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1、FuzzySets~mdSystems31(1989)343-349343North-HollandINTERVALVALUEDINTUITION
2、STICFUZZYSETSK.ATANASSOVInstituteofMicrosy~'tems,Sofia,BulgariaG.GARGOVLML,CICT-PAS,Sofia,BulgariaReceivedAugust1987RevisedJanuary1988Abstract:Ageneralizationofthenotionofintuitionisticfuzzy~ctisgiveninthespiritofordinary
3、intervalvaluedfuzzysets.Thenewnationiscalledintervalvaluedintuitionisticfuzzyset(IVIFS).HerewepresentthebasicpreliminariesofIVIFStheory.Keywords:Fuzzyset;intervalvaluedfuzzyset;intervalvaluedintuitionisticfuzzyset;intuitionisticfuzzyset;modaloperator.1.
4、n~du~onAnintuitionisticfuzzyset(IFS)A,for
5、agivenunderlyingsetEisrepresentedbyapair(#a,vA)offunctionsE--*[0,1].ForxeE,#a(x)givesthedegreeofmembershiptoA,vA(x)givesthedegreeofnon-membership.ThisinterpretationentailsthenaturalrestrictionClearlyordinaryfuzzysets(FS)overEmaybeviewedasspecialcasesofIFS's-herethedegreeofmembershipistheonlynec
6、essarydata,i.e.ordinaryfuzzysetsaretobeconsideredasIFS'swiththeadditionalconditionv~(x)=1-#~(x).ThetheoryofIFS'sisdevelopedin[1].Inthepresentpaperwebegintheinvestigationofageneralizationofthisnotion-theintervalvaluedIFS's(IVIFS's),butwefirstconsidertherelationshipbetweenIFS'sandanothergeneraliz
7、ationofFS's-theintervalvaluedFS's(IVFS's,cf.e.g.[2]).2.IVF$andIFSAgeneralizationofthenotionoffijzzyset,proposedbysomeresea.rchersintheareaintheseventies(cf.e.g.[2]),istheso-calledintervalvaluedfuzzyset.HerewegiveadefinitionandestablishthatinasenseintervalvaluedfuzzysetsareaversionoftheIF$(orify
8、oulike:-theotherwayaround!).0165-0114/89/$3.50C~)1989,ElsevierSciencePublishersB.V.(North-Holland)344K.Atanassov,G.GargovDefu~en1.AnintervalvaluedfuzzysetA(overabasicsetE)isgivenbyafunctionMA(x)~whereMA"E--*INT([0,1]),thesetofallsubintervalsoftheunitinterval,i.e.foreveryx¢E,MA(x)isanintervalwit
9、hin[0,1].Thejustificationofthisgeneralizationliesinthefollowingobservation:sometimesitisnotappropriatetoassumethatthedegreesofmembershipforcertainelementsofEareexactlydefined,soweadmitakindoffurtheruncertainty-thevalueofMAisnotanu
