þ c2;d1 þ d2Þ: ð2Þ

2. Subtraction:

A1HA2 ¼ ða1 � d2; b1 � c2; c1 � b2; d1 � a2Þ: ð3Þ

3. Multiplication:

A1 � A2 ffi ða1a2; b1b2; c1c2;d1d2Þ: ð4Þ

4. Division:

A1/A2 ffi ða1=d2; b1=c2; c1=b2;d1=a2Þ: ð5Þ

Note that the results of Eqs. (4) and (5) are not trapezoidal fuzzynumbers, trapezoidal fuzzy number approximations can be usedfor many practical applications [3,22].

2.3. Linguistic assessments

The linguistic assessment is an approximate method based onlinguistic variables. A linguistic variable is a variable whose valuesare not numbers but rather words or sentences in a natural or arti-ficial language [63]. For example, ‘important’ is a linguistic termwhose values are ‘high’, ‘middle’, ‘low’, etc. Linguistic values can alsobe defined by fuzzy numbers. The concept of linguistic variables isvery useful in dealing with decision situations, which are too com-plex or ill-defined to be described in conventional quantitativeexpressions [59]. However, in the real world, the fuzzy linguisticapproach is appropriate for application to many decision situa-tions; that is, while decision makers cannot generally specify pre-cise numerical values, they can take the form of linguistic variablesor fuzzy numbers for several reasons. First, a decision should bemade to experience time pressure and lack of knowledge or data[52]. Second, numerous attributes are subjective or intangibleowing to being unquantifiable in nature [59]. Third, as for objectiveattributes, precise quantitative or non-monetary information maynot be stated because it is either unavailable or too costly to com-pute [16, p. 43]. This approach allows the representation of expertinformation more directly and adequately [16, p. 45].

Lately, Zhang [60] has presented a 2-tuple linguistic informa-tion representation model with the traditional TOPSIS for evaluat-

ing computer network security systems. Aydin et al. [1] proposedan integrated approach based on fuzzy AHP and European Founda-tion for Quality Management model to evaluate the business per-formance excellence. Ju et al. [19] proposed a hybrid fuzzyapproach to evaluate emergency response capacity. The proposedmethod uses fuzzy AHP to determine the weights of criteria, andtakes advantage of 2-tuple linguistic representation approach tocompute the overall emergency response capacity of the emer-gency alternative. Kutlu and Ekmekcioglu [27] proposed a fuzzyapproach for failure modes and effects analysis by applying fuzzyTOPSIS integrated fuzzy AHP. Wu [54] has presented a fuzzy deci-sion making trial and evaluation laboratory (DEMATEL) method tosegment the critical factors for successful knowledge managementimplementations. Zhang and Guo [61] proposed a method to solvemulti-granularity uncertain linguistic group decision making prob-lems with incomplete weight information based on trapezoidalfuzzy numbers and two optimization models. Shen et al. [43] pro-posed a fuzzy multi criteria decision making approach based onfuzzy TOPSIS for green supplier selection and evaluation. Yue[57] has proposed an approach to partner selection with linguisticvalues and intuitionistic fuzzy information under a group decision-making environment. Doukas et al. [8] presented a methodologicalmulti-criteria framework based on 2-tuple TOPSIS method, usinglinguistic variables, for assessing companies’ energy and environ-mental policies. Orduna et al. [38] developed a color image seg-mentation algorithm using the decision-making based onlinguistic 2-tuple. Therefore, the fuzzy linguistic approach is usedin different fields, and decision-making includes numerousapproaches based on linguistic information.

In applying a fuzzy linguistic approach to supply chain RFIDselection, since numerous attributes have been considered in eval-uating RFID suitability, these attributes can be identified by consid-ering specific supply chain requirements. In general, the attributesare classified as subjective and objective. For each subjective attri-bute, expert opinions regarding individual alternative can be lin-guistic terms (labels), which are characterized by trapezoidalfuzzy numbers. For objective attributes, expert opinions areexpressed as approximate numerical values characterized withtrapezoidal fuzzy numbers.

