Sustainable supply chain management using approximate fuzzy DEMATEL method

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Sustainable supply chain management using approximate fuzzy DEMATEL method

Kuo-Ping Lin

^a,∗

, Ming-Lang Tseng

^b

, Ping-Feng Pai

^c

aDepartmentofInformationManagement,LunghwaUniversityofScienceandTechnology,Taoyuan333,Taiwan

bDepartmentofBusinessAdministration,LunghwaUniversityofScienceandTechnology,Taoyuan333,Taiwan

cDepartmentofInformationManagement,NationalChiNanUniversity,1,UniversityRd.,Puli,Nantou545,Taiwan

a r t i c l e i n f o

Articlehistory:

Received27April2016 Receivedinrevisedform 25September2016 Accepted22November2016 Availableonlinexxx

Keywords:

Approximatefuzzyarithmetic FuzzyDEMATEL

Fuzzycauseandeffectrelationships

a b s t r a c t

ThisstudydevelopstheapproximatefuzzyDecisionMakingTrialandEvaluationLaboratory(AFDEMA- TEL)toanalyzeuncertaininfluentialfactors.Theapproximatefuzzyarithmeticoperationsunderthe weakestt-norm(Tω)arithmeticoperationstoevaluatesustainablesupplychainmanagementbasedon AFDEMATEL.ThefuzzyDEMATELisoneofimportantdecision-makingmethodunderuncertainenvi- ronment.ThefuzzyDEMATELhadtobedevelopedforclearlydisplayexpert’soptionswithlinguistic variables.Thefuzzyoperationsusuallyadopt␣-cutarithmeticinfuzzyDEMATEL.Inthisresearch,the fuzzyDEMATELtechnologyissubstitutedwiththeAFDEMATELtechnology.Inthesustainablesupply chainmanagementexample,theAFDEMATELisemployedtofindfuzzycauseandeffectrelationships amongcriteria.Particularnoteshouldbemadeofthefollowing:[1]thefuzzyDEMATELwith␣-cutarith- meticmodelcannotexactlyhandlefuzzycauseandeffectrelationshipsunderuncertainenvironment, andthefuzzinessaccumulationphenomenonofthe␣-cutarithmeticmayinfluencefinalfuzzycause andeffectrelationships;and[2]theapproximatefuzzyarithmeticoperationsgivesajustifiablefuzzi- nessspreadtoanalyzefuzzycauseandeffectrelationships.Inthecaseofselectionofcanssuppliers,the AFDEMATELexaminestheinfluentialfactors.Proposedmethodprovidesjustifiablefuzzycauseandeffect relationshipswithapproximatefuzzyarithmeticandcananalyzeacrossquadrantsphenomenonunder uncertainenvironment,sincedecision-makersusuallywanttoaccuratelyestimateuncertaininfluential factors.

©2016ElsevierB.V.Allrightsreserved.

1. Introduction

Since environmental awareness affects almost all parts of society and is a special concern for industry, companies and decision-makersmustconsiderenvironmentalissuesinalladmin- istrativeactivities(MarcusandFremeth,2009).Sustainablesupply chainmanagementhasattractedgreatinterestfrompractitioners andsupplychainmanagerssuchasthestudiesofMirzapourAl- e-hashemetal.(2013),Govindanetal.(2014)andKannanetal.

(2014).Integratingenvironmentalfactorsintosupplychainman- agement, product design, supply network design, and material purchasinghasbecomeanessentialpartofcriticalthinking(Green etal.,1996;Hervanietal.,2005;Sarkis,2005;Srivastava,2007;Ren etal.,2015a,2015b,2016).Analyzingfactorsinfluencingsustain- ablesupplychainmanagementisalwaysobjective,andthusthe

∗Correspondingauthor.

E-mailaddresses:kplin@mail.lhu.edu.tw,hallinkimo@yahoo.com.tw(K.-P.Lin).

decisionmakingmodelforselectingsustainablesuppliersiscru- cialinsupplychainmanagement(Anetal.,2015).Kuoetal.(2010) proposedthehybriddecisionmodel,whichintegratestheartificial neuralnetwork(ANN)andtwomulti-attributedecision analysis methodsforgreensupplierselection.

DobosandVörösmarty(2014)utilizeddataenvelopmentanal- ysis(DEA)withthecommonweightsanalysis(CWA)methodto determinegreensuppliers.Whilethepreviousliteraturehaslooked attheimportanceofsustainablesupplierselection,somevague orambiguousinformationexistsinsustainablesupplychainman- agement.Thus,thefuzzysettheorycouldbeonepossiblewayto evaluatetheselectionofgreensuppliers.Somestudiesusedfuzzy decision modelstofacilitateevaluatingtheperformance ofsus- tainablesupplychainmanagement(Tseng,2011;TsengandChiu, 2013;Kannanetal.,2013;Tsengetal.,2014;Wuetal.,2015;Su etal.,2016).Thesefuzzydecisionmodelshavebeenprovenhighly effectiveinaggregatingtheviewsofexpertsandtherebyproviding informationofgreatercredibility.

http://dx.doi.org/10.1016/j.resconrec.2016.11.017 0921-3449/©2016ElsevierB.V.Allrightsreserved.

