Sustainability Indicator Selection by a Novel Triangular Intuitionistic Fuzzy Decision-Making

SustainabilityIndicatorSelectionbyaNovelTriangular IntuitionisticFuzzyDecision-MakingApproachinHighway ConstructionProjects

HassanHashemi 1 ,ParvizGhoddousi 1,*andFarnadNasirzadeh 2

1 SchoolofCivilEngineering,IranUniversityofScienceandTechnology,P.O.Box16765-163,Narmak, Tehran1684613114,Iran;hashemi.h@live.com

2 SchoolofArchitectureandBuiltEnvironment,DeakinUniversity,Geelong,VIC3220,Australia; farnad.nasirzadeh@deakin.edu.au

* Correspondence:ghoddousi@iust.ac.ir;Tel.:+98-21-77240398

Citation: Hashemi,H.;Ghoddousi, P.;Nasirzadeh,F.SustainabilityIndicatorSelectionbyaNovelTriangular IntuitionisticFuzzyDecision-Making ApproachinHighwayConstruction Projects. Sustainability 2020, 13,1477. https://dx.doi.org/10.3390/su13031

477

Received:1October2020

Accepted:13November2020

Published:1February2021

Publisher’sNote: MDPIstaysneutralwithregardtojurisdictionalclaims inpublishedmapsandinstitutional affiliations.

Abstract: Theconstructionindustryhasbeencriticizedasbeinganon-sustainableindustrythat requireseffectivetoolstomonitorandimproveitssustainabilityperformance.Themultiplicityof indicatorsofthethreepillarsofsustainability—economic,social,andenvironmental—complicates constructionsustainabilityassessmentsforprojectmanagers.Therefore,prioritizingandselecting appropriatesustainabilityindicators(SIs)isessentialpriortoconductingaconstructionsustainability assessment.ThemainpurposeofthisresearchistoselectthemostappropriatesetofSIstoaddress allthreepillarsofhighwaysustainabilitybyanewgroupdecision-makingapproach.Theproposed approachaccountsforriskattitudesofexpertsandentropymeasuresunderatriangularintuitionistic fuzzy(TIF)environment,tohandletheinherentuncertaintyandvaguenessthatispresentthroughout theevaluationprocess.Furthermore,newseparationmeasuresandrankingscoresareintroducedto distinguishthepreferenceorderofSIs.Eventually,theapproachisimplementedinacasestudyof highwayconstructionprojectsandtheapplicabilityoftheapproachisexamined.Toinvestigatethe stabilityandvalidityofcomputationalresults,asensitivityanalysisiscarriedoutandacomparison ismadebetweentheobtainedrankingoutcomesandthetraditionaldecision-makingmethods.

Keywords: sustainablehighwayconstruction;sustainabilityindicators;triangularintuitionistic fuzzy;multi-criteriadecision-making;entropymeasure;riskattitudes

1.Introduction

Thepreliminaryconceptofsustainabledevelopmentwasintroducedinthe1980s[1]. AccordingtotheWorldCommissiononEnvironmentandDevelopment(WCED)report, sustainabledevelopmentreferstodevelopmentthatcanbeusefulfornature,notharmful andaidsinmeetingtheneedsofpresentgenerationswithoutcompromisingtheneedsof futuregenerations.Sustainabledevelopmentisgenerallybalancedamongthreeaspects orpillars:economic,environmentalandsocialsustainabilityandaimstomeetallthese needs/objectivessimultaneously[2].

Copyright: ©2020bytheauthors.LicenseeMDPI,Basel,Switzerland.This articleisanopenaccessarticledistributed underthetermsandconditionsofthe CreativeCommonsAttribution(CCBY) license(https://creativecommons.org/ licenses/by/4.0/).

Inrecentdecades,sustainableconstruction—asafundamentalcontributortowards sustainabledevelopment—hasbeenthefocusofagreatdealofresearch.Recentresearch effortshavelargelyconcentratedontheperformancemeasurementprocessandsustainabilityassessmentinbuildingandconstructionprojects,basedonanalyticalandcomputational evaluationapproaches,sustainableconstructiontools,standardsandratingsystems,ora combinationofthese.Indeed,thesestudieshaveattempted—byvarioustechniques—toaid theconstructionindustryinreachingsustainabledevelopmentidealsandgoals.Asillustratedbelow,someoftheseresearchstudieshavebeenreviewed.Yuetal.[3]providedthe projectmanagementteamwithplanningstrategiesusingasustainability-assessingsystem. Theproposedsystemwasdevelopedtomonitorandevaluatethesustainabilityofwhole

activitiesthroughouttheconstructionprojects’lifecycle.GoubranandCucuzzella[4] presentedtwoanalyticalmappingtoolsfordesignteamsofbuildingprojectstoutilize SustainableDevelopmentGoals(SDGs)asasustainabilityanalyzingframeworkinthe designprocess.Thefirsttoolwasconstructedbasedondistinguishingbetweenthearchitectural,engineeringandoperationalconcerns,whilethesecondtoolwasdesigned basedonthecharacteristicsofthedesignapproach(eitherproductorhuman-focused) anditsinspiration(historyvs.futuredriven).Karacaetal.[5]developedarapidsustainabilityassessmentmethodusingindicatorsandtheirrelativeweightsattainedfrom stakeholders,andanassessmentapproachbasedontheresponsesofbuildings’occupantstomeasurethesustainabilityperformanceofresidentialbuildingsinNur-Sultan, Kazakhstan. Lietal. [6]providedacomprehensiveanalysisofvariousstakeholdergroups associatedwithsustainableconstructioninChina.Inaddition,thelevelofstakeholder influenceindecision/evaluationswasmeasuredusingsemi-structuredinterviewsand theDelphitechnique.OmerandNoguchi[7]developedaconceptualframeworkforthe selectionofappropriatebuildingmaterialsconsideringtheimplementationofthe2030 AgendaforSustainableDevelopment.Indeed,theypresentedaknowledge-baseddecision supportsystemtoassistpolicymakers,designersandconstructionstakeholdersinmaking appropriatedecisionstowardstheachievementofSDGs.Xuetal.[8]evaluatedthesustainabilityoftheconstructionindustrybyanassessmentmodelbasedontheentropymethod inChina.Thelevelofsustainabilityinconstructionprojectswasdeterminedbytwoindices namedthesocial,economic,andenvironmentalbenefitsindexandtheecologicalcosts index.Illankoonetal.[9]suggestedascoringmodelregardingtheinter-linksbetweenthe LeadershipinEnergyandEnvironmentalDesign(LEED)creditsandSDGstoevaluate buildingsconstructedinAustralia.TheirproposedmodelidentifiedaComprehensive ContributiontoDevelopmentIndex(CCDI)topolicymakersasaguidelineforevaluating buildingprojectsinordertoachievetheUnitedNations(UN)’sSDGs.Olawumietal.[10] introducedagradingsystemofbuildingsinNigeria,namedtheBuildingSustainability AssessmentMethod(BSAM)scheme.Theschemeinvolvestheidentificationofkeysustainabilityassessmentcriteriaandassignsweighted-scorestothevariouscriteriabythe multi-expertconsultationmethod.Manselletal.[11]usedempiricalevidencetoidentify agoldenthreadbetweensustainabilityreportingframeworksattheprojectlevelandthe organizationallevel,andimpactsoftheUN’sSDGs.Theframeworksbenefitfromthe CeequalreportingmethodologyattheprojectlevelandtheGlobalReportingInitiative (GRI)methodologyattheorganizationallevel.Accordingly,adatabaseofindicatorswas extractedthatalignedwiththespecificSDGtargets.Additionally,arobustinvestment appraisalwasprovidedforthedesignstageofinfrastructureprojects.

Sincehighwayprojectsareoneofthemostimportantaspectsforthedevelopment oftransportationinfrastructure—necessaryduetohigherpopulationconcentrationsand greatertransportationdemandsinurbanareas[12,13]—theyhavebeenconsideredas oneofthemostcrucialcomponentsofsustainabledevelopment.Moreover,highway constructionprojectsuseavastquantityofenergyandnaturalmaterials,generatewaste, andproducegreenhousegasesthatcangreatlyaffectthesustainabilityoftheconstruction industry.