In order to establish the decision matrix for each expert, agroup of experts express their opinions (or preferences) for eachalternative with respect to each attribute. These opinions can beobtained by direct assignment in utility functions, and can belinguistic terms or approximate numerical values. With respectto each alternative, the performance ratings and importancegrade for each subjective attribute should be rated scored on alinguistic term set (or linguistic scale). The strongest assessmentis assigned the highest (or lowest) term ‘Definitely high’ (or ‘Def-initely low’) on a linguistic scale. The elements of the term setdetermine the granularity of the uncertainty. Furthermore, letS = {s0, s1, . . . , sT} be a finite and totally ordered term set with anodd cardinal, where the middle term represents ‘average’, i.e., aprobability of ‘approximately 0.5’, and the remaining terms areordered symmetrically around it, and exhibit the following prop-erties [16, p. 46].

1. The set is ordered: si = sj if i = j.2. The negation operator is defined as Neg(si) = sj such that

j = T � i.3. The maximization operator is Max(si, sj) = si if si = sj.4. The minimization operator is Min(si, sj) = si if si 5 sj.

For example, a linguistic scale S1 comprising seven terms couldbe represented as follows:

S1 ¼ fs0 ¼ DL; s1 ¼ VL; s2 ¼ L; s3 ¼ M; s4 ¼ H; s5 ¼ VH; s6 ¼ DHg

214 S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220

where DL = Definitely Low, VL = Very Low, L = Low, M = Middle,H = High, VH = Very High, DH = Definitely High.

As mentioned above, Mata et al. [33] proposed an adaptive con-sensus support system model for multi-granular fuzzy linguisticgroup decision-making problems that improves the convergencerate toward the consensus, and therefore decrease the number ofrounds to achieve it. It consists of four phases: making the informa-tion uniform, computing the consensus degree and control of theconsensus process, adaptive search for preference, and productionof advice. With respect to those presented in Mata et al. [33], theproposed method is limited in that it uses an appropriate linguisticscale chosen by experts using qualitative assessment versus sub-jective attributes. Future studies should focus on more detailed lin-guistic information about subjective attributes that could beevaluated by multi-granular linguistic information, and moreeffective consensus reaching process.

2.4. 2-Tuple fuzzy linguistic representation model

The semantics of the terms of the linguistic scale is provided byfuzzy numbers defined on the interval [0,1], which are character-ized by membership functions. The use of linguistic variablesincreases the flexibility and reliability of decision maker evalua-tions, but complicates the aggregation of the linguistic terms. Gen-erally, the approach for dealing with linguistic information can beclassified into two categories [17]. The first one is based on theextension principle. It makes operations on the fuzzy numbers thatsupport the semantics of the linguistic terms. The second one is thesymbolic method. It makes computations on the indexes of the lin-guistic terms. In both approaches, some results may not exactlymatch any of the initial linguistic terms, and then an approxima-tion process must be developed to express the result in the initialexpression domain. This produces the consequent loss of informa-tion and hence the lack of precision [2,12,17]. To preserve all thegiven information, Herrera and Martinez [17,18] develop a 2-tuplefuzzy linguistic representation model based on the symbolic trans-lation. The main advantage of this representation can be summa-ries as the continuous treatment of linguistic domain, and theminimization of the loss of information and thus the lack of preci-sion [10,12,51].

The 2-tuple fuzzy linguistic representation model is based onthe concept of symbolic translation [17,18]. It is used for represent-ing the linguistic assessment information by means of a 2-tuples(si, ai), where si is a linguistic term from predefined linguistic termset S and ai is the value of symbolic translation, and ai e [�0.5, 05).

Definition 1. Let S = {s0, s1, . . . , sT} be a linguistic term set andb 2 [0, T] be a value representing the result of a symbolicaggregation operation, then 2-tuple that express the equivalentinformation to b is obtained with the following function [17,18]:

D : ½0; T� ! S� ½�0:5;05Þ;

DðbÞ ¼si; i ¼ roundðbÞa ¼ b� i; a 2 ½�0:5;05Þ;

�ð6Þ

where round (�) is the usual round operation, si has the closest indexterm to b and a is the value of the symbolic translation.

Definition 2. Let S = {s0, s1, . . . ,sT} be a linguistic term set and (si, a)be a linguistic 2-tuple, then there exists a function D�1, such that,from a 2-tuple it returns its equivalent numerical value b2 [0,T] R. This function is defined as [17,18]

D�1 : S� ½�0:5;05Þ ! ½0; T�;D�1ðsi;aÞ ¼ iþ a ¼ b:

ð7Þ

Definition 3. The comparison of linguistic information repre-sented by 2-tuples is carried out according to an ordinary lexico-graphic order. Let (si, a1) and (sj, a2) be two linguistic 2-tuples,with each one representing a linguistic assessment [17]:

(1) If i < j then (si, a1) is smaller than (sj, a2).(2) If i = j then

(i) if a1 = a2 then (si, a1) and (sj, a2) represent the sameinformation.

