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1、IEEETRANSACTIONSONFUZZYSYSTEMS,VOL.6,NO.2,MAY1998195FuzzyClusteringforSymbolicDataYasserEl-SonbatyandM.A.IsmailAbstractÐMostofthetechniquesusedintheliteratureinclus-symbolicobjectsmayincludeoneormoreelementaryobjectsteringsymbolicdataarebasedonthehierarchicalmethodology,andth
2、edatasetmayhaveavariablenumberoffeatures[4].whichutilizestheconceptofagglomerativeordivisivemethodsStructuredobjectshavehighercomplexitythancontinuousandasthecoreofthealgorithm.Themaincontributionofthispapersymbolicobjectsbecauseoftheirstructure,whichismuchistoshowhowtoapplyt
3、heconceptoffuzzinessonadatasetofsymbolicobjectsandhowtousethisconceptinformulatingthemorecomplex,andtheirrepresentation,whichneedshigherclusteringproblemofsymbolicobjectsasapartitioningproblem.datastructurestopermitthedescriptionofrelationsbetweenFinally,afuzzysymbolicc-means
4、algorithmisintroducedasanelementaryobjectcomponentsandfacilitatehierarchicalobjectapplicationofapplyingandtestingtheproposedalgorithmonmodelsthatdescribehowanobjectisbuiltupfromtherealandsyntheticdatasets.Theresultsoftheapplicationoftheprimitives.Asurveyofdifferentrepresentat
5、ionsandproximitynewalgorithmshowthatthenewtechniqueisquiteefficientand,inmanyrespects,superiortotraditionalmethodsofhierarchicalmeasuresofstructuredobjectscanbefoundin[10].nature.Diday[3]andGowdaandDiday[4],[5]presenteddis-similarityandsimilaritymeasuresbasedonposition,span,In
6、dexTermsÐFuzzyclustering,hierarchicaltechniques,parti-tioningtechniques,softclustering,symbolicobjects.andcontentofsymbolicobjects.Thedistancemeasureisusedintheareaofconventionalhierarchicalclusteringofsymbolicdata.MoreworkcanbefoundinthefieldofI.INTRODUCTIONconceptualhierarch
7、icalclusteringofsymbolicdata.FisherHEobjectiveofclusteranalysisistogroupasetofob-[6]introducedatop-downincrementalconceptualclusteringTjectsintoclusterssuchthatobjectswithinthesameclusterusingacategoryutilitymetriccalledtheCOBWEB.Chenghaveahighdegreeofsimilarity,whileobjectsb
8、elongingtoandFu[7]developedHUATUOwhichproducedintermediatedifferentc