Thesustainabilityindicators(SIs)aresignificantfactorsinthesustainabilityassessmentofhighwayprojects.VariousstudiesandtoolshaveintroducednumerousSIsforthe assessmentofthesustainabilityofconstructionprojectsthathasledtothecomplication oftheassessmentprocess.Therefore,theprioritizationofindicatorsandtheadoptionof anoptimalnumberofSIsaremajorissues.Inaddition,theevaluationofSIsiscomplex fordecision-makers,owingtoinadequateevidenceanduncertaintysurroundinghighway constructionprojects[13–15].Hence,Multi-CriteriaDecision-Making(MCDM)techniques underuncertaintyareusefultoolstocopewiththeseproblems[16–20].Whiletheconstructionindustryplaysanimportantroleinglobalsustainabledevelopment,numerousresearch effortshavestudieddifferentsubjectsregardingthesustainabilityoftheconstructionindustryandtheuseofmulti-criteriadecisionmakingtoevaluatesustainabilityinthisindustry.

HuangandYeh[21]developedaframeworktoanalyzethegreenhighwayprojectsapplyingthemax-minfuzzyDelphimethodtorecognizethemainclassificationsandrelated items.Chenetal.[22]proposedamodelcalledtheconstructionmethodselectionmodel aimedatlendingsupporttoassesstheprefabricationfeasibilityattheinitiallevelutilizing thesimplemulti-attributeratingtechniqueandsubsequentlytoadoptthebeststrategy toemployprefabricationatthefollowinglevel.Rezaetal.[23]proposedathoroughassessmenttechniqueusingTripleBottomLine(TBL)criteriatoassessflooringsystemswith respecttothecombinationofAnalyticHierarchyProcess(AHP)andLifeCycleAnalysis (LCA)techniques.Warisetal.[24]establishedcriteriaforselectingsustainableconstructionequipmentbasedonqualitativeandquantitativefeedbacksofconstructionindustry expertsandfinallyselectedthetopfivecriteria.Lietal.[25]proposedacomprehensive methodologyusingentropy,whichissuitableforcalculatingweights,andtheTechnique forOrderofPreferencebySimilaritytoIdealSolution(TOPSIS)methodsatthesametime toevaluatethedevelopmentofhighwaytransportation.Kucukvaretal.[26]presenteda fuzzyMCDMmethodforprioritizingpavementsandselectingthebestonebasedonthe respectivesustainabilityperformanceusingtheTOPSISmethod.Medineckieneetal.[27] proposedanovelMCDMtechniquetoadoptcriteriafromwhichtheirsetsandweightsare determinedinaccordancewiththeSwedishcertificationsystemMiljöbyggnadandused AHPforbuildingsustainabilityassessment.KamaliandHewage[28]identifiedsustainabilityperformanceindicatorstoevaluatelifecyclesustainability.Subsequently,anorganized frameworkwasdevelopedbasedondesigningandconductingasurveytochoosethemost suitablesustainabilityperformanceindicatorsformodularandconventionalconstruction methodsinNorthAmerica.Panetal.[29]developedasustainabilityindicatorframework toreliablyassesstheperformanceofconstructionautomationandroboticsinthebuilding industrycontext.Indeed,thestudyproposedguidelinesforsustainableautomatedand roboticoptionsforadvancedconstructiontechnology.Zolfanietal.[30]presentedahybrid MCDMmethodologyapplyingStep-wiseWeightAssessmentRatioAnalysis(SWARA) andComplexProportionalAssessment(COPRAS)forcriteriaweightsandprioritizing alternatives,respectively.

LiuandQian[31]developedanintegratedsustainabilityassessmentmethodologyin accordancewiththelifecyclesustainabilityassessmentframework.Inaddition,acombinationofAHPandELiminationEtChoiceTranslatingREality(ELECTRE)wasappliedto derivecriteriaweightsandprioritizealternatives.Reddyetal.[32]introducedadecisionmakingmethodtoadoptasustainablematerialwithoutLifeCycleInventory(LCI)informationrequirements.Inthismethod,criteriathathighlyinfluencematerialsustainability wereinvestigatedandconsequentlyappliedtoanalyzetheperformanceofmaterialsin differentaspectsofthemateriallifecycletodevelopasustainablematerialperformance indexutilizingAHP.Chen[33]usedanewmulti-criteriaassessmentapproachintegrating theGreyRelationalAnalysis(GRA)andTOPSIStechniques,whichoperateaccording totheintuitionisticfuzzyentropymethod,forselectionoftheappropriatesustainable supplierofconstructionmaterials.Royetal.[34]developedacombinativedistance-based evaluationmethodutilizingInterval-ValuedIntuitionisticFuzzyNumbers(IVIFNs)to decidecomprehensivelyandlogicallytodealwiththeproblemofmaterialadoptionunder uncertainty.Tsengetal.[35]introducedvariousfeaturesandmeasurestobuildamodel andassesstheconstructionprojectsinEcuador,employingfuzzydecision-makingtrials withDecisionMakingTrialandEvaluationLaboratory(DEMATEL)inadditiontoan AnalyticNetworkProcess(ANP)toevaluateinterdependencebetweenthefeaturesof asustainableproduct–servicesystem.HendianiandBagherpour[14]presentedanovel socialsustainabilityperformanceassessmentinconstructionprojectsusingfuzzynumberstoevaluatethepresentsocialsustainabilitypositionassociatedwithconstruction. Furthermore,thebarriers thatreducethevalueofthesocialsustainabilityindexwererecognizedandaddressed.Alawnehetal.[36]proposedanovelframeworkthatidentifiesand weighsSIsforsustainablenon-residentialbuildingsandcontributestoachievingtheSDGs inJordan.TheframeworkappliestheDelphitechniquetoidentifyandcategorizeSIsand

thenintegratesAHPandRelativeImportanceIndex(RII)methodstoweighSIs.Inaddition, amanagementtool(Ganttchart)integratesSIsintotheprojectphasestowardssustainable constructionmanagement.Dabousetal.[37]proposedamulti-criteriadecision-support approachtohandledecision-makinginsustainablepavementadoption.Themainsustainabledecisionfactorswererecognizedthroughahierarchystructureintheirapproach. Inaddition,theAHPtechniqueincombinationwithmulti-attributeutilitytheorywas usedtorankthenetworksofpavementsections.Forsustainablelandfillsiteselection, Rahimietal.[38]introducedaGeographicalInformationSystem(GIS)-MCDMmethodologyconsideringthegroupfuzzyBest-WorstMethod(BWM),fuzzyMULTIMOORA methodandGIS-basedsuitabilitymaps.ThemethodologywasemployedinMahallatcity, Iran,anditcouldprovidesuitableguidanceforthewastemanagementdepartmentof municipalities.Navarroetal.[39]developedanassessmentmethodologytomeasurethe sustainabilityperformanceoftheconcretebridgedeckbasedonaneutrosophicgroupAHP approach.Inaddition,theTOPSIStechniquewasutilizedtoaggregatethesustainability criteria.

Theaforementionedstudiesdemonstratethatthepreviousresearchdidnotpaymuch attentiontothesustainabilityperformanceofhighwayconstructionprojects.Furthermore, therearenostudiesfocusingonprioritizingandselectingtheindicatorsofthethree sustainabilitypillars.Fortherecognizedgaps,anewmulti-criteriaweightingandranking approach,accordingtogroupdecision-making,ispresentedinthepresentstudytoanalyze andadoptSIsinhighwayconstructionprojects.Initially,SIsandcriteriaarecollectedand listedconcerningexperts’viewsandtheliteraturereview.Thus,triangularintuitionistic fuzzy(TIF)decisionmatricesareconstructedbasedonexperts’viewsintermsoflinguistic variables.Subsequently,theweightsofexpertsaregainedaccordingtotheconceptof entropy.Afterward,primaryweightvectorsofcriteriaarespecifiedbyentropymeasures andexperts’views.Finally,SIsarerankedbasedonthepositiveandnegativeideal separationmatricesviapresentinganewrankingscore.Moreover,acasestudyinhighway constructionprojectsisaddressedtodemonstratetheefficiencyofthepresentedapproach. Therestofthispaperisorganizedasfollows.InSection 2,anovelmulti-criteria groupdecision-makingapproachisproposedandappliedinacasestudyofahighway constructionproject.Section 3 presentstheresultsoftheapproachimplementationin detail.Theobtainedresultsarecomparedwiththeprevalentdecision-makingmethods andothermentionedSIsinthecitedliterature,andthesensitivityanalysesareconducted inSection 4.Toconcludethepaper,Section 5 depictstheconcludingremarks.

2.MaterialsandMethods

2.1.TIFGroupDecision-MakingApproach

Theproposedapproachaimstoassistprojectmanagersinselectingthemostsignificant SIsforsustainabilityassessmentofhighwayconstructionprojectsbasedonanovelTIF groupdecision-makingapproach.Figure 1 presentstheproposedapproachfortheselection ofSIs.