DecisionMakingTrial andEvaluationLaboratory (DEMATEL) (Gabus and Fontela, 1973; Fontela and Gabus, 1976) hasbeen widelyappliedindecision-makingmethodwiththeaimofinves- tigatingcomplexandintertwinedproblematicgroup.(Fontelaand Gabus,1976).TheDEMATELmethodadoptsmathematicaltech- niquestoobtainanalysisoflogicalrelationshipsanddirectimpact relationsbetweensystematiccriteria.Thismethodcanenhance understandingofthespecificexperts’viewpointsofinteractedfac- tors, and criteriaand providea feasible solutionby applying a visualizationstructuremodel(HeandCheng,2012).TheDEMA- TELtechniqueiswidelyusedinsolvingcomplexproblems,such ascontrolsystems(HoriandShimizu,1999),e-learningevaluation (Tzengetal.,2007),strategyorpolicyanalysis(Huangetal.,2007;

Hsuetal.,2007;Weietal.,2010),measurementevaluating(Liou etal.,2007,2008),hospitalservicequality(Jiunn-Ietal.,2010), decisionmaking(Michnik,2013),sustainablesupplychainman- agement(Renetal.,2013;Liangetal.,2016).

Because of the uncertain or vague environment, DEMATEL methodalsoshouldbeextendedtoanalyzecriteriaunderuncer- tainenvironmentwhichconsidersthefuzzyorlinguisticvariables inDEMATELmethod.Table1summarizessomedevelopmentsof fuzzyDEMATEL.WuandLee(2007)combinedDEMATELmethod withfuzzylogic,andappliedinhigh-techCompany.Theresultspre- sentedthecausegroupandtheeffectgroupofcompetencies.For theR&DprojectselectionofaTaiwanesecompany,fuzzyDEMATEL alsohasadopted tosolve groupdecision-making under uncer- tain environment (Lin and Wu, 2008). Tseng (2009) developed grey-fuzzyDEMATELtoestimaterealestate agentservicequal- ityexpectationranking.Changetal.(2011)analyzedkeyinfluence factorusingfuzzyDEMATELmethodforsupplierselectioninthe electronicsindustry.Chouetal.(2012)proposedahybridmodel, whichcombinesfuzzyAnalyticHierarchyProcess(AHP)withfuzzy DEMATELmethod,toevaluatehumanresourcesforscienceand technology(HRST).Theresultsshowedthatimprovinginfrastruc- turemaybeabetterlong-termchoiceinHRST.Lin(2013)adopted thefuzzyDEMATELingreensupplychainmanagement(GSCM).

ThecauseandtheeffectcriteriainGSCMwereinvestigatedand discussed.Horngetal.(2013)proposedanewmodelforcreativity assessmentwithinthecontextoftheDEMATELmethodapplication.

Thisstudyusesmultiplestagesofsampleselectionanddatacollec- tion,includingqualitativeandquantitativesurveys.TheDEMATEL methodwasusedtoconductarelationshipanalysisofcreativity forfuture restaurant spacedesign. Yehand Huang (2014)used thehybridapproach,whichcombinedfuzzyDEMATELwithAna- lyticNetworkProcess(ANP)approaches,tofindcorrelationsamong thedimensionsandtherelativeweightsofcriteria,respectively, in determiningwind farm locations.Lin et al. (2014)proposed theweakestt-norm(T_ω)fuzzyGERTandappliedthemethodto GSCM.Govindanetal.(2015)proposedintuitionisticfuzzybased DEMATELmethodwhichadoptedtheintuitionisticfuzzysetsto DEMATEL,andappliedtoevaluateGSCM.Jeng(2015)usedfuzzy DEMATELtosupplychaincollaboration.ThisstudyadoptedTai- wanese manufacturingfirms as anexample case, and provides discussionandinsightsforsupplychainpractitioners.

InthefuzzyDEMATELmechanism,totalrelationfuzzymatrix iscalculated by usingfuzzyarithmetic. The␣-cutarithmetic is popularly employed to calculate total relation fuzzy matrix in pastresearches.However,Changetal.(2006)mentionedthat␣- cutarithmeticwasfuzzierbecauseofthefuzzinessaccumulation phenomenon. Lin et al. (2011) and Garg (2014)also employed theweakestt-normbasedmethodtodecreasethephenomenon offuzzinessaccumulation.Therefore,fuzzyDEMATELwith␣-cut arithmeticcannoteffectivelyanalyzefuzzyintervalofresult.

