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Vague集转化为Fuzzy集方法及Vague集相似度量的研究.docx

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Vague集转化为Fuzzy集方法及Vague集相似度量的研究 Abstract Vaguesetsareanimportanttoolinreasoningunderuncertainty.Theyareusedtorepresentuncertaintyindecision-makingproblemswheretheboundariesofthesetsarenotclearlydefined.Thispaperfocusesontheconversionofvaguesetstofuzzysetsandthemeasurementofsimilaritybetweenvaguesets.Itdiscussesthedifferentapproachesusedfortheconversionofvaguesetstofuzzysetsandhighlightstheprosandconsofeachapproach.Thepaperalsopresentssomepopularsimilaritymeasuresforvaguesetsanddiscussesthelimitationsofthesemeasures. Introduction VaguesetswereintroducedbyGeorgeKlirin1995asageneralizationoffuzzysets.Invaguesets,theboundariesofthesetsarenotclearlydefined.Thismakesvaguesetssuitableformodelinguncertaintyindecision-makingproblems.Vaguesetshavebeenusedinvariousfieldsincludingdatamining,expertsystems,anddecision-making.However,thelackofwell-definedboundariesmakesitdifficulttousevaguesetsforquantitativeanalysis.Thishasledtothedevelopmentoffuzzysetswhichhaveclearlydefinedboundaries. Fuzzysetshavebeenwidelystudiedandtherearemanymethodsforconvertingvaguesetstofuzzysets.Inthispaper,wewilldiscussthedifferentmethodsusedfortheconversionofvaguesetstofuzzysetsandanalyzetheireffectiveness.Wewillalsoreviewsomepopularsimilaritymeasuresforvaguesetsanddiscusstheirlimitations. ConversionofVagueSetstoFuzzySets Thereareseveralmethodsforconvertingvaguesetstofuzzysets.Someofthecommonmethodsinclude: 1.TruncationMethod:Thismethodinvolvessettingathresholdvalueforthevaguesetandtruncatingthesetatthatvalue.Thisresultsinafuzzysetwithclearlydefinedboundaries.However,thismethodcanresultinlossofinformation. 2.ConvexificationMethod:Thismethodinvolvestransformingthevaguesettoaconvexsetwhilepreservingthemembershipvalues.Thismethodiseffectiveinpreservingtheinformationinthevagueset. 3.IntervalValuedFuzzySets(IVFS):ThismethodinvolvesconvertingthevaguesettoanIVFS.AnIVFSisafuzzysetwhosemembershipfunctionisdefinedbyarangeofvaluesinsteadofasinglevalue.Thismethodiseffectiveinmodelingtheuncertaintyinthevagueset. 4.