Thephasesofthepresentedapproachareasfollows:

Step1. Constituteagroupofexperts (Ee; e = 1,2, , t),whoseviewsandjudgmentswill beemployedtobuildandassesstheproblem.

Step2. Gatheralistofindicatorsthatarepossibletobeappliedforthesustainability evaluationofhighwayconstructionprojects(Ii; i = 1,2,..., m). Step3. RecognizeasetofcriteriaforanalyzingSIsthroughconsensusofexperts’views (Cj; j = 1,2,..., n). Step4. Assigntheriskattitudetoeachexpertandincorporateitintotherelatedtriangular intuitionisticfuzzynumbers(TIFNs)(DefinitionA1).

Linguistic Variables

TIFN Derived from ⟨(��,��,��);��,��⟩ for Benefit Criteria

TIFN Derived from ⟨(��,��,��);��,��⟩ for Cost Criteria

Absolutely optimistic (AO) ⟨(��,��,��);��+��,��⟩ ⟨(��,��,��);��,��+��⟩

Optimistic (O) ⟨(��, (��+��)⁄2 ,��);��+��2 ⁄ ,��⟩ ⟨(��, (��+��)⁄2 ,��);��,��+��2⁄⟩

Neutral (N) ⟨(��,��,��);��,��⟩ ⟨(��,��,��);��,��⟩

Pessimistic (P) ⟨(��, (��+��)⁄2 ,��);��,��+��2⁄⟩ ⟨(��, (��+��)⁄2 ,��);��+��2 ⁄ ,��⟩

Absolutely pessimistic (AP) ⟨(��,��,��);��,��+��⟩ ⟨(��,��,��);��+��,��⟩

Figure1. Theproposedapproachfortheselectionofsustainabilityindicators(SIs).

Figure 1. The proposed approach for the selection of sustainability indicators (SIs).

Eachexpertisassignedariskattitudeaccordingtohisorhercharacter.Therisk attitudesareabletobespecifiedbyahighermanagementlevelandexpressedbylinguistic variables,likeabsolutelyoptimistic(AO),optimistic(O),neutral(N),pessimistic(P), andabsolutelypessimistic(AP)[40,41],for5-scaleTIFNs(Table 1).

In Table 1, �� indicates the hesitation degree of TIFN ⟨(��,��,�� );��,�� ⟩ and is equal to 1−��− Step 5. Construct the primary decision matrices based on the experts' views.

The primary decision matrices are constructed from the performance rating of each indicator versus each criterion based on the experts' view in terms of linguistic terms (Table 2) and converted into TIFNs.

Table1. Linguisticvariablesoftheriskattitudesassignedtoeachexpertfor5-scaletriangular intuitionisticfuzzynumbers(TIFNs).

�� = �� × = �� ,�� ,�� ;�� ,�� ×

LinguisticVariables

TIFNDerived from 〈(a,b, c);µ, ν〉 forBenefit Criteria

TIFNDerived from 〈(a,b, c);µ, ν〉 forCost Criteria

Table 2. Linguistic variables applied for the rating of SIs.

Linguistic Variables Triangular Intuitionistic Fuzzy Numbers

Extremely high (EH) 〈(0.95,1.00,1.00);0.95,0.05〉

Very very high (VVH) 〈(0.90,1.00,1.00);0.90,0.10〉

Absolutelyoptimistic(AO) (a, c, c) ; µ + π, ν (a, a, c) ; µ, ν + π Optimistic(O) (a, (b + c)/2, c) ; µ + π/2, ν (a, (a + b)/2, c) ; µ, ν + π/2 Neutral(N) (a, b, c) ; µ, ν (a, b, c) ; µ, ν Pessimistic(P) (a, (a + b)/2, c) ; µ, ν + π/2 (a, (b + c)/2, c) ; µ + π/2, ν Absolutelypessimistic(AP) (a, a, c) ; µ, ν + π (a, c, c) ; µ + π, ν

Very high (VH) 〈(0.80,0.90,1.00);0.80,0.10〉

High (H) 〈(0.70,0.80,0.90);0.70,0.20〉

Medium high (MH) 〈(0.50,0.60,0.70);0.60,0.30〉

Medium (M) 〈(0.30,0.50,0.70);0.50,0.40〉

InTable 1, π indicatesthehesitationdegreeofTIFN (a, b, c) ; µ, ν andisequalto 1 µ ν

Medium low (ML) 〈(0.30,0.40,0.50);0.40,0.50〉

Step5. Constructtheprimarydecisionmatricesbasedontheexperts’views.

Low (L) 〈(0.10,0.20,0.30);0.25,0.60〉

Very low (VL) 〈(0.00,0.10,0.20);0.10,0.75〉

Theprimarydecisionmatricesareconstructedfromtheperformanceratingofeach indicatorversuseachcriterionbasedontheexperts’viewintermsoflinguisticterms (Table 2)andconvertedintoTIFNs. Xe = xe ij m×n = axe ij , bxe ij , cxe ij ; µxe ij , νxe ij m×n

Very very low (VVL) 〈(0.00,0.00,0.10);0.10,0.90〉

Step 6. Convert the primary decision matrices to the individual decision matrices based on expert's risk attitude.

Table2. LinguisticvariablesappliedfortheratingofSIs.

LinguisticVariablesTriangularIntuitionisticFuzzyNumbers

Extremelyhigh(EH) (0.95,1.00,1.00) ;0.95,0.05 Veryveryhigh(VVH) (0.90,1.00,1.00) ;0.90,0.10 Veryhigh(VH) (0.80,0.90,1.00) ;0.80,0.10 High(H) (0.70,0.80,0.90) ;0.70,0.20 Mediumhigh(MH) (0.50,0.60,0.70) ;0.60,0.30 Medium(M) (0.30,0.50,0.70) ;0.50,0.40 Mediumlow(ML) (0.30,0.40,0.50) ;0.40,0.50 Low(L) (0.10,0.20,0.30) ;0.25,0.60 Verylow(VL) (0.00,0.10,0.20) ;0.10,0.75 Veryverylow(VVL) (0.00,0.00,0.10) ;0.10,0.90

Step6. Converttheprimarydecisionmatricestotheindividualdecisionmatricesbasedon eachexpert’sriskattitude.

Theprimarydecisionmatricesareconvertedtodecisionmatricestakingintoaccount eachexpert’sriskattitudeaccordingtoTable 1 Re = re ij m×n = are ij , bre ij , cre ij ; µre ij , νre ij m×n (2) Step7. Computeeachexpert’sentropy-weightaccordingtotheindividual decisionmatrices Theentropymeasure Fe ij iscalculatedby[42]: Fe ij = f e ijln f e ij ln(t) ,(3) where f e ij = are ij + bre ij + cre ij × 1 + µre ij νre ij ∑t e=1 are ij + bre ij + cre ij × 1 + µre ij νre ij

.(4)

Thus,eachexpert’sentropy-weightisdeterminedasfollows[42,43]: αe ij = ∑t e=1 Fe ij + 1 2 × Fe ij ∑t e=1 ∑t e=1 Fe ij + 1 2 × Fe ij ,(5) where0 ≤ αe ij ≤ 1,and ∑t e=1 αe ij = 1. Step8. BuildtheaggregatedTIFdecisionmatrixtakingintoaccounttheentropy-weights ofexperts.

AccordingtotheTIFweightedgeometricaggregation(TIFWGA)operator[44],theaggregatedTIFdecisionmatrixconcerningtheentropy-weightsofexpertsisgainedas follows: R = rij m×n = arij , brij , crij ; µrij , νrij m×n (6) where rij = r1 ij α1 ij ⊗ r2 ij α2 ij ⊗···⊗ rt ij αt ij .

Step9. Constructtheprimaryweightvectorsofcriteriabasedonexperts’views. Thesignificanceofcriteriaisprovidedbasedontheexperts’viewsintermsoflinguistic terms(Table 3). ωe = ωe j = aωe j , bωe j , cωe j ; µωe j , νωe j ,(7)

Table3. Linguisticvariablesappliedforratingthesignificanceofcriteria.

LinguisticVariablesTriangularIntuitionisticFuzzyNumbers

Veryimportant(VI) (0.80,0.90,1.00) ;0.90,0.10 Important(I) (0.60,0.70,0.80) ;0.75,0.20 Medium(M) (0.40,0.50,0.60) ;0.50,0.45 Unimportant(UI) (0.20,0.30,0.40) ;0.35,0.60 Veryunimportant(VUI) (0.00,0.10,0.20) ;0.10,0.90

Step10. Converttheprimaryweightvectorstotheindividualweightvectorsbasedon eachexpert’sriskattitude.

