Page - 183 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 270 3.ResearchMethod 3.1. FuzzyLogic Fuzzy theory, proposedbyZadeh in1965, isused tomap linguistic terms tonumerical terms withinhumandecisions. The fuzzy set is oftendefined to solve theuncertainty andvagueness in criteriaweightingandalternativesratingsofmulti-criteriadecisionmakingproblems[39].Afuzzyset, featuredbyamembershipfunction,assignseachcriterionamembershipratingamong(0,1), reflects criteriagradesbelongingtoaset. Inaddition, linguistic termssuchas“good”,“fair”and“bad”are put forwardtodefinenumerical intervals [40]. A triangular fuzzynumber ĂM, denotedby (a,b,c), is themostpopular fuzzynumber in fuzzy applications [41]. Themembershipfunction isdefinedas follows: μMpxq“ $’’’&’’’% x´a b´a , aď xď b c´x c´b , bď xď c 0, otherwise (1) and–8<aďxďb<8. Inconcrete terms, themembership functionμMpxq“ 1 indicates thatvariablex fullybelongs to the fuzzysetĂM. Conversely, if thevariablexdoesnotbelongto the fuzzysetĂM, thenμMpxq“0 [42]. LetĂM1 “pl1,m1,r1qandĂM2 “pl2,m2,r2qbetwotriangular fuzzynumbers, theoperation laws areshownasbelow: ĂM1‘ĂM2 “pl1` l2,m1`m2,r1`r2q (2)ĂM1dĂM2 «pl1l2,m1m2,r1r2q (3) λĂM1 “pλl1,λm1,λr1q ,λą0 (4)ĂM1´1 «p1{l1,1{m1,1{r1q (5) AndthedistanceofĂM1 “pl1,m1,r1qandĂM2 “pl2,m2,r2qcanbedefinedas follows[43]: d ´ĂM1,ĂM2¯“ 12 ż 1 0 rl1`pm1´ l1qα`r1´pr1´m1qα´ l2´pm2´ l2qα´r2`pr2´m2qαsdα (6) InmostMCDMprocesses,decisionmakersoftenprovideuncertainanswersrather thanprecise values. Linguisticvaluesandfuzzysettheoryarerecommendedtoratepreferenceinsteadoftraditional numericalmethod. Therefore, the fuzzyset theoryhasbeen integrated intovariousMCDMmethods, suchas fuzzyAHP, fuzzyTOPSIS, fuzzyVIKOR,andsoon,whichshouldbemoreappropriateand effective thanconventionalones inrealproblemsinvolvinguncertaintyandvagueness [44–46]. 3.2. FuzzyDelphiMethod TheDelphimethod (DM) is a techniqueused toobtain themost reliable consensus amonga groupofexperts. ItwasproposedbyDalkyandHelmer in1963andhasbeenwidelyused indecision andpredictionmaking. This techniqueoffersexpertsopportunities toreceive feedbackandmodify previousopinions throughseveral roundsof consulting. Furthermore, owning to itsdeficiency in handlingambiguityanduncertaintywithinexpertsurveys, fuzzyDelphimethod(FDM)wasproposed tosolvethesedefectscombingDMwithfuzzylogic theory. Expertscanprovidetheiropinionsthrough triangular fuzzynumbers (TFNs),andarenotrequiredtomodify themagainandagain.Moreover, nouseful informationwouldbe lost,becauseallopinionscanbeeffectively taken intoaccountbythe membershipdegrees.Dueto itsadvantages inevokinggroupdecisions,FDMisembracedinvarious studies toconstructevaluation. Torecognize thevital criteria for theoptimalsitingofEVCS, theFDM is introducedin thispaper. Essential stepsof theFDMare listedas follows: 183