Thisstudy proposestheAFDEMATEL which adoptsapproxi- matefuzzyarithmeticoperationsundertheweakestt-norm(Tω) arithmeticoperations. Thepurpose is toimprove onthe tradi-

tionalfuzzyDEMATEL,andextendsTωfuzzyDEMATELmethod(Lin etal.,2014)toovercometheaccumulatingphenomenonoffuzzi- nessorcrediblyreducefuzzyspreads.Theproposedmodelwill helptoaccuratelyevaluatecauseandeffectrelationshipswhile thefuzzyintervalsmayacrossquadrants.Furthermore,selection ofcanssuppliers(Dalalahetal.,2011)wasexaminedand com- pareditwiththetraditionalfuzzyDEMATEL(LinandWu,2004).

Therestofthispaperisorganizedasfollows.Section2introduces the␣-cutandtheapproximatefuzzyarithmeticoperations.InSec- tion3,thetraditional fuzzyDEMATELisdescribes. InSection4, proposedapproximatefuzzyDecisionMakingTrialandEvaluation Laboratory(AFDEMATEL)aredescribed.Section5presentsasus- tainableSCMexampletoexaminetheAFDEMATELmodel.Section 6providedconcludingremarks.

2. Thebasicoffuzzyarithmetic

ThefuzzyarithmeticisoneofmaintechniqueinfuzzyDEMATEL technology.Inthissection,somebasicdefinitionsoffuzzyarith- meticarepresented.

Definition1.Let ˜Mbea fuzzynumber(FN)on.Atriangu- larfuzzynumber ˜Mcanbedefinedasatriplet(m₁,m₂,m₃).The membershipfunctionM(x)˜ thatdefinesthemembershipgradesof elementsx∈to ˜M:

M(x)˜ =

⎧ ⎪

⎪ ⎪

⎪ ⎨

⎪ ⎪

⎪ ⎪

⎩

0, x<m1,

(m−a₁)/(m₂−m₁), m₁≤x≤m₂, (m₃−x)/(m₃−m₂), m₂≤x≤m₃,

0, x>m3,

wherem₂isthecenterandm₁andm₃denotetheleftandright boundsof ˜Mrespectively,with

Definition2.ATFNischaracterizedbyitsmembershipfunc- tion ˜Por,alternatively,byits␣-cutsA˛ whichcanbedefinedas following:

P˛=

x|P(x)˜ ≥˛

, (1)

orgivenforaTFN

P_˛=[p^(˛)₁ ,p^(˛)₂ ]=[p₁+˛(p₂−p₁),p₃−˛(p₃−p₂)], (2) wherep^(˛)₁ andp^(˛)₂ respectivelydenotetheleftandrightboundsof P˛.

AccordingtothecharacteristicsofTFNandtheZadeh’ssup-min operator(Zadeh,1965)canbestatedas

( ˜P◦Q˜)(z)=sup_x◦y=zmin( ˜P(x),Q˜(y)), (3) where◦denotesanyarithmeticoperation.

The␣-cutsoffuzzynumbers, ˜P=(a1,a2,a3)and ˜Q=(b1,b2,b3)

∀P,^˜ Q˜ ∈,areasfollows:

(1)Additionoftwofuzzynumbers:

P˜+Q˜=(p₁+q₁,p₂+q₂,p₃+q₃) (4) (2)Subtractionoftwofuzzynumbers:

P˜−Q˜=(p1−q3,p2−q2,p3−q1) (5) (3)Multiplicationoftwofuzzynumbers:

P˜×Q˜∼=(p₁×q₁,p₂×q₂,p₃×q₃) (6) (4)Divisionoftwofuzzynumbers:

P/˜ Q˜∼=(p₁/q₃,p₂/q₂,p₃/q₁) (7)

Table1

SomedevelopmentsoffuzzyDEMATEL.

Author(s) year methods Appliedfields

Wu&Lee 2007 FuzzyDEMATEL Globalmanagers’competencies

Lin&Wu 2008 FuzzyDEMATEL R&Dproject

Tseng 2009 Grey-fuzzyDEMATEL Customerexpectation

Changetal. 2011 FuzzyDEMATEL Supplierselection

Chouetal. 2012 FuzzyAHP+fuzzyDEMATEL HRST

Linetal. 2013 FuzzyDEMATEL Greensupplychainmanagement

Horngetal. 2013 FuzzyDelphi+DEMATEL Restaurantspacedesign

Yeh&Huang 2014 FuzzyDEMATEL+ANP Windfarmlocation

Linetal. 2014 TωFuzzyDEMATEL Greensupplychainmanagement

Govindanetal. 2015 IntuitionisticfuzzyDEMATEL Greensupplychainmanagement

Jeng 2015 FuzzyDEMATEL Supplychainmanagement

InZadeh’sextensionprinciple(Zadeh,1965),theoriginal‘min’

isreplacedbyt-normontheinterval[0,1].Thenthebasicconcepts anddefinitionoftheweakestt-normarithmeticoperationsisas follows:

( ˜P◦Q˜)(z)=sup_x◦y=zT( ˜P(x),Q˜(y)), (8)

Definition3.Eacht-normmaybeshowntosatisfythefollowing inequalities:

Tω(p₂,q₂)≤T(p₂,q₂)≤T_M(p₂,q₂)=min(p₂,q₂), where

Tω(p₂,q₂)=

⎧ ⎪

⎨

⎪ ⎩

p2, if q2=1, p₂, if q₂=1, 0, otherwise,

Tω isthe weakestt-norm. Theoperations ofTω fuzzy arith- metic canbeseenin theresearchofChang etal.(2006), Hong (2001a,2001b),Hong(2006),Kolesárová(1995)andMesiar(1997).