Theprimaryweightvectorsareconvertedtotheindividualweightvectorstakinginto accounteachexpert’sriskattitudeaccordingtoTable 1 we = we j = awe j , bwe j , cwe j ; µwe j , νwe j ,(8)

Step11. Computeeachexpert’sentropy-weightaccordingtotheweightvectors. Theentropymeasure Ge j iscalculatedby[42]: Ge j = ge j ln ge j ln(t) ,(9) where ge j = awe j + bwe j + cwe j × 1 + µwe j νwe j ∑t e=1 awe j + bwe j + cwe j × 1 + µwe j νwe j

.(10)

Thus,eachexpert’sentropy-weightaccordingtotheexpert-basedweightvectoris determinedasfollows[42,43]: βe j = ∑t e=1 Ge j + 1 2 × Ge j ∑t e=1 ∑t e=1 Ge j + 1 2 × Ge j ,(11) where0 ≤ βe j ≤ 1,and ∑t e=1 βe j = 1.

Step12. ProvidetheTIFweightvectorofthecriteria. TheTIFweightvector W isbuiltaccordingtoexperts’entropy-weightbyusing DefinitionA2asfollows: W = Wj = W1, W2, , Wn ,(12) where Wj = aWj , bWj , cWj ; µWj , νWj = w1 j β1 j ⊗ w2 j β2 j ⊗···⊗ wt j βt j .(13)

Step13. ComputetheTIFpositive-idealsolution(PIS)andtheTIFnegative-idealsolution (NIS)vectors.

TheTIFPIS r∗ j andtheTIFNIS rj are,respectively,definedasfollows:

max i crij , max i crij , max i crij ; max i µrij , min i νrij forj ∈ J1 min i arij , min i arij , min i arij ; min i µrij , max i νrij forj ∈ J2,

min i crij , min i crij , min i crij ; min i µrij , max i νrij forj ∈ J1 max i arij , max i arij , max i arij ; max i µrij , min i νrij } forj ∈ J2, (15)

where J1 and J2 arethebenefitcriteriaandcostcriteria,respectively.

Step14. Determinethepositive-idealseparation(PISE)andthenegative-idealseparation (NISE)matrices.

The PISE matrix(∆∗)andthe NISE matrix(∆ )aredefinedbasedonhamming distance[45].

1 , r11 ∆(r∗ 2 , r12) ∆(r∗ n, r1n )

r

1 , r21 . ∆(r∗ 2 , r22) . . ∆(r∗ n, r2n )

r∗ 1 , rm1 ∆(r∗ 2 , rm2) ··· ∆(r∗ n, rmn )

 ,(16) and

= ∆ij m

n =

∆ r1 , r11 ∆ r2 , r12 ∆(rn , r1n ) ∆ r1 , r21 .

∆ r2 , r22 ··· . ∆(rn , r2n ) ∆ r1 , rm1 ∆ r2 , rm2 ∆(rn , rmn )

     .(17) Step15. Computethe Ai, Bi, Ai,and Bi values.

The Ai, Bi, Ai,and Bi valuesarecomputedaccordingtothescorefunction[46] asfollows:

Ai = ∑n j=1 ∆∗ ij · Wj = 1 4 n ∑ j=1 ∆∗ ij aWj + 2∆∗ ij bWj + ∆∗ ij cWj 1 n ∏ j=1 1 µWj

Bi = max j d∗ ij Wj = max j 1 4 ∆∗ ij · aWj + 2∆∗ ij · bWj + ∆∗ ij · cWj 1 1 µWj

Ai = ∑n j=1 ∆ij · Wj = 1 4 n ∑ j=1 ∆ij aWj + 2∆ij bWj + ∆ij cWj 1 n ∏ j=1 1 µWj

Bi = max j ∆ij Wj = max j 1 4 ∆ij · aWj + 2∆ij · bWj + ∆ij · cWj 1 1 µWj

Step16. Calculatethe κi and ϑi values.

Thevaluesofindices κi and ϑi arecalculatedasfollows:

∆∗ ij n ∏ j=1 ν ∆∗ ij Wj

∆∗ ij ν ∆∗ ij Wj

∆ij n ∏ j=1 ν ∆ij Wj

(18)

(19)

(20)

∆ij ν ∆ij Wj

(21)

κi = χ Ai A∗ A A∗ + (1 χ) Bi B∗ B B∗ ,(22) and ϑi = ψ Ai A A ∗ A + (1 ψ) Bi B B ∗ B ,(23)

and1 ψ aretherelativeimportanceoftheindividualregret.

Computethenovelrankingscore.

aredefinedasfollows:

Step18. RanktheSIsaccordingtotherankingscore (Ci values). TheSIsaresortedbythe Ci valuesindecreasingorder.Themaximumvalueofthe Ci indicatesthehigherimportance.

2.2.CaseStudy

Theefficiencyofthepresentedapproachwasexaminedthroughacasestudyofa highwayconstructionproject.Tothatend,anIranianconstructionfirmwasinvolvedin transportationinfrastructures.Thefirmhasnumeroushighwayconstructionprojectsbeing builtinvariousareasofthecountry.Toevaluatetheprojectsaccordingtosustainable constructionprinciples,thefirmmanagersintendedtorecognizeandprioritizeSIstoadopt thekeyevaluationindicatorsfromapoolofnumerousSIsintheseprojects.

Accordingtostep1,fiveexpertsworkingonhighwayprojectswereadoptedfrom employeesofthefirm.Theparticipantscomprisedconstructionprojectmanagersand sustainableconstructionexperts.Theyhadenoughexperienceandknowledgeofnearly allthesustainableaspectsofconstructionprojects.Assuch,agroupoffiveexperts(E1, E2, ,E5)wasconsideredforanalyzingpotentialSIs.Afterformingthecommittee, theexpertspickedoutasetofpotentialSIsinadditiontoasetofrelevantcriteriafor SIsassessment(Steps2and3).Tothatend,abrainstormingsessionwasheldwiththe expertsandthirtysustainabilityindicators(SoI1, SoI2, , SoI9, EcI1, EcI2, , EcI9, EnI1, EnI2, , EnI12),aswellassevencriteria(C1, C2, ,C7)wereobtainedfromthevarious investigationsintheliterature(e.g.,[22,47–64])andtheconsensusopinionofthegroup members (Tables 4 and 5).Furthermore,theprojectmanagerutilizingTable 1 specifies theexperts’riskattitudeaccordingtohisorherrecognitionofthem.Theoutcomesare representedinTable 6 (Step4).

Sustainabilityaspects

Social

Economic

Environmental

Table4. Listofobtainedsustainabilityindicators.

SustainabilityIndicatorsDescription

SoI1:HealthHighlightingon-sitesanitation,andtheprovisionofhealthcare

SoI2:EducationNumberandtimeoftrainingcoursetodifferentlevelsofemployees

SoI3:CultureandheritageMeasureofnegativeimpactsfromconstructionoperationsonanyculturalheritage

SoI4:Safety Numberofaccidents,thesupplyrateofon-sitesupervisionandtrainingcoursetoemployeestoprovideasafeand reliableworkplace

SoI5:StakeholdersatisfactionMeasureofstakeholdersatisfactionbyusingstakeholdermanagementmodels

SoI6:JobopportunitiesProvidingdirectandindirectjobs

SoI7:TourismImpactsontourismdevelopment

SoI8:TrafficVehicletrafficcongestion

SoI9:AccesstopublictransportationExtensionofpublictransportationservicesandproximitytoit

EcI1:Netpresentvalue(NPV)

NPV = ∑n t=1 Rt (1+i)t where Rt isthenetcashinflow-outflowsduringasingleperiodt, i isthediscountrateofreturnthatcould beearnedinalternativeinvestmentsandtisthenumberoftimeperiods

EcI2:PaybackperiodInitialInvestment/NetCashFlowperPeriod

EcI3:InvestmentplanningCompliancewiththeinvestmentplan

EcI4:Benefit–costratioRelationshipbetweentherelativecostsandbenefitsofaproposedprojectexpressedinmonetaryorqualitativeterms

EcI5:Debt–assetratio(Short-termDebt+Long-termDebt)/TotalAssets

EcI6:ProjectbudgetCompliancewithbudget

EcI7:Internalrateofreturn(IRR)

