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1、FuzzySetsandSystems28(1988)15-3315North-HollandSTRU~~IDE~
2、CATIONOFFUZZYMODELM'SUGENOandG.T.KANGDepartmentofSystemsScience,TokyoInstituteofTechnology,4259Nagatsuda,Midori-ku,Yokohama227,JapanReceivedMay1986RevisedFebruary1987Theproblemsofstructureidentificationofa
3、~zzymodelareformulated.Acriterionfortheverificationofastructureisdiscussed.Usingthecriterion,analgorithmforidentifyingastructureissuggested.Further,asuccessiveidentificationalgorithmoftheparametersissuggested.Theproposedmethodsareappliedtoanexample.Keywords:Fuzzy
4、model,Identificationoffuzzymodel,Structureidentification.1.Inb'odu~onInmoststudiesofidentificationofe,processbyusingitsinput-outputdata,itisassumedthatthereexistsaglobalfunctionalstructurebetweentheinputandtheoutputsuchasalinearrelation,gtatisticalmethodsareusedt
5、oidentifytheparametersinamathematicalmodel.Itis,however,verydifficulttofindaglobalfunctionalstructureforanonlinearprocess.Ontheotherhand,fuzzymodellingisbasedontheideatofindasetoflocalinput-outputrelationsdescribingaprocess.Soitisexpectedthatthemethodoffuzzymodel
6、lingcanexpressanonlinearprocessbetterthananordinarymethod.Thereare,however,manyproblemsconcernedwiththestructureidentification~ofafuzzymodelwhenthereisnoaprioriinf'~rmationaboutitsstructure.Thispaperdiscussestheproblemsofstructureidentificationofafuzzymodel.Secti
7、on2describesafuzzymodel.Section3formulatestheproblemsandshowstheirsolutions.Section4showsanexample.2.F~zymodelAstheexpressionofafuzzymodelweusethefuzzyimplicationsandthefuzzyreasoningmethodsuggestedbyTakagiandSugeno[1].Afuzzyimplicationisofthefollowingform:U:Ifxl
8、isA~,x2isA~,...,xpisA~,,thenyi=do+c~xl+c~x2+..+%xp,i(1)0165-0114/88/$3.50©1988,ElsevierSciencePublishersB.V.(Non,h-Holland)I6M.Sugeno,G.T.KangL1:IfxIis,thenyl=1.Oxl+O.5x2+1.039/iiL2:IfxIisL/-__,x2is~_theny2=-O,lx1+4Ox2+l.239413L3:IfxIis//.~_,x2is_~~.theny3=O.9Xl
9、+O.7x2+9.0391118413L4:Ifxlis_~,x2is~thenyA~O.2xl+O.Ix2-~-O.2II18413Fig.1.Fuzzyimplication.whereUmeansthei-thimplicationandA~isafuzzyvariable,xjaninputvariable,
