ANFIS-adaptive-network-based-fuzzy-inference-syste

IEEETRANSACTIONSONSYSTEMS,MAN,ANDCYBERNETICS,VOL.23,NO.3,MAYIJUNE1993b65ANFIS:Adaptive-Network-BasedFuzzyInferenceSystemJyh-ShingRogerJangAbstract-ThearchitectureandlearningprocedureunderlyingANF’IS(adaptive-network-basedfuzzyinferencesystem)ispre-sented,whichisafuzzyinferencesystemimplementedintheframeworkofadaptivenetworks.Byusingahybridlearningprocedure,theproposedANFIScanconstructaninput-outputmappingbasedonbothhumanknowledge(intheformoffuzzyif-thenrules)andstipulatedinput-outputdatapairs.Inthesim-ulation,theANFISarchitectureisemployedtomodelnonlinearfunctions,identifynonlinearcomponentson-linelyinacontrolsystem,andpredictachaotictimeseries,allyieldingremarkableresults.Comparisonswithartificialneuralnetworksandearlierworkonfuzzymodelingarelistedanddiscussed.OtherextensionsoftheproposedANFISandpromisingapplicationstoautomaticcontrolandsignalprocessingarealsosuggested.I.INTRODUCTIONYSTEMMODELINGbasedonconventionalmathemati-Scaltools(e.g.,differentialequations)isnotwellsuitedfordealingwithill-definedanduncertainsystems.Bycontrast,afuzzyinferencesystememployingfuzzyif-thenrulescanmodelthequalitativeaspectsofhumanknowledgeandreason-ingprocesseswithoutemployingprecisequantitativeanalyses.Thisfuzzymodelingorfuzzyidentification,firstexploredsystematicallybyTakagiandSugeno[54],hasfoundnumerouspracticalapplicationsincontrol[36],[46],predictionandinference[16],[17].However,therearesomebasicaspectsofthisapproachwhichareinneedofbetterunderstanding.Morespecifically:1)Nostandardmethodsexistfortransforminghumanknowledgeorexperienceintotherulebaseanddatabaseofafuzzyinferencesystem.2)Thereisaneedforeffectivemethodsfortuningthemembershipfunctions(MF’s)soastominimizetheoutputerrormeasureormaximizeperformanceindex.Inthisperspective,theaimofthispaperistosuggestanovelarchitecturecalledAdaptive-Network-basedFuzzyInferenceSystem,orsimplyANFIS,whichcanserveasabasisforconstructingasetoffuzzyif-thenruleswithappropriatemembershipfunctionstogeneratethestipulatedinput-outputpairs.Thenextsectionintroducesthebasicsoffuzzyif-thenrulesandfuzzyinferencesystems.SectionI11describesthestructuresandlearningrulesofadaptivenetworks.ByembeddingthefuzzyinferencesystemintotheframeworkofManuscriptreceivedJuly30,1991;revisedOctober27,1992.ThisworkwassupportedinpartbyNASAGrantNCC2-275,inpartbyMICROGrant92-180,andinpartbyEPRIAgreementRP8010-34.TheauthoriswiththeDepartmentofElectricalEngineeringandComputerScience,UniversityofCalifornia,Berkeley,CA94720IEEELogNumber9207521.adaptivenetworks,weobtaintheANFISarchitecturewhichisthebackboneofthispaperanditiscoveredinSectionIV.ApplicationexamplessuchasnonlinearfunctionmodelingandchaotictimeseriespredictionaregiveninSectionV.SectionVIconcludesthispaperbygivingimportantextensionsandfuturedirectionsofthiswork.11.FUZZYIF-THENRULESANDFUZZYINFERENCESYSTEMSA.FuzzyIf-ThenRulesFuzzyif-thenrulesorfuzzyconditionalstatementsareex-pressionsoftheformIFATHENB,whereAandBarelabelsoffuzzysets[66]characterizedbyappropriatemembershipfunctions.Duetotheirconciseform,fuzzyif-thenrulesareoftenemployedtocapturetheimprecisemodesofreasoningthatplayanessentialroleinthehumanabilitytomakedecisionsinanenvironmentofuncertaintyandimprecision.AnexamplethatdescribesasimplefactisIfpressureishigh,thenvolumeissmallwherepressureandvolumearelinguisticvariables[67],highandsmallarelinguisticvaluesorlabelsthatarecharacterizedbymembershipfunctions.Anotherformoffuzzyif-thenrule,proposedbyTakagiandSugeno[53],hasfuzzysetsinvolvedonlyinthepremisepart.ByusingTakagiandSugeno’sfuzzyif-thenrule,wecandescribetheresistantforceonamovingobjectasfollows:Ifvelocityishigh,thenforce=IC*where,again,highinthepremisepartisalinguisticlabelcharacterizedbyanappropriatemembershipfunction.How-ever,theconsequentpartisdescribedbyanonfuzzyequationoftheinputvariable,velocity.Bothtypesoffuzzyif-thenruleshavebeenusedextensivelyinbothmodelingandcontrol.Throughtheuseoflinguisticlabelsandmembershipfunctions,afuzzyif-thenrulecaneasilycapturethespiritofa“ruleofthumb”usedbyhumans.Fromanotherangle,duetothequalifiersonthepremiseparts,eachfuzzyif-thenrulecanbeviewedasalocaldescriptionofthesystemunderconsideration.Fuzzyif-thenrulesformacorepartofthefuzzyinferencesystemtobeintroducedbelow.A.FuzyInferenceSystemsFuzzyinferencesystemsarealsoknownasfuzzy-rule-basedsystems,fuzzymodels,fuzzyassociativememories(FAM),orfuzzycontrollerswhenusedascontrollers.Basicallyafuzzy0018-9472/93$03.0001993IEEE666IEEETRANSACTIONSONSYSTEMS,MAN,ANDCYBERNETICS,VOL.23,NO.3,MAYIJUNE1993knowed@3b.r,inputoutputFig.1.Fuzzyinferencesystem.inferencesystemiscomposedoffivefunctionalblocks(seeFig.1):arulebasecontaininganumberoffuzzyif-thenrules;adatabasewhichdefinesthemembershipfunctionsofadecision-makingunitwhichperformstheinferenceafuzzijicationinterfacewhichtransformsthecrispinputsadefuzzificationinterfacewhichtransformthefuzzyUsually,therulebaseandthedatabasearejointlyreferredtoastheknowledgebase.Thestepsoffuzzyreasoning(inferenceoperationsuponfuzzyif-thenrules)performedbyfuzzyinferencesystemsare:thefuzzysetsusedinthefuzz