NPV = ∑T t=1 Ct (1+IRR)t C0 = 0 where Ct isthenetcashinflowduringtheperiodt, C0 isthetotalinitialinvestmentcostandt isthenumberoftimeperiods

EcI8:FinancialriskPossibilityoflosingmoneyontheinvestment

EcI9:Life-cyclecostTotalcostforaconstructionprojectoveritslife

EnI1:MaterialconsumptionEfficiencyrateofusingmaterialsandresources

EnI2:AirpollutionMeasureofmixtureofsolidparticlesandgasesintheair

EnI3:landscaperespectProtectionoflandscapefeaturesduringconstruction

EnI4:NoiseemissionsRateofnoisepollutionduringtheconstructionphaseintheenvironmentoftheproject

EnI5:ErosionRateofsoilerosionduringtheconstructionphaseintheenvironmentoftheproject

EnI6:EcologicalimpactsMeasureofnegativeimpactsfromprojecttoflora,fauna,andecosystems

EnI7:HabitatlossanddamageDestructiveeffectsonthelivingenvironmentforbothhumanbeingandanimals

EnI8:SoilcontaminationMeasureofalterationinthephysical,chemicalandbiologicalcharacteristicsofthesoilenvironment

EnI9:AestheticalandvisualimpactsAestheticqualityoftheprojectduringtheconstructionphase

EnI10:WaterpollutionMeasureofalterationinthephysical,chemicalandbiologicalcharacteristicsofwaterenvironment

EnI11:WatersavingRateofreductionwaterconsumptionduringtheconstructionphase

EnI12:HazardouswasteProductionrateofhazardouswaste

Criteria

C1:Measurability

Table5. Listofobtainedcriteria.

CriteriaType Description BenefitCost

Measurabilityinqualitativeorquantitativeterms

C2:Applicability Practicalityandstraightforwarduseofsustainabilityindicator(SI)forevaluation

C3:Dataavailability RelativesimplicitytogatherthenecessarydataforevaluationofSI

C4:Acceptant AcceptanceofSIbymajorstakeholders

C5:Complexity

RelativedifficultyinmeaningfulinterpretationofSI

C6:Timeconsuming RequiredtimefortheevaluationofSI

C7:Uncertainty

AmbiguityinassigningthevaluetoSIduringevaluation

Table6. Experts’riskattitudes.

Experts E1 E2 E3 E4 E5

Riskattitudes Neutral Absolutely optimistic PessimisticOptimisticNeutral

3.Results

Theprimarydecisionmatricesareconstructedbyexpertsemployinglinguisticterms inTable 2.ThematricesareshowninTable 7 (Step5).Afterward,theprimarydecision matricesareconvertedtodecisionmatricestakingintoaccounteachexpert’sriskattitude accordingtoTable 1 (Table 8)(Step6).Owingtospacelimitations,onlytheoutcomes associatedwiththreeSIs(SoI6, EcI4 and EnI10)areshownasasampleofeachdimensionof sustainabilityinsomeofthefollowingtables.

Then,eachexpert’sentropy-weightandaggregatedTIFdecisionmatrixiscalculated. TheoutcomesofthesestepsarerepresentedinTables 9 and 10,respectively(Steps7and8). Inaddition,thecriteriaweightvectorisachievedaccordingtoexperts’preferencesandis illustratedinTable 11 (Step9).Accordingtosteps10to12,basedoncriteriaweightvector, expert’sriskattitudeandexpert’sentropy-weight,theTIFcriteriaweightvectorsarebuilt. TheresultsarepresentedinTable 12.Next,theTIFPISandNISvectorsarespecifiedas giveninTable 13 (Step13).Then,asshowninTable 14,thePISEmatrix(D∗)andNISE matrix(D )arebuilt(Step14).

Table7. Performanceratingofeachindicatorversuseachcriterionbasedonexperts’viewsinterms oflinguisticterms.

Table7. Cont.

SIs Experts

SoI3

SoI4

SoI5

SoI6

SoI7

SoI8

SoI9

EcI1

EcI2

EcI3

Criteria

C1 C2 C3 C4 C5 C6 C7

E1 VLMLMHMHHMHVH E2 LLHHMHHH E3 VVLLHVHVHHVH E4 VLVLVHHHMHVH E5 VLLVHVHMHMHH

E1 HMHHHMLLML E2 VHMHVHVHMVVLL E3 HMVVHVHMLVLML E4 HMVHHLVVLL E5 VHMHVHVVHMLVLL

E1 LHMLVHVHHH E2 VLVHLHHMHVVH E3 MLVHVLVVHHVHVH E4 MLVVHVLVHVHHVH E5 LVVHMLVHVVHVHH

E1 VHVHHMHLLL E2 MHHHHVLMLL E3 HHMHMHVLLM E4 HVHMHMLMLM E5 VHVVHHHLLL

E1 VHMHMHLMHH E2 VHHMMHVLMHVH E3 VVHHMLVHVLHH E4 VHMHMLHVVLHMH E5 VVHMHMLHVLVHMH

E1 HMHMMHLHVH E2 MHHMHMHVLVHVVH E3 HHMHMVLHVH E4 HVHMHMVVLVHVVH E5 VHHMHLVHVH

E1 VHMHLMLVLMH E2 HHMLMHVLMLM E3 VHMHMLMLVLLM E4 HVHMLMVLLH E5 HHMMVVLMLMH

E1 EHEHHMLVLVVLH E2 EHVVHVVHMVVLVVLMH E3 EHEHVHMHVLVVLMH E4 EHVHVHMHVVLVVLM E5 EHEHVVHMLVVLVVLH

E1 VVHHHMLVLMH E2 VHVHHMLVLLH E3 VHHHLLLVH E4 VHHHLLVLH E5 VVHHVHMLVLVLVH

E1 HMHMHLMMLH E2 MHMHMVLMMLMH E3 HHMLMHMVH E4 VHHMLVLMHMMH E5 VHHMMLMHMHH

Table7. Cont.

SIs Experts

EcI4

EcI5

EcI6

EcI7

EcI8

EcI9

EnI1

EnI2

EnI3

EnI4

Criteria

C1 C2 C3 C4 C5 C6 C7

E1 EHEHVHMLMLML E2 EHVVHVVHMHMLLM E3 EHVVHVVHMLLML E4 EHEHVVHMHLMLML E5 EHEHEHMHVLLL

E1 VHHHMLLMLH E2 HHMHLLMLMH E3 VVHMHHLMLMMH E4 HMHMHLLMH E5 HHMHMLLMMH

E1 HVHHMLLMMH E2 VHVHHMVLMHH E3 HHMHMLVVLMH E4 VHVHVHMLVLMHMH E5 VHVVHVHMVVLMLH

E1 VVHEHVHMLVLVLMH E2 EHEHVHMLVVLVLH E3 EHEHVHMVVLVLMH E4 EHEHHMVLVVLMH E5 EHEHVVHMHVVLVVLML

E1 MLVVHMMLHMHEH E2 MHMLMLMHMHVVH E3 MHMLLMHHVH E4 MLMHMLMHVVH E5 MVVHMMLMMHVH

E1 MHHMMHMVHH E2 MHVHMLHMLHVH E3 HVHMLHMHVHVH E4 HHLVHMLVVHH E5 HVVHMLHMHMHMH

E1 HMHHMHLLH E2 HMHVHMLLVLMH E3 HMHHMLVLVLM E4 HHVHMHLLH E5 VHHVVHMVLVVLM

E1 VHVHMLMHMMLVH E2 HHMHMHMHMH E3 HHMHHMMLVH E4 VHVHMLHMHMLH E5 HVVHMHHMLH

E1 MLLMLMMHHVH E2 LLMLMHHHH E3 LMLMLMMHVHMH E4 VLLMLMHHMH E5 MLMLMMHMHHVH

E1 MMLMMLMHH E2 MHMLVLMHMMH E3 MLMLLMMLMLMH E4 MLMLMLMLMVH E5 MHMMLMHLMLMH

Table7. Cont.