(ii) if a1 < a2 then (si, a1) is smaller than (sj, a2).(iii) if a1 > a2 then (si, a1) is bigger than (sj, a2).

Definition 4. Let U = {u0, u1, . . . ,uG} be a fuzzy set defined in V,which is a basic linguistic term set. A transformation function vthat transforms U into a numerical value in the interval of granu-larity of V, [0, G] is defined as [18]

v : FðVÞ ! ½0;G�;

vðFðVÞÞ ¼ vðfðuj; v jÞ; j ¼ 0;1; . . . ;GgÞ ¼PG

j¼0j� ujPGj¼0uj

¼ c: ð8Þ

where F(V) is the set of fuzzy sets defined in V.

Definition 5. Let A = {(r1, a1), (r2, a2), . . . , (rn, an)} be a set of linguis-tic 2-tuples and an associated maximum entropy weighting vectorW = [w1

, w2, . . . ,wn

], with wi 2 [0, 1] and

Pni¼1wi = 1, then 2-tuple

MEOWA operation Ue is defined as

Ueððr1;a1Þ; ðr2;a2Þ; . . . ; ðrn;anÞÞ ¼ DXn

J¼1

wj D�1ðrrðjÞ;arðjÞÞ

!; ð9Þ

where (r(1), r(2), . . . ,r(n)) is the permutation of (1,2, . . . ,n), suchthat (rr(j), ar(j)) P (rr(j+1), ar(j+1)) for all j = 1, 2, . . . ,n � 1.

3. Fusion of fuzzy information

Numerous effects can be considered in evaluating the suitabilityof supply chain RFID technology. These effects in general are clas-sified into subjective and objective attributes. Subjective attributesare characterized by fuzzy linguistic assessments, and objectiveattributes are these that can be evaluated numerical scales. Inorder to ensure compatibility between approximate numerical val-ues and linguistic terms, this study presents a fusion method offuzzy information, which is performed in two phases:

1. Making the information uniform.2. Computing the collective information.

They are analyzed in the following subsections.

3.1. Making the information uniform

In order to manage the information assessed in multi-granular-ity linguistic term sets in decision making, Herrera et al. [16] pro-posed that the multi-granularity linguistic information is madeuniform using a basic linguistic term set (BLTS). Recently, in orderto handle the information assessed using both linguistic andnumerical scales, several studies have proposed that the informa-tion must be transformed (under a transformation function) intoa BLTS [7,10]. To ensure compatibility between approximatenumerical values and linguistic terms, all the fuzzy informationmust be transformed into a BLTS. Each assessment value is definedas a fuzzy set on the basic linguistic scale. With respect to the

S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220 215

assessments made by linguistic terms in the linguistic term set, letS = {s0, s1, . . . ,sT} and V = {v0, v1, . . . ,vG} be two linguistic term sets,such that G P T. A transformation function hSV is then defined as[16]:

hSV : S! FðVÞ;

hSV ðsiÞ ¼ fðuij; v jÞ=j 2 f0;1; . . . ;Ggg for si 2 S;

uij ¼maxx

minflsiðxÞ;lvjðxÞg; ð10Þ

where F(V) denotes the set of fuzzy sets defined in V, which is aBLTS, and lsi(x), lvj(x) represents the membership functions of thefuzzy sets associated with the terms si and vj, respectively.

As mentioned above, all the information sources using the samescale ([0,1]) are considered. Regarding the fuzzy assessmentsassessed by approximate numerical values, the transformationfunction also appropriately implemented to converting the stan-dardized fuzzy assessments, the ranges of which belong to [0,1],into a BLTS. The max–min operation has been used in hSV, becauseit is a classical tool for setting the degree of matching betweenfuzzy sets [63]. The following subsection presents how to obtainthe collective assessments for each attribute (or expert).

3.2. Computing the collective information

The converted information provided by an expert is defined asthe fuzzy set on the BLTS. The collection information of experts isthen obtained by aggregating these fuzzy sets. This informationis also a new fuzzy set defined on BLTS. This paper considers theMEOWA operator as the aggregation operator.