Lin etal. (2011)proposedapproximatefuzzyarithmeticopera- tionsundertheweakestt-norm(T_ω)arithmeticoperations.The approximatefuzzyarithmeticextendedtheTω fuzzyarithmetic, andobtainedtheadvantagesofapproximatefuzzyarithmetic.The approximate fuzzy arithmeticcan obtain fitterdecision values, which have smaller fuzzinessaccumulating, under vague envi- ronment.Theapproximatefuzzyarithmeticoperationsunderthe weakestt-norm(Tω)arithmeticoperationsareasfollows:

(1)Addition:

P(+˜ Tω)^˛Q˜=[p1(˛=1)+q^(˛=1)₁ −max((p1(˛=1)−a1(˛)),(q^(˛=1)₁ −q^(˛)₁ )), p2(˛=1)+p^(˛=1)₂ +max((p2(˛)−p2(˛=1)),(q^(˛)₂ −q^(˛=1)₂ ))]

(9) (2)Subtraction

P(−˜ Tω)^˛Q˜=[p1(˛=1)−q^(˛=1)₁ −max((p1(˛=1)−p1(˛)),(q^(˛)₂ −q^(˛=1)₂ )), p2(˛=1)−p^(˛=1)₂ +max((q^(˛=1)₁ −q^(˛)₁ ),(p2(˛)−p2(˛=1)))]

(10) (3)Multiplication

P(ט Tω)^˛Q˜=[p2q2−max((p^(˛=1)₁ −p^(˛)₁ )q2,(q^(˛=1)₁ −q^(˛)₁ )p2)), p2q2+max((p^(˛)₂ −p^(˛=1)₂ )q2,(q^(˛)₂ −q^(˛=1)₂ )p2))]

(11) (4)Division

P(÷˜ Tω)^˛Q˜=[(p2/q2−max((p^(˛=1)₁ −p^(˛)₁ )/q2,p2(1/q^(˛=1)₂ −1/q^(˛)₂ )), p2/q2+max((p^(˛)₂ −p^(˛=1)₂ )/q2,p2(1/q^(˛)₁ −1/q^(˛=1)₁ ))]

(12)

3. TraditionalfuzzyDEMATELmethod

Indecision-making systems,peopleusuallymake judgments accordingtotheirexperienceandexpertise.Thisishumancen- tricactivityprocessedinuncertainenvironments.Traditionalor crispDEMATELmaynotbeeffectiveorsuitableforsolvinggroupor

multi-criteriadecision-makinginuncertainenvironments.There- fore,it is necessarytobuildan extended DEMATELmethodby applyingfuzzytheory.Todealwithhumanassessments,thepref- erencesof decision-makers areemployed tofuzzy numbersby adoptingfuzzylinguisticscale.Inthissection,thefuzzyDEMATEL (LinandWu,2004)willbebrieflyintroduced.

Step1:Designthefuzzylinguisticscaleandaveragetheassess- ment. Todeal withtheambiguities ofhumanassessments, the linguisticvariable shouldbedetermined.Moreover,in order to formexpertcommitteesforgroupknowledgerequiredtoachieve thegoals.Itmustacquireandaveragetheassessmentofexperts’

preferencesusingLinandWu(2004).

Step2:Initialdirect-relationfuzzymatrix.ThefuzzyDEMATEL turnfuzzymatrix ˜Zintonormalizedinitialdirect-relationmatrix whichiscalledfuzzymatrix ˜Xisproducedasfollows:

Z˜=

⎡

⎢ ⎢

⎢ ⎢

⎢ ⎣

0 z₁₂˜ ··· z_1n˜ z21˜ 0 ··· z2n˜

..

. ... . .. ...

˜

z_n1 z_n2˜ ··· 0

⎤

⎥ ⎥

⎥ ⎥

⎥ ⎦

(13)

Inthematrix, ˜z_ij=(z_ij,z_ij,z_ij)∀ⁱ=1,...,n.j=1,...,n.and ˜z_ij= (0,0,0)∀ⁱ=j.

Bynormalizingtheinitialdirect-relationfuzzymatrix,thenor- malizingdirect-relationfuzzymatrix ˜Xcanbeobtainedasfollows:

X˜

˛=0

=

⎡

⎢ ⎢

⎢ ⎢

⎢ ⎣

x˜11 x˜nn ··· x1n˜

˜

x₂₁ x˜₂₂ ··· x_2n˜ ..

. ... . .. ...