SIs Experts

EnI5

EnI6

EnI7

EnI8

EnI9

EnI10

EnI11

EnI12

Criteria

C1 C2 C3 C4 C5 C6 C7

E1 MHMLLMLHHVH E2 MLVLLMHVHH E3 MLVLVLLHVHVH E4 MLLLVLVHHH E5 MHLMLMLMHHMH

E1 MHHMMHHH E2 MMHMLMHVHMHVH E3 MHMMHMHH E4 MHHMMLVHHMH E5 HVHMHMHVVHVHMH

E1 MLMHMLMMLMHH E2 MMLLMLMLMMH E3 MHMHMLLMMHMH E4 MMHMLMMH E5 MHMMMMLMH

E1 HVHHMHMLMHH E2 MHHMHMHMLMMH E3 HMHMHVLMH E4 MHMHMHHMLMHVH E5 VHVHHHLMLMH

E1 MMHMLMHMHMVH E2 MLHLHHMH E3 MLMHVLHHMHH E4 MLMHLVHMHHMH E5 MHMLVHMHMMH

E1 HHMHHMMM E2 VHHHHMMHMH E3 HMHMVHMMMH E4 VHHMHMLMHM E5 VVHVHMHVHMLMML

E1 HHMHHVLMH E2 HMHHMHVLMLVH E3 HMHMHHVLMHH E4 HHMMHLMLH E5 VHVHMHVHVLMLMH

E1 VHLMHMHVLMLVH E2 HMLMHLLH E3 MHLHMVLMLVH E4 MHMLMHMHVLMLH E5 HLHHVVLLMH

Table8. Experts’viewconcerningtheratingofsampleindicatorswithrespecttothecriteriabytakingintoaccounteachexpert’sriskattitude.

SIs

Criteria Experts

C1

C2

C3

SoI6 EcI4 EnI10

E1 (0.800,0.900,1.000) ;0.800,0.100 (0.950,1.000,1.000) ;0.950,0.050 (0.700,0.800,0.900) ;0.700,0.200

E2 (0.500,0.700,0.700) ;0.700,0.300 (0.950,1.000,1.000) ;0.950,0.050 (0.800,1.000,1.000) ;0.900,0.100

E3 (0.700,0.750,0.900) ;0.700,0.250 (0.950,0.975,1.000) ;0.950,0.050 (0.700,0.750,0.900) ;0.700,0.250

E4 (0.700,0.850,0.900) ;0.750,0.200 (0.950,1.000,1.000) ;0.950,0.050 (0.800,0.950,1.000) ;0.850,0.100

E5 (0.800,0.900,1.000) ;0.800,0.100 (0.950,1.000,1.000) ;0.950,0.050 (0.900,1.000,1.000) ;0.900,0.100

E1 (0.800,0.900,1.000) ;0.800,0.100 (0.950,1.000,1.000) ;0.950,0.050 (0.700,0.800,0.900) ;0.700,0.200

E2 (0.700,0.900,0.900) ;0.800,0.200 (0.900,1.000,1.000) ;0.900,0.100 (0.700,0.900,0.900) ;0.800,0.200

E3 (0.700,0.750,0.900) ;0.700,0.250 (0.900,0.950,1.000) ;0.900,0.100 (0.500,0.550,0.700) ;0.600,0.350

E4 (0.800,0.950,1.000) ;0.850,0.100 (0.950,1.000,1.000) ;0.950,0.050 (0.700,0.850,0.900) ;0.750,0.200

E5 (0.900,1.000,1.000) ;0.900,0.100 (0.950,1.000,1.000) ;0.950,0.050 (0.800,0.900,1.000) ;0.800,0.100

E1 (0.700,0.800,0.900) ;0.700,0.200 (0.800,0.900,1.000) ;0.800,0.100 (0.500,0.600,0.700) ;0.600,0.300

E2 (0.700,0.900,0.900) ;0.800,0.200 (0.900,1.000,1.000) ;0.900,0.100 (0.700,0.900,0.900) ;0.800,0.200

E3 (0.500,0.550,0.700) ;0.600,0.350 (0.900,0.950,1.000) ;0.900,0.100 (0.300,0.400,0.700) ;0.500,0.450

E4 (0.500,0.650,0.700) ;0.650,0.300 (0.900,1.000,1.000) ;0.900,0.100 (0.300,0.600,0.700) ;0.550,0.400

E1 (0.500,0.600,0.700) ;0.600,0.300 (0.300,0.500,0.700) ;0.500,0.400 (0.700,0.800,0.900) ;0.700,0.200

E2 (0.700,0.900,0.900) ;0.800,0.200 (0.500,0.700,0.700) ;0.700,0.300 (0.700,0.900,0.900) ;0.800,0.200

E3 (0.500,0.550,0.700) ;0.600,0.350 (0.300,0.400,0.700) ;0.500,0.450 (0.800,0.850,1.000) ;0.800,0.150

E5 (0.700,0.800,0.900) ;0.700,0.200 (0.950,1.000,1.000) ;0.950,0.050 (0.500,0.600,0.700) ;0.600,0.300 C4

E4 (0.300,0.600,0.700) ;0.550,0.400 (0.500,0.650,0.700) ;0.650,0.300 (0.700,0.850,0.900) ;0.750,0.200

E5 (0.700,0.800,0.900) ;0.700,0.200 (0.500,0.600,0.700) ;0.600,0.300 (0.800,0.900,1.000) ;0.800,0.100

E1 (0.100,0.200,0.300) ;0.250,0.600 (0.100,0.200,0.300) ;0.250,0.600 (0.300,0.500,0.700) ;0.500,0.400

E2 (0.000,0.000,0.200) ;0.100,0.900 (0.300,0.300,0.500) ;0.400,0.600 (0.300,0.300,0.700) ;0.500,0.500

C5

E3 (0.000,0.100,0.200) ;0.175,0.750 (0.100,0.167,0.300) ;0.325,0.600 (0.300,0.400,0.700) ;0.550,0.400

E4 (0.100,0.150,0.300) ;0.250,0.675 (0.100,0.150,0.300) ;0.250,0.675 (0.300,0.350,0.500) ;0.400,0.550

E5 (0.100,0.200,0.300) ;0.250,0.600 (0.000,0.100,0.200) ;0.100,0.750 (0.300,0.400,0.500) ;0.400,0.500

E1 (0.100,0.200,0.300) ;0.250,0.600 (0.300,0.400,0.500) ;0.400,0.500 (0.300,0.500,0.700) ;0.500,0.400

E2 (0.300,0.300,0.500) ;0.400,0.600 (0.100,0.100,0.300) ;0.250,0.750 (0.500,0.500,0.700) ;0.600,0.400

C6

E3 (0.100,0.167,0.300) ;0.325,0.600 (0.100,0.167,0.300) ;0.325,0.600 (0.300,0.400,0.700) ;0.550,0.400

E4 (0.300,0.350,0.500) ;0.400,0.550 (0.300,0.350,0.500) ;0.400,0.550 (0.500,0.550,0.700) ;0.600,0.350

E5 (0.100,0.200,0.300) ;0.250,0.600 (0.100,0.200,0.300) ;0.250,0.600 (0.300,0.500,0.700) ;0.500,0.400

E1 (0.100,0.200,0.300) ;0.250,0.600 (0.300,0.400,0.500) ;0.400,0.500 (0.300,0.500,0.700) ;0.500,0.400

E2 (0.100,0.100,0.300) ;0.250,0.750 (0.300,0.300,0.700) ;0.500,0.500

(0.500,0.500,0.700) ;0.600,0.400

C7

E3 (0.300,0.400,0.700) ;0.550,0.400 (0.300,0.300,0.500) ;0.450,0.500

E4 (0.300,0.400,0.700) ;0.500,0.450 (0.300,0.350,0.500) ;0.400,0.550

E5 (0.100,0.200,0.300) ;0.250,0.600 (0.100,0.200,0.300) ;0.250,0.600

(0.500,0.433,0.700) ;0.650,0.300

(0.300,0.400,0.700) ;0.500,0.450

(0.300,0.400,0.500) ;0.400,0.500

SIs Experts

SoI6

EcI4

EnI10

Criteria

Table9. Entropy-weightassignedtoeachexpert.

Criteria

C1 C2 C3 C4 C5 C6 C7

E1 0.1960.1990.1970.2020.1870.2060.208 E2 0.2070.2020.1950.1930.2280.1910.217

E3 0.2020.2050.2070.2040.2080.2050.184 E4 0.1990.1980.2040.2070.1900.1900.184

E5 0.1960.1970.1970.1940.1870.2060.208

E1 0.2000.1990.2020.2040.1960.1880.196

E2 0.2000.2010.2000.1950.1870.2140.193 E3 0.2000.2010.2000.2070.1950.2040.197 E4 0.2000.1990.2000.1960.2000.1890.198 E5 0.2000.1990.1980.1970.2220.2050.217

E1 0.2040.1990.1990.2020.1960.2020.200 E2 0.1970.1970.1910.2000.2000.1980.196 E3 0.2050.2100.2080.1990.1960.2020.195 E4 0.1980.1980.2030.2010.2050.1970.202 E5 0.1970.1950.1990.1980.2030.2020.208

Table10. Aggregatedtriangularintuitionisticfuzzy(TIF)decisionmatrix(R).