An MEOWA operator of dimension n is a mapping:

U : Rn ! R

which has an associated maximum entropy weighting vectorW = [w1

, w2, . . . ,wn

], with wi2 [0, 1] and

Pni¼1wi ¼ 1 such that

Uða1; a2; . . . ; anÞ ¼Xn

J¼1

wj bj; ð11Þ

where bj is the jth largest element in the collection {a1, a2, . . . ,an}.An algorithm for calculating W is as follows [6,13,20,56]:

Step1: Determine a non-decreasing proportional linguisticfuzzy quantifier Q for representing the fuzzy majority over deci-sion makers or attributes, as follows:

QðrÞ ¼0 if r < a;

ðr � aÞ=ðb� aÞ if a5r5b;

1 if r > b;

8><>: ð12Þ

Rit ¼

ðeit=lþt ; git=lþt ; hit=lþt ; lit=lþt Þ; t 2 sets of benefit� related objective attributes;i ¼ 1;2; . . . ;m; t ¼ 1;2; . . . ; s

ðe�t =eit ; e�t =git; e�t =hit ; e�t =litÞ; t 2 sets of cost� related objective attributes;

i ¼ 1;2; . . . ;m; t ¼ 1;2; . . . ; s

8>>><>>>:

ð17Þ

with a, b, re [0, 1]. For example, some non-decreasing propor-tional linguistic fuzzy quantifiers are typified by terms ‘most’,‘at least half’, and ‘as many as possible’, the respective parameters(a, b) of which are (0.3, 0.8), (0, 0.5) and (0.5, 1), respectively.Step 2: Compute the weighting vector W,

WðiÞ ¼ Qði=nÞ � Qðði� 1Þ=nÞ; for i ¼ 1;2; . . . ; n: ð13Þ

Step 3: Compute the orness value a,

a ¼Xn

i¼1

ðn� iÞWðiÞ !

=ðn� 1Þ: ð14Þ

Step 4: Compute the W, using the two-step process.4-1: Find one and only one positive solution h of the algebraicequation,

Xn

i¼1

ððn� iÞ=ðn� 1Þ � aÞhðn�iÞ ¼ 0: ð15Þ

4-2: Obtain W from the following equation, using b = (n � 1)lnh,

WðiÞ ¼ eb�ððn�iÞ=ðn�1ÞÞ=Xn

j¼1

eb�ððn�jÞ=ðn�1ÞÞ; for i ¼ 1;2; . . . ;n:

ð16Þ

4. Evaluating the suitability of supply chain RFID technology

This section presents a new supply chain RFID technology selec-tion method using 2-tuple linguistic representation model withMEOWA operators to overcome above problems. This methodenables the experts’ fuzzy assessments with the linguistic andnumerical information corresponding to subjective and objectiveattributes, respectively, can be considered in the aggregation pro-cess. The stepwise representation of the proposed evaluationapproach is given below, as shown in Fig. 1.

Step 1: Construct a decision-makers’ committee of K experts,and identify the alternatives available for consideration, andrequired selection attributes (subjective or objective) withtypes (cost or benefit) of them.Step 2: Determine the appropriate linguistic term set chosen byexperts using qualitative assessment versus subjective attri-butes, and identify the appropriate numerical scales usingquantitative evaluation versus objective attributes.Step 3: Construct the decision matrices for each expert thatdenote the important grades of attributes, the linguistic assess-ments corresponding to subjective attributes, and the appropri-ate numerical values corresponding to objective attributes forthe performance ratings of considered alternatives.Step 4: Normalize appropriated numerical values to obtainunit-free and comparable objective attribute values. The nor-malized values for appropriate numerical values regarding ben-efit-related as well as cost-related objective attributes arecalculated via a linear scale transformation as

where Rit denotes normalized values of Hit = (eit, git, hit, lit), which isappropriated numerical values assigned to alternative i withrespect to the objective attribute t by experts, m is the number ofalternatives, s is the number of objective attributes, and lt

+ =max ilit, et

� = minieit.Step 5: Considering the important grades of each attribute, cal-culate the weighted ratings of each alternative as

Fig. 1. Flow chart of supply chain RFID technology evaluation process.