˜

x_n1 x˜_n2 ··· xnn˜

⎤

⎥ ⎥

⎥ ⎥

⎥ ⎦

˛=0

(14)

where

˜

x_ij= z˜_ij max

1≤i≤n

n j=1

˜ z_ij

=( z_ij max

1≤i≤n

n j=1

˜ z_ij

, z_ij max

1≤i≤n

n j=1

˜ z_ij

, z_ij max

1≤i≤n

n j=1

˜ z_ij

) (15)

Step3:Attainthefuzzytotal-influencematrix.Thefuzzytotal- influencematrix ˜Tcanbecomputed(LinandWu,2004):

T˜^˛=0= lim

k→∞( ˜X1+X˜2+···+X˜_k)=[X×(I−X)]^˛=0 (16)

Step4:Defuzzifyintothecrispvalues.Thesumofrowsandthe sumofcolumnsarerespectivelydenotedasvectors ˜Dand ˜Rwithin thetotalrelationfuzzymatrix.

D˜=

_n

i=1

t˜_ij

˛=0 1×n

(17)

R˜=

⎡

⎣

ⁿ

j=1

t˜_ij

⎤

⎦

˛=0

1×n

(18)

Usingtraditional␣-cutarithmeticthe ˜D_i+R˜_iand ˜D_i−R˜_iarecalcu- lated.Then ˜D_i+R˜_iand ˜D_i−R˜_iaredefuzzifiedintocrispvaluesand mapintothetotalinfluencematrix.( ˜D_i+R˜_i)^defprovidesanindexof thestrengthoftheinfluencesdispatchedandreceivedispositive, thenthecriterionaffectsothers.If( ˜D_i−R˜_i)^def ispositivethatthe criterionaffectsothers,and( ˜D_i−R˜_i)

def

isnegativethatcriterionis influencedbyothers.

Step5:Establishandanalyzethestructuralmodel.Thecausal relationmapcanbedrawn.

4. ApproximatefuzzyDEMATEL

This study extends Tω fuzzy DEMATEL (Lin et al., 2014) to AFDEMATELfor sustainablesupply chainmanagement. Because theapproximatefuzzyarithmeticoperationsundertheweakest t-norm(T_ω)caneffectivelyreducethefuzzinessaccumulationphe- nomenon(Linetal.,2011),thisstudyadoptstheapproximatefuzzy arithmeticoperationstosubstitute traditional ␣-cutarithmetic.

TheAFDEMATELcanbeasanalternativefordecisionmaking.The proceduresoftheAFDEMATELareshowninFig.1.

Step1:Designthefuzzylinguisticscaleandaveragetheassess- ment.ThestepisthesameasintraditionalfuzzyDEMATEL.

Step2: Initial(Tω)^˛direct-relationfuzzymatrix.Inthisstep, theapproximatefuzzyarithmeticoperationsnormalizingdirect- relationfuzzymatrix ˜X

(Tω)^˛

canbecomputedthroughEqs.(9)–(12).

X˜^(Tw)

a

=

⎡

⎢ ⎢

⎢ ⎢

⎣

X˜₁₁ X˜₁₂ ... X˜_1n X˜₂₁ X˜₂₂ ... X˜_2n ..

. ... . .. ... X˜_n1 X˜_n2 ... X˜nn

⎤

⎥ ⎥

⎥ ⎥

⎦

(Tw)^a

(19)

( ˜x_ij)^(Tω)˛=(x_ij,x_ij,x¯_ij)^(Tω)˛ (20) where

(x_ij)^(Tω)˛= z_ij

1≤i≤nmax

n j=1

˜ z_ij

− z_ij−z_ij

1≤i≤nmax

n j=1

˜ z_ij

,(x_ij)^(Tω)˛= z_ij

1≤i≤nmax

n j=1

˜ z_ij

,(¯x_ij)^(Tω)˛= z_ij

1≤i≤nmax

n j=1

˜ z_ij

+ z_ij−z_ij

1≤i≤nmax

n j=1

˜ z_ij .

Step3:Attainthe(T_ω)^˛fuzzytotal-influencematrix.Thetotal (Tω)^˛ relationfuzzymatrixcanbedefinedand computedusing (Tω)^˛operationsasfollows:

T˜

(Tω)^˛

=lim

k→∞( ˜X1(+Tω)^˛X˜2(+Tω)^˛···(+Tω)^˛X˜k)=

X(×Tω)^˛(I(−Tω)^˛X)

(21)

Average the assessment Collecting Expert’s viewpoints

Design the fuzzy linguistic scale

Initial approximate direct-relation fuzzy matrix

Attain the approximate fuzzy total-influence matrix

Defuzzify into the crisp values

Establish and analyze the approximate fuzzy DEMATELstructural model

Fig.1.ProceduresofAFDEMATEL.

Step4:Defuzzifyintothecrispvalues.Thesumofrowsandthe sumofcolumnsarerespectivelydenotedasvectors ˜Dand ˜Rwithin thetotal(Tω)^˛relationfuzzymatrix.