SIs

SoI6 EcI4 EnI10

C1 (0.688,0.814,0.890) ;0.748,0.196 (0.950,0.995,1.000) ;0.950,0.050 (0.775,0.892,0.958) ;0.803,0.154

C2 (0.776,0.895,0.958) ;0.806,0.153 (0.930,0.990,1.000) ;0.930,0.070 (0.670,0.784,0.872) ;0.724,0.216

C3 (0.610,0.726,0.812) ;0.685,0.254 (0.888,0.969,1.000) ;0.888,0.090 (0.432,0.596,0.734) ;0.600,0.338

C4 (0.512,0.674,0.772) ;0.642,0.297 (0.405,0.557,0.700) ;0.583,0.355 (0.738,0.859,0.938) ;0.769,0.171

C5 (0.000,0.000,0.251) ;0.188,0.746 (0.000,0.169,0.302) ;0.234,0.654 (0.300,0.384,0.610) ;0.465,0.475

C6 (0.152,0.232,0.365) ;0.316,0.591 (0.151,0.210,0.364) ;0.315,0.614 (0.367,0.487,0.700) ;0.548,0.390

C7 (0.150,0.222,0.410) ;0.328,0.587 (0.236,0.300,0.478) ;0.386,0.533 (0.366,0.444,0.653) ;0.521,0.415

Table11. Criteriaweightvectorbasedonexperts’preferences.

Experts

Criteria

C1 C2 C3 C4 C5 C6 C7

E1 IIIIMMI E2 MVIIVIIUII E3 IIIIIMI E4 MIVIIMMVI E5 IVIIIIMVI

Table12. TIFandcrispcriteriaweightvectors.

Criteria

WeightVectors

~ W

C1 (0.509,0.637,0.712) ;0.655,0.317 C2 (0.672,0.789,0.874) ;0.811,0.167 C3 (0.635,0.752,0.836) ;0.788,0.186 C4 (0.635,0.750,0.836) ;0.783,0.186 C5 (0.509,0.587,0.712) ;0.640,0.328 C6 (0.346,0.413,0.552) ;0.469,0.504 C7 (0.672,0.751,0.874) ;0.811,0.173

Table13. TIFpositive-idealsolution(PIS)andTIFnegative-idealsolution(NIS)vectors.

Criteria

IdealSolutions

TIFPISTIFNIS

C1 (0.950,0.995,1.000) ;0.950,0.050 (0.000,0.248,0.332) ;0.302,0.625 C2 (0.950,0.995,1.000) ;0.950,0.050 (0.151,0.263,0.363) ;0.318,0.584 C3 (0.888,0.969,1.000) ;0.888,0.090 (0.000,0.190,0.301) ;0.243,0.676 C4 (0.858,0.959,1.000) ;0.869,0.100 (0.000,0.202,0.278) ;0.253,0.672 C5 (0.123,0.176,0.330) ;0.279,0.637 (0.775,0.788,0.958) ;0.786,0.171 C6 (0.151,0.210,0.364) ;0.315,0.614 (0.758,0.773,0.958) ;0.769,0.171 C7 (0.151,0.199,0.363) ;0.305,0.623 (0.867,0.865,1.000) ;0.878,0.090

Table14. Positive-idealseparation(PISE)andnegative-idealseparation(NISE)matrices.

IdealSeparation SIs

PISE

NISE

Criteria

C1 C2 C3 C4 C5 C6 C7

SoI6 0.3130.2080.3440.3920.0490.0060.016 EcI4 0.0000.0280.0000.4900.0220.0000.063 EnI10 0.2110.3480.4860.1560.1460.2150.188

SoI6 0.5540.6290.4660.3920.6600.5720.718 EcI4 0.8670.8100.8100.2940.6330.5780.670 EnI10 0.6560.4900.3240.6280.4650.3630.545

Ultimately,the Ai, Bi, Ai, Bi, κi and ϑi valuesarecalculated(χ and ψ areconsidered 0.5).Then,thenovelrankingscoreiscalculated(η considered0.5),andSIsareprioritized accordingtorankingscore(Ci values).ThegatheredresultsarepresentedinTable 15 (Step15to18).

are represented for �� and �� values above 0.7.

Sustainability 2020, 13,1477

As can be seen in Figure 2b, changing the graph for �� and �� values above 0.7 leads to few changes in the ranking order of SIs. In addition, for variations of �� and �� between 0.2 and 0.7, the rank of all SIs remains unchanged, and also a set of the top ten SIs remains in a range from 1 to 10. Hence, the conclusion can be drawn that the top ten SIs have the lowest sensitivity to the values of �� and �� between 0.2 and 0.7, and the assumed value of 0.5 for this variable in the case study is suitable.

As can be seen in Figure 2b, changing the graph for �� and �� values above 0.7 leads to few changes in the ranking order of SIs. In addition, for variations of �� and �� between 0.2 and 0.7, the rank of all SIs remains unchanged, and also a set of the top ten SIs remains in a range from 1 to 10. Hence, the conclusion can be drawn that the top ten SIs have the lowest sensitivity to the values of �� and �� between 0.2 and 0.7, and the assumed value of 0.5 for this variable in the case study is suitable.

(a) (b)

(a) (b)

Figure 2. (a) Sensitivity analysis on the ℭ values and (b) preference ranking order of top ten SIs related to majority attributes (�� and �� ).

Figure 2. (a) Sensitivity analysis on the ℭ values and (b) preference ranking order of top ten SIs related to majority attributes (�� and �� ).

Figure2. (a)Sensitivityanalysisonthe C valuesand(b)preferencerankingorderoftoptenSIsrelatedtomajorityattributes (χ and ψ).

(a) (b)

(a) (b)

Figure 3. (a) Sensitivity analysis on the ℭ values and (b) preference ranking order of top ten SIs related to �� coefficient.

Figure 3. (a) Sensitivity analysis on the ℭ values and (b) preference ranking order of top ten SIs related to �� coefficient.

Figure3. (a)Sensitivityanalysisonthe C valuesand(b)preferencerankingorderoftoptenSIsrelatedto η coefficient.

InFigure 3a,b, C valuesandrankingordersversus η valuesrangingfrom0to1are represented,respectively.Figure 3arepresentsthatthegraphof C valuesforallSIsis ascendingbyincreasingthe η valuefrom0to1.However,accordingtothefigure,thegap betweenthevaluesof C increasesbydecreasing η.Thus,forsmallervaluesof η,thegap betweenthe C valuesofdifferentSIsislarger,allowinganaccuratedistinctionfordecisionmakers.Inaddition,accordingtoFigure 3b,itcanbeconcludedthattherankingorderof alltopSIsisconstantfor η valuesotherthan EnI2 forthevalueof η = 0.2.

Withtheseinmind,thisconclusioncanbedrawnthat C valuesandrankingorders havenosensitivityto η.Hence,choosing0.5asamediannumberoftheintervalfor η in thecasestudyisasuitablechoice.

4.2.ComparisonbetweentheProposedApproachandOtherCitedLiterature

Tovalidatethepresentedapproachoutcomes,acomparisonismadebetweenthe achievedresultsbytheproposedapproachandthetraditionalfuzzyMCDMmethods. Table 16 showstheoutcomesofthiscomparison.ThecomparisonresultsforthetoptenSIs arealsorepresentedinFigure 4

Table16. Comparativeoutcomesofthepresentedapproachandothertraditionalfuzzymulti-criteriadecision-making (MCDM)methods.

FuzzyMCDMMethods

SIs

ProposedApproach

Ranking Score

FuzzyVIKOR[65]FuzzySAW[66]FuzzyTOPSIS[67]

Preference Order Ranking Ranking Score

Preference Order Ranking Ranking Score

Preference Order Ranking Ranking Score Preference Order Ranking

SoI1 0.78650.17850.86650.6485

SoI2 0.363160.486150.756160.48316

SoI3 0.154280.721250.678240.39123

SoI4 0.75660.16040.87630.6802

SoI5 0.295210.755260.685230.40121

SoI6 0.82240.24160.85160.6286

SoI7 0.438140.490160.757150.49015

SoI8 0.302200.707230.701210.38924

SoI9 0.361170.491170.755170.46517

EcI1 0.87030.15030.87540.6674

EcI2 0.480130.380100.796100.53710

EcI3 0.238230.607200.712200.40520

EcI4 1.00010.00010.93710.7351

EcI5 0.341180.459140.766140.49214

EcI6 0.61090.36790.79890.5609

EcI7 0.90720.12520.88520.6743

EcI8 0.220240.839280.646280.30628

EcI9 0.430150.586190.731180.45718

EnI1 0.61880.35380.80280.5648

EnI2 0.544100.450130.770130.50313

EnI3 0.062290.916290.612290.25029

EnI4 0.161270.704220.677250.37025

EnI5 0.000301.000300.588300.19530

EnI6 0.315190.802270.662270.31027

EnI7 0.197260.712240.674260.36426

EnI8 0.515110.426120.775120.52911

EnI9 0.251220.661210.692220.39622

EnI10 0.63770.30470.82070.6037

EnI11 0.500120.420110.778110.52712

EnI12 0.211250.557180.730190.44119

Figure 4. Preference order ranking of top ten SIs prioritized by the proposed approach and other fuzzy MCDM methods.