216 S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220

Xijt ¼

Wjt�Rit ;t 2 sets of objective attributes; i¼ 1;2; . . . ;m;

j¼ 1;2; . . . ;n; t¼ 1;2; . . . ;sWjt�Rijt; t 2 sets of subjective attributes; i¼ 1;2; . . . ;m;

j¼ 1;2; . . . ;n; t¼ sþ1;sþ2; . . . ;k;

8>>><>>>:

ð18Þ

where Xijt is weighted ratings of alternative i with respect toexpert j and attribute t, and � denotes the fuzzy multiplicationoperator.Step 6: Convert the weighted ratings Xijt into the BLTS (V) byusing Eq. (10). The fuzzy assessment vector on V, (F(Xijt)), canbe represented as

FðXijtÞ ¼ ðuðXijt;v0Þ;uðXijt;v1Þ; . . . ;uðXijt; vGÞÞ;i ¼ 1;2; . . . ;m; j ¼ 1;2; . . . ; n; t ¼ 1;2; . . . ; k ð19Þ

Step 7: Aggregate F(Xijt) to yield the fuzzy assessment vector(F(XA(it))). The aggregated parameters obtained from the assess-ment data of n experts can be calculated by Eq. (11) as

XAðitÞðvyÞ ¼ UQ1ðuðXi1t; vyÞ;uðXi2t; vyÞ; . . . ;uðXint; vyÞÞ;i ¼ 1;2; . . . ;m; t ¼ 1;2; . . . ; k; y ¼ 0;1; . . . ;G ð20Þ

where UQ1 denotes the MEOWA operator with the maximumentropy weighting vector W1

, obtained from a fuzzy linguisticquantifier Q1, which represents the fuzzy majority over the nexperts. Then, the fuzzy assessment vector on V with respectto attribute Ct, F(XA(it)) is defined as

FðXAðitÞÞ ¼ ðuðXAðitÞ;v0Þ;uðXAðitÞ; v1Þ; . . . ;uðXAðitÞ;vGÞÞfor i ¼ 1;2; . . . ;m; t ¼ 1;2; . . . ; k ð21Þ

Step 8: Compute the cit values of alternatives with respect toattribute and transform these values into a linguistic 2-tuple,(vit, ait), by using Eqs. (8) and (6), respectively.Step 9: Aggregate (vit, ait) to yield the ranking index RIi of alter-native i. Using the concept of fuzzy majority over the attributesspecified by a linguistic quantifier Q2, and using the 2-tupleMEOWA operator associated with W2

, yields the RIi for alterna-tive i, by using Eq. (9), as follows:

Table 1The supply chain RFID technology selection attributes.

Objective attribute Type of assessment Type ofattribute

Importantgrade

Performancerating

C1: Investmentcosts

Linguistic Fuzzy Cost

($ � 10,000) (as approximately between)C2: Cost reductions Linguistic Fuzzy Benefit($ � 1000) (as approximately between)

Type of assessment

Subjective attribute Important grade Performance rating

C3: Operating efficiency Linguistic LinguisticC4: Accuracy Linguistic LinguisticC5: Visibility Linguistic LinguisticC6: Security Linguistic Linguistic

Fig. 2. Decision hierarchy of supply chain RFID technology evaluation problem.

Table 2Linguistic variables and fuzzy numbers of basic linguistic term set.

Linguistic variable Fuzzy number

v0: Definitely low (DL) (0.0, 0.0, 0.0, 0.1)v1: Extra low (EL) (0.0, 0.1, 0.1, 0.2)v2: Very low (VL) (0.1, 0.2, 0.2, 0.3)v3: Low (L) (0.2, 0.3, 0.3, 0.4)v4: Slightly low (SL) (0.3, 0.4, 0.4, 0.5)v5: Middle (M) (0.4, 0.5, 0.5, 0.6)v6: Slightly high (SH) (0.5, 0.6, 0.6, 0.7)v7: High (H) (0.6, 0.7, 0.7, 0.8)v8: Very high (VH) (0.7, 0.8, 0.8, 0.9)v9: Extra high (EH) (0.8, 0.9, 0.9, 1.0)v10: Definitely high (DH) (0.9, 1.0, 1.0, 1.0)

S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220 217

RIi ¼ UeQ2ððv i1;ai1Þ; ðv i2;ai2Þ; . . . ; ðv ik;aikÞÞ

¼ DXn

J¼1

wj D�1ðrrðjÞ;arðjÞÞ

!¼ vw

i ;awi

� �ð22Þ

where (r(1), r(2), . . . ,r(n)) is the permutation of (1,2, . . . ,n), suchthat (rr(j), ar(j)) P (rr(j+1), ar(j+1)) for all j = 1, 2, . . . ,n � 1.Step 10: Rank alternatives according to RIi values in descendingorder. Identify the alternative with the highest RIi as the bestalternative.Step 11: Decision analysis. According to a group of experts ana-lyze the evaluation results, the process has to go back the initialstages or has to accept the evaluation.

