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1、IntuitionisticFuzzySets-AnAlternativeLookAnnaPankowskaandMaciejWygralakFacultyofMathematicsandComputerScienceAdamMickiewiczUniversityUmultowska87,61-614Poznan′,Polande-mail:wygralak@math.amu.edu.plAbstractwillshowinSection3thatsomefundamentalno-tionsofthattheorydore
2、quirearevisionwhennon-Thispaperconcernsthetheoryofintui-strictArchimedeantriangularnormsareused.ThattionisticfuzzysetsaccordingtoAtanassov.modifiedlookwillbeappliedinSection4togroupIftriangularnorms,especiallynonstrictdecisionmaking.Section2recollectstheoriginalArch
3、imedeanones,areused,weproposeaconceptofintuitionisticfuzzysetswithtriangularrevisionandaflexibilizinggeneralizationofnormsusingabitmodifiednotationandterminology.somefundamentalnotionsandconstructionsofthattheory.Itsapplicationtogroupde-2IntuitionisticFuzzySetscisio
4、nmakingisoutlined.AfuzzysetisanebularcollectionofelementsKeywords:Intuitionisticfuzzyset,Trian-fromauniverseMdescribedbyandidentifiedwithgularnorm,Scalarcardinality,Groupdeci-a(membership)functionA:M→[0,1].Anintui-sionmaking.tionisticfuzzysetisinsteadanebularcollect
5、ionofelementsfromMidentifiedwithapair=(A,Ad),1IntroductionwhereA,Ad:M→[0,1]andTheterm"intuitionisticfuzzysets"doesfunction?x∈M:A(x)+Ad(x)≤1.(2.1)intwocontextsintheliteraturedevotedtofuzziness.Inthefirstone,wethenmeanintuitionisticlogic-Again,oneinterpretsAasamembers
6、hipfunction:-basedfuzzysetsdevelopedin1984byTakeutiandA(x)isadegreeofmembershipofxintheintui-Titani(see[11,12]).Atalmostthesametimeandtionisticfuzzyset,whereasAd,afunctiondualdisregardingthattheadjective"intuitionistic"isre-toA,isunderstoodasanonmembershipfunction,s
7、ervedforcontructionsrelatedtointuitionisticlogic,i.e.Ad(x)doesexpressadegreeofnonmembershipAtanassovproposedageneralizationoffuzzysetsofxinthatintuitionisticfuzzyset.Adoubleopticsandcalledhisconstructionsintuitionisticfuzzysets,isthusexploitedinintuitionisticfuzzyse
8、ttheorytoo(seee.g.[1,2]).Thisabitunfortunateandcolli-byapplyinginAamany-valuedformoftheclas-dingnamewasandisasourceofsomereservationssical
