Choice processes for non-homogeneous group decisio

DECSAIDepartmentofComputerScienceandArticialIntelligenceChoiceProcessesforNon-HomogeneousGroupDecisionMakinginLinguisticSettingF.Herrera,E.Herrera-Viedma,J.L.VerdegayTechnicalReport#DECSAI-95121.October,1995ETSdeIngenieraInformatica.UniversidaddeGranada.18071Granada-Spain-Phone[phone],Fax[phone]ChoiceProcessesforNon-HomogeneousGroupDecisionMakinginLinguisticSettingF.Herrera,E.Herrera-Viedma,J.L.VerdegayDept.ofComputerScienceandArticialIntelligenceUniversityofGranada,18071-Granada,Spaine-mail:herrera,viedma,[e-mail]rocessesofalternativesfornon-homogeneousgroupdecisionmakingproblems,assuminglinguisticpreferencerelationsforexpressingtheopinionsofindividualsandlinguisticval-uesforexpressingtheirrespectivepowerorimportancedegrees,arepresented.Theseprocessesaredesignedusingtwochoicedegreesofalternativesbasedontheconceptoffuzzymajority:quanti-erguidedlinguisticdominancedegreeandquantierguidedlinguisticnon-dominancedegree,beingthelastoneageneralizationofOrlovski’snon-dominatedalternativeconcept.Inordertodealwithnon-weightedlinguisticinformation,thelinguisticorderedweightedaveraging(LOWA)operatorisapplied.Todealwithweightedlinguisticinformation,threeoperatorsoflinguisticweightedinforma-tionaggregationareused:thelinguisticweighteddisjunction(LWD)operator,thelinguisticweightedconjunction(LWC)operatorandthelinguisticweightedaveraging(LWA)operator.Keywords:Linguisticmodelling,groupdecisionmaking,linguisticpreferencerelation,fuzzylinguisticquantier.1IntroductionHumanbeingsareconstantlymakingdecisionsinmostoftheirday-to-dayactivities.Sothestudyofdecisionmakingprocesseshasalwaysbeenaeldofgreatinteresttomanyresearchers.Abriefhistoricalsurveycoveringthestudyofdecisionmakingprocessessmaybedividedintothreedistinctperiods[34]:(i)optimizationperiod,wheretheproblemisdenedexactly,(ii)multiplecriteriaperiod,thatisasastrictoptimizationperiod,andmorerecently,(iii)fuzzydecisionperiod,thatisbasedinapplicationofFuzzySetTheory.Frequently,realworlddecisionmakingproblemsareilldened,i.e.,theirobjetivesandparametersarenotpreciselyknown.Theseobstaclesoflackofprecisionhavebeendealtwithusingtheprobabilisticapproach.But,duetothefactthattherequirementsonthedataandontheenvironmentareveryhighandthatmanyrealworldproblemsarefuzzybynatureandnotrandom,theprobabilityapplicationshavenotbeenverysatisfactoryinalotofcases.Ontheotherhand,theapplicationofFuzzySetTheoryinrealworlddecisionmakingproblemshasgivenverygoodresults.Itsmainfeatureisthatitprovidesamoreexibleframework,whereitispossibletosolvesatisfactorilymanyoftheobstaclesoflackofprecision.Insomehumanactivitiesitshouldbeverysuitabletohavethehelpofacomputerizeddecisionsupportsysteminthedecisionmakingprocesses,e.g.inmedicaldiagnosis,nancialorpoliticalworldprocesses.Thestudyofrealworlddecisionmakingproblemstodesigncomputerizeddecisionsupportsystemsimpliestwosteps:(1)establishingappropriatemathematicaldecisionmodelsclosetorealworldproblemsand,(2)implementationofthexedmodels.Applicationsonbothsenseshavebeendealtwithusingfuzzytechniquesin[3,6,5,15,29].Here,weareinterestedinprovidingnewdecisionmodelsforgroupdecisionmakingproblems.Groupdecisionmakingproblemsmaybedenedasadecisionsituationinwhich(i)therearetwoormoreindividuals,eachofthemcharacterizedbyhisorherownperceptions,attitudes,motivations,andpersonalities,(ii)whorecognizetheexistenceofacommonproblem,and(iii)attempttoreachacollectivedecision.Insuchasituation,twoclassicalwaystorelatetodierentdecisionschemesareknown[3].Therstway,calledthealgebraicway,consistsofestablishingagroupchoiceprocesswhichobtainsadecisionschemeassolutiontogroupdecisionmakingproblem.Thesecondone,calledthetopologicalway,consistsofestablishingagroupconsensusprocessfordierentdecisionschematauntilachievingthepossiblemaximumconsensusdegreeaboutsolutionalternative(s)set.Bothprocessesmaybecombinedinaresolutionscheme:rstly,consensusprocessisapplied,ineachstep,thedegreeofexistingconsensusamongexperts’opinionsismeasured;iftheconsensusdegreeissatisfactory,thenchoiceprocessisappliedinordertoobtainasolution,otherwisetheexpertsarepersuadedtoupdatetheiropinions.Inthisway,agroupdecisionmakingprocessmaybedenedasadynamicanditerativeprocesswheretheexperts,viaexchangeofinformationandrationalarguments,updatetheiropinionsuntiltheybecomesucientlysimilar.ThisisrepresentedinFigure1.GCGC-++-QUESTIONOPTIONSETOFINDIVIDUALSRECOMMENDATIONSCDCDOPTIONSGROUPDECISIONMAKINGnon-satisfactoryconsensusdegreesatisfactoryconsensusdegreeSETCONSENSUSPROCESSRESOLUTIONSCHEMECONSENSUSSOLUTIONCHOICEPROCESSFigure1:GroupDecisionMakingProcessSometimes,onemayadmitthatthevariousindividualsthatgivetheopinionsarenotequallyimpor-tant(e.g.reliable).Insuchacase,itiscallednon-homogeneousgroupdecisionmakingproblemand,otherwise,homogeneousgroupdecisionmakingproblem.Onewayofmodellingthisaspectistoconsidertheexistenceofamanagerthatassignsaweighttoeachexpert.Theweightsmaybeinterpretedinatleasttwodierentways[14]:1.Eachindividualisviewedasasubgroupandtheweightreectstherelativesiz