5. Illustrative example

In this section, the proposed methodology is applied to the caseof a G-company in the bicycle industry. The G-company has beenin operation for 40 years, employs approximately 2000 employees,as well as its group revenues are approximately $130 million. Gen-erally, a bike product consists of 11 subsystems including a frame,suspension fork, derailleur shifters, brokers, hubs and rims, tires,pedals, handle bar, stem, saddle, and seat post. Each subsystemhas several models that customers can select. Thus a bicycle supplychain comprises bicycle parts suppliers, a bicycle assembly com-pany, distributors and dealers (or retailers), and customers.Recently, due to increasing customization, consumer demand forglobal bicycle product markets has changed so rapidly that com-petitiveness of supply chain has become increasingly important.To enhance its competitiveness G-company aims to effectivelymanage inventory in its supply chain and prompt delivery time.It expected that RFID technology/Electronic Product Code (EPC)system combined with Global Positioning Systems (GPS) wouldhelp achieve this goal. RFID is regarded as a promising technologyfor the optimization of supply chain process since it improvesmanufacturing and retail operations from forecasting demand toplanning, managing inventory, and distribution [49]. Followingpreliminary screening, three competing RFID alternatives, A1, A2

and A3, are identified that are capable of performing this task. Acommittee of three experts, E1, E2 and E3, has been formed to con-duct further evaluation and select the most suitable RFIDalternative.

The effects of adopting a RFID system include both quantitativeand qualitative effects. Subjective attributes are used to assess thequalitative effects of RFID system, while objective attributes areused to evaluate the quantitative effects of RFID system. Objectiveattributes have been considered including investment costs andcost reductions. In the feasibility analysis, hardware costs, softwarecosts and services costs are regarded as main cost items of theinvestment, and cost reductions include labor cost reduction,inventory cost reduction and shrinkage cost reduction [50]. Inthe industry considered, the subjective attributes identified areoperating efficiency, accuracy, visibility, and security [44,49]. Theselection decision is made based on two objective attributes andfour subjective attributes. Table 1 lists the properties of these attri-butes, including attribute type and assessment type, which arecritical to RFID function. Since it is useful to develop a hierarchicalstructure showing the overall goal, as well as the attributes andalternatives, this hierarchy for the RFID system selection problemis shown in Fig. 2. This research chooses a BLTS (V1) with 11 terms,as listed in Table 2. The experts use the linguistic term set S1 pre-sented in Table 3 to evaluate the suitability of the alternativesunder each of the subjective attributes, and to assess the impor-tance of the attributes, respectively. The data related to RFID sys-tem selection problem is given in Table 4. The computationalprocess is summarized as follows.

First, the fuzzy numerical values are normalized using Eq. (17).Next, the weighted rating of each alternative are calculated usingEq. (18). These fuzzy numbers are then converted into the BLTSemploying Eq. (19). The results for the first alternative A1 areobtained as

F(X111) = (0, 0, 0, 0, 0, 0, 0.762, 1, 0.7143, 0, 0),F(X112) = (0, 0, 0, 0.298, 0.7449, 0.9766, 0.4883, 0, 0, 0, 0),

Table 3Linguistic variables of performance rating and importance grade.

Seven ranks of performance rating Fuzzy number Seven ranks of importance grade Fuzzy number

s0: Definitely low (DL) (0, 0, 0.1, 0.2) s0: Definitely low (DL) (0, 0, 0.1, 0.2)s1: Very Low (VL) (0.1, 0.2, 0.2, 0.3) s1: Very Low (VL) (0.1, 0.2, 0.2, 0.3))s2: Low (L) (0.2, 0.3, 0.4, 0.5) s2: Low (L) (0.2, 0.3, 0.4, 0.5)s3: Middle (M) (0.4, 0.5, 0.5, 0.6) s3: Middle (M) (0.4, 0.5, 0.5, 0.6)s4: High (H) (0.5, 0.6, 0.7, 0.8) s4: High (H) (0.5, 0.6, 0.7, 0.8)s5: Very High (VH) (0.7, 0.8, 0.8, 0.9) s5: Very High (VH) (0.7, 0.8, 0.8, 0.9)s6: Definitely high (DH) (0.8, 0.9, 1.0, 1.0) s6: Definitely high (DH) (0.8, 0.9, 1.0, 1.0)

Table 4The importance grades and performance ratings evaluated by three experts for three alternatives.