D˜=t˜_1j(+Tω)^˛t˜_2j(+Tω)^˛···(+Tω)^˛t˜_nj=

_n

i=1

t˜_ij

(Tω)^˛ 1×n

(22)

R˜=t˜_i1(+Tω)^˛t˜_i2(+Tω)^˛···(+Tω)^˛t˜_in=

⎡

⎣

ⁿ

j=1

t˜_ij

⎤

⎦

(Tω)^˛

1×n

(23)

UsingT_ω operationsthe ˜D_i(+Tω)^˛R˜_iand ˜D_i(−Tω)^˛R˜_iarecalcu- lated. Then ˜D_i(+Tω)^˛R˜_i and ˜D_i(−Tω)^˛R˜_iare defuzzified into crisp valuesandmapintothetotalinfluencematrix.

Step5:EstablishandanalyzetheAFDEMATELstructuralmodel.

TheAFDEMATELcausalrelationmapcanbedrawn.TheAFDEMA- TELcanobtainmoreobjective ˜D_i(+Tω)^˛R˜_iand ˜D_i(−Tω)^˛R˜_i.Thisis becausethatAFDEMATELcananalyzefuzzyintervalcrossesdiffer- entquadrants.ThefuzzyDEMATELwith␣-cutarithmeticcouldnot achievethisduetothefuzzinessaccumulationphenomenon.

5. Numericalexample

ThisstudyappliestheAFDEMATELforsustainablesupplychain management.Theselectionofcanssuppliersareexaminedinthis study.

5.1. Thecase:theselectionofcanssuppliers

ThisproposedAFDEMATELwillapplyonanindustrycasestudy fortheselectionofcanssuppliersatNutridarFactoryinAmman-

Jordan(Dalalahetal.,2011)todemonstratetheproposedmodel.

Table2showsthecriteriaofcanssuppliers,whichincludeseven- teeninfluencefactors.Byadoptingafuzzytriangularnumber,a fuzzyDEMATELexertionwillbeputinplacebyexpressingdiffer- entdegreesofinfluenceorcausalityincrispDEMATEL,withfive

Table2

Thelistofcriticalcriteriaofcanssuppliers(Dalalahetal.,2011).

Criticalcriteria C1:Unitpriceand paymentterms

C10:Compensationforwaste C2:Deliveryterms C11:Printingcompliestodesign

andcolor C3:Supplierfactory

capacity

C12:Easyopenandspoonleveling C4:Shippingmethod C13:Testingmethodsforpackaging

materialsandavailabletestsfrom supplier

C5:Leadtime C14:Variationofdimensions C6:Locationofcan

supplier

C15:Stretchwrappingandclean separators,palletsizeandheight C7:Technical

specifications

C16:Majorcustomerswiththe samebusiness

C8:Certifications C17:Certificateofsupplier materials

C9:Servicesand communicationswith thesupplier

Table3

Correspondingrelationbetweenlinguisticvariableandfuzzynumberinexample2 (Dalalahetal.,2011).

Linguisticvariable CorrespondingTFNs

NoInfluence(NO) (0,0,0.25)

VeryLowInfluence(VL) (0,0.25,0.25)

LowInfluence(L) (0.25,0.5,0.75)

HighInfluence(H) (0.5,0.75,1.0)

VeryHighInfluence(VH) (0.75,1.0,1.0)

linguistictermsas{NO,VL,L,H,VH}andtheircorrespondingpos- itivetriangularfuzzynumbers.Theselinguistictermsareshown inTable3.Thisexamplewasexperimentedtohelpidentifythe bestsupplieramongasetofsuppliers.Thisgroupincludesthepro- ductionmanager,thequalitymanager,thematerialmanager,the maintenancemanager,theresearchanddevelopmentmanagerand theplanningmanagerwhichhassixworkingexperts.Theinitial- directfuzzymatrixfromtheassessmentdataofexpertsisdepicted inTable4.

In order to access the casual relationships between strate- gicobjectives,thisstudyexamines ˜D_i+R˜_i, ˜D_i−R˜_i,( ˜D_i+R˜_i)^def,and ( ˜D_i−R˜_i)^defwithtwofuzzyoperations(␣-cutand(Tω)^˛). ˜D_iisrethe sumofrowstotal-relationfuzzymatrixand ˜R_iissumofcolumns

ofthetotal-relation fuzzymatrix. Inthis study,thedefuzzifica- tionprocedureusesCOG(centerofgravity)defuzzificationmethod.

TheresultsareshowninTable5.Thisyieldstwosetsofnumbers:

( ˜D_i+R˜_i)^def,which shows theimportance of all strategic objec- tivesbyaggregatingallexpertpreferences,and( ˜D_i−R˜_i)^def,which assignsstrategicobjectivesintocauseandeffectgroups.Moreover, thefuzzyspreadsof ˜D_i+R˜_iand ˜D_i−R˜_iareshowninTable5.In Table5,thephenomenacanbeobservedthatAFDEMATELmethod canobtainsmallerfuzzyspreadswhichmeanstheAFDEMATELcan crediblyreducefuzzyspreads.