Figure4. PreferenceorderrankingoftoptenSIsprioritizedbytheproposedapproachandotherfuzzyMCDMmethods.

As presented in Table 16 and Figure 4, the priority of SIs derived from the presented approach is not very different from other methods in most cases (in most cases, the number of ranks is changed by up to three or four rank shifts in SIs priority). Besides, EcI4 has the first priority in all methods, and EnI5 has the last priority in the presented approach and all methods. For the ten first priorities

Sustainability 2020, 12, x FOR PEER REVIEW 19 of 24

AspresentedinTable 16 andFigure 4,thepriorityofSIsderivedfromthepresented approachisnotverydifferentfromothermethodsinmostcases(inmostcases,thenumber ofranksischangedbyuptothreeorfourrankshiftsinSIspriority).Besides, EcI4 hasthe firstpriorityinallmethods,and EnI5 hasthelastpriorityinthepresentedapproachand allmethods.Forthetenfirstprioritiesthatarekeyindicators,despitesomechangesof ranks(atmostfourranks)insomemethods,theprioritiesofindicatorsremainwithinthe tenfirstprioritiesexcept EnI2.Furthermore,ascanbeobservedinthefigure,mostkey indicatorshavethesameranksintheproposedapproachandalltraditionalmethods. However, SoI4 hadrelativelymorechanges,whichcanbeconsideredasthemostsensitive keyindicator.

Fromtheabove,theconclusioncanbedrawnthattheproposedapproachisreliable anditsresultsbenefitfromthemeritsoftakingintoaccountriskattitudesofexperts, conceptsofentropyindeterminingweightsofexperts,andanewTIFS-rankingapproach concurrently.

Asanotheraspect,theresultsoftheapproachfortenSIswithahigherpriority arecomparedwiththeindicatorsprovidedbysevencitedliteraturestudiesandtools. ThecomparisonresultsareindicatedinTable 17 Table17. ComparisonoftenSIswithhigherpriorityandotherliteraturestudiesandtools.

AspresentedinTable 17,mostofthetenfirstprioritieshavebeenutilizedasSIs’ assessmentinthecitedliterature.MuchhigheradaptationisrelatedtoYaoetal.[59]and Envision[64]andlessadaptationisrelatedtoAwasthietal.[47].ThreeSIsoftenkey indicators, SoI1, SoI4 and EnI2,existinallcitedliterature.Inaddition, EnI10 isintroduced inalltheliteratureexceptAwasthietal.[47].Inaddition,itcanbeobservedthatthesocial andenvironmentalindicatorshavebeenincorporatedinallcitedtools(except SoI6 in Invest)buteconomicindicatorshavenotbeenconsideredinthecitedtools(except EcI4). Thesecomparisonsdemonstratethattheoutcomesoftheapproacharereliableandcanbe employedinasustainableassessmentofhighwayconstructionprojects.

5.ConcludingRemarks

Analyzingsustainabilityindicators(SIs)inconstructionprojectsbetweendifferent potentialindicatorsandconsideringvariousassessmentcriteriaconcurrentlycanbeconsideredasacomplicatedgroupdecisionproblem.Anewtriangularintuitionisticfuzzy set(TIFS)groupdecisionapproachforthemulti-criteriaevaluationispresentedinthis studytodealwiththisproblemunderuncertainty.Anovelmulti-criteriagroupdecisionmakingapproachconsidersexperts’riskattitudesandviewsandentropyconceptswere developedintheTIFSenvironment.Furthermore,newrankingscoreswereproposed throughsimilaritytoidealsolutionsbytheconceptofclosenesscoefficienttoprioritizeand choosethesustainableindicators.Acasestudyregardinghighwayconstructionprojects waspresentedtoanalyzethesustainableindicatorsunderuncertainty.Theconsideredcase studywassolvedusingtheintroducedgroup-decisionapproach.

Theprimaryaimofthispaperistopresentasoundapproachfortheassessmentand adoptionofSIsinhighwayconstructionprojects.Theprincipalnoveltiesofthisstudyare asfollows:

• Tocopewithuncertaintyinhighwayconstructionprojects,triangularintuitionistic fuzzysets(TIFSs)areused.TheTIFSsmaketheprocessofdecision-makingmore flexibleregardingdegreesofagreement,disagreement,andhesitancyutilizinga triangularfunction.

• Riskattitudesofexpertsareconsideredwithintheassessmentandprocessofgroup decision-makingbecausetheycanhavevariousperspectives,suchasoptimisticor pessimistic,intheirviewsowingtotheirvariousbackgroundsandcharacteristics.

• Anovelmethodologyisproposedtospecifyexperts’weightswithintheprocessof groupdecision-makingbasedontheconceptsofentropy.

• Anewcompromiserankingscoreisproposedtoevaluateandchoosesustainability indicatorsinhighwayconstructionprojects.

Ultimately,somesensitivityanalyseswereperformedonthepreferenceorderranking ofthetoptenSIsinacasestudyaccordingtothechangeofapproachcoefficientsand differentriskattitudesofexperts.Thedrawnconclusionofthesensitivityanalyseswas thatapproachcoefficientsselectedinthecasestudyweresuitablechoices.Moreover, thepresentedapproachwascomparedwiththetraditionalfuzzyMCDMtechniques, includingfuzzySAW andfuzzyVIKOR.Thecomputationalresultsrepresentedthatthere wasnomajordifferencebetweentheproposedapproachandotherfuzzyMCDMtechniquesregardingthepriorityofSIsinmostcases.Inaddition,boththefirstandlast prioritiesderivedfromthisapproachwerethesameinalltheaforementionedmethods.

Theintroducedcomprehensiveapproachhasproposedanefficientdecision-making methodforhighwayconstructionregardingsustainabledevelopmentprinciples.Infact, itpresentedadependablemodelinwhichtheresultsbenefitedfromthemeritsoftaking intoaccounttheriskattitudesofexpertsandthenewTIFS-rankingmethod.Furthermore, theappliedfundamentalconceptswereintelligibletothecommitteeofexpertsandproject managers,andtherequiredcalculationswerestraightforward.Hence,byintroducing evaluatedsustainableindicators,thispaperhelpsprojectmanagersimprovehighway projects’sustainabilityandmakethemostsustainabledecisions.Asfutureresearch, aholisticframeworkcanbedevelopedthatutilizesthementionedcriteriaandconsiders environmentalandsocialimpactsascriteriaintheevaluationofsustainabilityindicators. Inaddition,therankedSIswithhigherprioritycanbeusedaskeyindicatorsinthe sustainabilityassessmentofhighwayconstructionprojects.

AuthorContributions:

havereadandagreedtothepublishedversionofthemanuscript.

AppendixA

References

andnon-membershipfunctionisdefinedasfollows: νA (x) =







b x+(x a)ν b a ifa ≤ x < b ν ifx = b x b+(c x)ν c b ifb < x ≤ c 0 otherwise (A2)

wherea, bandcarerealnumbers,0 ≤ µ ≤ 1,0 ≤ ν ≤ 1 and 0 ≤ µ + ν ≤ 1. DefinitionA2. [44] Let A = (a, b, c) ; µ, ν and B = (a , b , c ) ; µ , ν betwoTIFNs,thenthe arithmeticoperationsaredefinedasfollows: A ⊕ B = a + a , b + b , c + c ; µ + µ µ µ , ν ν ,(A3) A ⊗ B = a a , b b , c c ; µ µ , ν + ν ν ν ,(A4) λ A = (λa, λb, λc) ;1 (1 µ)λ , νλ (λ ≥ 0),(A5) Aλ = aλ , bλ , cλ ; µλ ,1 (1 ν)λ (λ ≥ 0).(A6)

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