Objective attribute Importance grade Performance rating

E1 E2 E3 A1 A2 A3

C1 VH DH VH (90, 100, 110, 120) (130, 140, 145, 150) (140, 150, 155, 160)C2 VH H DH (50, 60, 65, 70) (75, 80, 85, 95) (80, 85, 95, 105)

Subjective attribute Importance grade Performance rating

E1 E2 E3

E1 E2 E3 A1 A2 A3 A1 A2 A3 A1 A2 A3

C3 VH DH DH L M DH VL H VH DL L VHC4 H M M VL M VH DL L DH L M DHC5 DH VH DH VL H VH L M VH VL M DHC6 H M M DL H DH VL M VH DL H VH

Table 52-Tuple linguistic rating terms for each alternative.

Alternative Attribute

C1 C2 C3 C4 C5 C6

A1 (v7, 0.3631) (v5, �0.3325) (v2, �0.1106) (v1, 0.272) (v2, 0.2216) (v1, �0.2585)A2 (v5, 0.4102) (v7, 0.0988) (v5, 0.4506) (v3, �0.3988) (v6, �0.4086) (v4, �0.4586)A3 (v5, 0.0831) (v7, �0.0443) (v7, 0.3704) (v5, �0.1647) (v7, 0.0297) (v5, �0.1269)

218 S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220

F(X113) = (0, 0.3, 0.8, 1, 0.6522, 0.2174, 0, 0, 0, 0, 0),F(X114) = (0.2941, 08823, 0.7, 0.2, 0, 0, 0, 0, 0, 0, 0),F(X115) = (0.1, 0.6, 1, 0.5, 0, 0, 0, 0, 0, 0, 0),F(X116) = (0, 0.8421, 0.3158, 0, 0, 0, 0, 0, 0, 0, 0),F(X121) = (0, 0, 0, 0, 0, 0, 0.423, 0.846, 1, 1, 0.5),F(X122) = (0, 0, 0.3024, 0.7909, 1, 0.6667, 0.1667, 0, 0, 0, 0),F(X123) = (0.1, 0.6, 1, 0.5, 0, 0, 0, 0, 0, 0, 0),F(X124) = (1, 0.7059, 0.1176, 0, 0, 0, 0, 0, 0, 0, 0),F(X125) = (0, 0.3, 0.8, 1, 0.6522, 0.2174, 0, 0, 0, 0, 0),F(X126) = (0.375, 1, 0.4444, 0, 0, 0, 0, 0, 0, 0, 0),F(X131) = (0, 0, 0, 0, 0, 0.3488, 0.814, 1, 0.7143, 0.3571, 0),F(X132) = (0, 0, 0, 0.0184, 0.5101, 0.9387, 1, 0.4516, 0, 0, 0),F(X133) = (1, 1, 0.5, 0, 0, 0, 0, 0, 0, 0, 0),F(X134) = (0.1177, 07059, 1, 0.5, 0, 0, 0, 0, 0, 0, 0),F(X135) = (0.1, 0.6, 1, 0.5, 0, 0, 0, 0, 0, 0, 0),F(X136) = (1, 0.7059, 0.1176, 0, 0, 0, 0, 0, 0, 0, 0).