Fig.2showsthecauseandeffectdiagramwithdifferentfuzzy arithmetic.QuadrantIcontains thecorefactors(C₁,C₇,C₈,C₁₆) shouldbeconsidered.Thesecriteriaaretheimportantinselection ofcanssuppliers.QuadrantIIcontainsdrivingcriteria(C3,C4,C6, C₁₂,C₁₄)onlyaffectsafewothercriteria.QuadrantIIIcontainsinde- pendentcriteria(C₅,C₉,C₁₁,C₁₃,C₁₅)canbeindividuallyhandled becausetheymaynotaffectothercriteria.QuadrantIVcontains affectedcriteria(C₂,C₁₀,C₁₇)shouldbeindirectlyconsidered.Fur- thermore, fromobserving Fig.2(b)–(d)also shows AFDEMATEL methodwithdifferent␣valuescanobtainthereasonablefuzzy bound.Thefuzzyboundsofcriteria(C1,C2,C4,C5,C11,C12,C14, C₁₅,C₁₆,C₁₇)crossdifferentquadrants,whichshouldgiveamore credibleanalysis.InAFDEMATELmethod,thecrossdifferentquad- rantsphenomenonalsomaybechangedwithdifferent␣values.

ThisphenomenoncannotbeobservedinfuzzyDEMATELmethod orTωfuzzyDEMATEL.

Fig.3AFDEMATELshowsacausalrelationmapwiththeAFDE- MATEL method, and displays results of defuzzified and fuzzy bounds values. Again, AFDEMATEL may change the decision- makingprocessinthatmoreaccurateevaluationsarepossiblein uncertainenvironments.

5.2. Theoreticalandmanagerialimplications

Aneffectivedecisionmodelforsupplierselectionisessentialin sustainablesupplychainmanagement.Theoretically,thefuzzyset theorycanbeemployedtodesignanAFDEMATELmodelforsup- plierselectioninsustainablesupplychainmanagementsystems.

TheAFDEMATELmodelutilizesfuzzyboundswithvarious␣val- uestoprioritizedecisions.Themethodproposedinthisstudyis betterthantheconventionalfuzzyDEMATEL.Inreal-worldprac- tice,theAFDEMATELmodelemploysfuzzynumbersorlinguistic variablestodealwithcomplicatedtrade-offsinsustainablesupply chainmanagementsystems.

Table4

Theassessmentdatafuzzymatrixofageneralmanager(Dalalahetal.,2011).

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17

C1 – VH L H H NO VH L H H H VH L L H H H

C2 H – H H H NO NO L L H NO L NO NO NO NO NO

C3 H VH – L VH L NO NO H H NO NO NO NO NO H NO

C4 VH H NO – NO NO NO L L H NO NO NO NO H H NO

C5 H H L NO – NO L NO L NO NO L NO NO L VH NO

C6 H H NO H H – NO L L H NO L NO NO NO VH L

C7 VH NO NO NO H NO – H NO VH H NO L H H H L

C8 L L L H NO NO H – H H H NO H VH NO H H

C9 NO NO NO NO L NO NO L – NO NO NO NO NO NO H NO

C10 H H NO VH NO NO H NO L – H L H H H H H

C11 H L NO NO L NO NO NO NO H – NO L NO NO H VH

C12 VH H NO NO H NO NO NO NO H NO – NO NO NO L H

C13 NO NO NO NO NO NO H NO H NO NO NO – H NO H H

C14 H L NO NO NO NO VH H VH VH H NO L – NO H NO

C15 H NO NO H L NO NO NO L VH NO NO NO NO – H L

C16 H H H NO H H H VH H H H L H VH H – H

C17 L NO NO NO L NO H H H H H L NO NO L H –

−:meanstriangularfuzzynumber[0,0,0].

Table5

Thevaluesof ˜Di+R˜i, ˜Di−R˜i,( ˜Di+R˜i)^def,and( ˜Di−R˜i)^defwithdifferentfuzzyDEMATELmethods.