The results for other alternatives can be obtained in a similarway. By using Eqs. (12)–(16), respectively, the manager (modera-tor) of the decision problem assigns a linguistic quantifier ‘most’to the corresponding experts; i.e., the MEOWA operator UQ1 guidedby ‘most’ with its parameters (0.3, 0.8), and the algorithm for calcu-lating the maximum entropy weighting vector yields the weightingvector W1, orness value a 1 and maximum entropy weighting vec-tor W1

, as follows:

W1 ¼ ½0:0667;0:6667;0:2667�;a1 ¼ 0:4;W

1 ¼ ½0:2384;0:3233;0:4383�:

Then, we aggregate the fuzzy assessment vectors on BLTS, to obtainthe aggregated fuzzy assessment vectors of each alternative withrespect to each attribute using Eqs. (20) and (21). Then the resultsare obtained:

F(XA(11)) = (0, 0, 0, 0, 0, 0.0832, 0.6259, 0.932, 0.7825, 0.3539,0.1192),

F(XA(12)) = (0, 0, 0.0721, 0.293, 0.7029, 0.8286, 0.4678, 0.1077, 0, 0, 0),F(XA(13)) = (0.2707, 0.5639, 0.7162, 0.4001, 0.1555, 0.0518, 0, 0, 0,

0, 0),F(XA(14)) = (0.3815, 0.7448, 0.5127, 0.1821, 0, 0, 0, 0, 0, 0, 0),F(XA(15)) = (0.0558, 0.4664, 0.9008, 0.6157, 0.1531, 0.051, 0, 0, 0, 0, 0),F(XA(16)) = (0.7225, 0.8165, 0.258, 0, 0, 0, 0, 0, 0, 0, 0),

The values of these vectors are computed and transformed intoa linguistic 2-tuple with Eqs. (8) and (6), respectively. The resultsare shown in Table 5, where, the values c11 and (v11,a11) areobtained by Eqs. (8) and (6), respectively:

c11 ¼ 5�0:0832þ6�0:6259þ7�0:932þ8�0:7825þ9�0:3539þ10�0:11920:0832þ0:6259þ0:932þ0:7825þ0:3539þ0:1192 ¼ 7:3631

Dðc11Þ ¼v7;7 ¼ roundð7:3631Þ;0:3631 ¼ 7:3631� 7:

�¼ ðv7;0:3631Þ

Using Eqs. (12)–(16), respectively, the 2-tuple MEOWA operatorUe

Q2guided by ‘most’ with the pair (0.3, 0.8), and the algorithm for

calculating W2 yields W2 = [0, 0.0667, 0.3333, 0.3333, 0.2667, 0],

a2 = 0.44, and W2 = [0.1267, 0.1405, 0.1558, 0.1728, 0.1917,

0.2125]. Finally, the ranking index for each alternative is computedusing Eq. (22) as RI1 = (v3, 0.3373), RI2 = (v5, �0.4793), and RI3 = (v6,

S.-J. Chuu / Knowledge-Based Systems 66 (2014) 210–220 219

�0.1548). For a group of experts, based on ranking index, the rank-ing order of the three alternatives is given as A3� A2� A1.

With respect to the detailed analysis of evaluation results suchas competing RFID system alternatives, effects of RFID system,properties of attributes and computational process, the decision-making process will be completed if experts accept the evaluationresults. Otherwise, experts can modify their opinions step by stepthrough the collection of additional information, or modify the lin-guistic quantifier until a consistent decision is obtained. After thedetailed decision analysis of this case study, group of expertsaccepts that the best alternative is A3, while A2 and A1 are rankedsecond and third, respectively.

6. Conclusions

RFID technology selection is important to improving supplychain system competitiveness. Supply chain RFID technologyselection problem considers several individual attributes exhibit-ing vagueness and imprecision. The classical multiple attributesdecision-making methods that consider deterministic or randomprocesses cannot effectively handle group decision-making prob-lems including imprecise and linguistic information. This studyfirst identified two groups of attributes, and then classified themas either subjective or objective. A fuzzy multiple attributes andgroup decision-making scenario was modeled to solve the RFIDtechnology evaluation problem. The proposed fuzzy linguisticmethod with the group decision-making, used to evaluate the suit-ability of RFID, is very useful in supply chain development. In thispaper, the proposed method is apt to manage information assessedusing both linguistic and numerical scales in the decision-makingproblem with multiple information sources. Moreover, the pro-posed algorithm based on 2-tuple linguistic representation modelwith MEOWA operators has the advantages that include avoidingloss and distortion of experts’ assessment information, obtainingthe computation results as linguistic terms, and simplifying thecalculation process. A case study of RFID technology evaluationhas been conducted to exemplify the feasibility of the proposedmethod.

Acknowledgements

This research is partially supported by Grant No. NSC 101-2410-H-253-001 from the National Science Council of the Republic ofChina. The author would very grateful to thank the anonymous ref-erees for their valuable comments that have led to an improvedversion of this paper.

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