FuzzyDEMATELmethod AFDEMATELmethodwith␣=0

D˜i+R˜i D˜i−R˜i Fuzzy spread

( ˜Di+R˜i)^def ( ˜Di−R˜i)^def D˜i(+Tω)^aR˜i D˜i(−Tω)^˛R˜i Fuzzy spread

( ˜Di(+Tω)^aR˜i)^def ( ˜Di(−Tω)^˛R˜i)^def

C1 (1.33,2.52,5.83) (−2.23,0.03,2.28) 4.50 3.22 0.02 (2.44,2.52,2.60) (−0.04,0.03,0.11) 0.16 2.50 0.02 C2 (0.80.1.57,4.36) (−2.10,−0.32,1.46) 3.56 2.24 −0.32 (1.50,1.57,1.65) (−0.40,−0.32,−0.24) 0.16 1.60 −0.30 C3 (0.56,1.14,3.60) (−1.19,0.32,1.86) 3.04 1.76 0.32 (1.06,1.14,1.21) (0.25,0.32,0.39) 0.15 1.12 0.30 C4 (0.65,1.27,3.81) (−1.57,0.01,1.58) 3.15 1.90 0.00 (1.20,1.27,1.35) (−0.06,0.01,0.09) 0.15 1.30 0.00 C5 (0.73,1.51,4.24) (−2.07,−0.26,1.44) 3.50 2.15 −0.29 (1.43,1.51,1.58) (−0.33,−0.26,−0.19) 0.15 1.50 −0.27 C6 (0.49,1.00,3.40) (−0.74,0.67,2.18) 2.91 1.62 0.70 (0.93,1.00,1.07) (0.60,0.67,0.75) 0.15 1.00 0.70 C7 (0.91,1.75,4.53) (−1.65,0.15,1.97) 3.61 2.39 0.15 (1.68,1.75,1.83) (0.07,0.15,0.23) 0.16 1.76 0.14 C8 (0.86,1.73,4.62) (−1.53,0.30,2.24) 3.76 2.40 0.33 (1.66,1.73,1.82) (0.22,0.30,0.38) 0.16 1.73 0.30 C9 (0.59,1.25,3.85) (−2.47,−0.77,0.79) 3.26 1.90 −0.82 (1.18,1.25,1.33) (−0.85,−0.77,−0.70) 0.15 1.25 −0.80 C10 (1.20,2.24,5.44) (−2.29,−0.18,1.95) 4.24 2.96 −0.17 (2.17,2.24,2.32) (−0.26,−0.18,−0.10) 0.15 2.24 −0.20 C11 (0.65,1.30,3.92) (−1.75,−0.08,1.52) 3.27 1.95 −0.10 (1.23,1.30,1.37) (−0.15,−0.08,−0.01) 0.14 1.30 −0.10 C12 (0.53,1.11,3.53) (−1.42,0.05,1.58) 3.00 1.72 0.07 (1.04,1.11,1.19) (−0.02,0.05,0.14) 0.15 1.10 0.06 C13 (0.49,1.02,3.48) (−1.59,−0.10,1.41) 2.99 1.66 −0.09 (0.96,1.02,1.08) (−0.15,−0.10,−0.03) 0.12 1.00 −0.10 C14 (0.78,1.49,4.04) (−1.37,0.24,1.89) 3.25 2.10 0.25 (1.41,1.49,1.57) (0.17,0.24,0.32) 0.15 1.50 0.24 C15 (0.60,1.24,3.81) (−1.66,−0.03,1.55) 3.20 1.88 −0.04 (1.17,1.24,1.31) (−0.10,−0.03,0.04) 0.14 1.22 0.00 C16 (1.42,2.67,6.19) (−2.37,0.03,2.40) 4.76 3.42 0.02 (2.60,2.67,2.75) (0.05,0.03,0.11) 0.16 2.70 0.01 C17 (0.81,1.64,4.53) (−1.90,−0.05,1.82) 3.72 2.32 −0.04 (1.57,1.64,1.71) (−0.12,−0.05,0.02) 0.14 1.63 −0.05

Fig.2.Comparisonofcauseandeffectdiagramintheselectionofcanssupplier.

TheAFDEMATELmodelutilizesdefuzzifiedvalues, unitprice andpaymentterms(C₁),technicalspecifications(C₇),certifications (C8),andmajorcustomerswiththesamebusiness(C16)asthose factorsmeasuredbyfirms.Certificationsarealsoincludedbythe InternationalOrganizationforStandardization(ISO)14000Envi- ronmentalmanagement.Inthefuzzyrightbound,thevariationof dimensions(C14)andcertificateofsuppliermaterials(C17)should beconsidered.Intheexampleherein,thecertificateofsupplier materialsshouldsatisfytheISO14000whenthedecision-maker adoptstheresultsofthefuzzyrightbound.Inthefuzzyleftbound, onlycertifications(C₈)andtechnicalspecifications(C₇)areconsid- ered.Inanuncertainenvironment,theimportantcriteriaofcans

suppliersareC₈andC₇,whicharerelatedtoenvironmentalissues.

Insustainablesupplychainmanagement,theproposedAFDEMA- TELmodeloffersguidelinesformanagementtoallocateresources.

Inaddition,theAFDEMATELmodelcandividethecriteriaofcans suppliersintofourquadrantswithfuzzyboundsand␣values.

ThisstudyimprovesthetraditionalfuzzyDEMATELmethodand extendstheTωfuzzyDEMATELmethod(Linetal.,2014)bydecreas- ingthephenomenonoffuzzinessaccumulation.TheAFDEMATEL modelisabletoaccuratelyevaluatethecauseandeffectrelation- shipswhenthefuzzyintervalsareacrossquadrantswithdifferent

␣values for decision makers.In theexample of cans suppliers selection,theAFDEMATELmodelsuggeststhatdecisionmakersin

Fig.3. ThecausalrelationmapwithAFDEMATELwith␣=0method.