Úvod
BasicContent
FuzzlogicreferstotheoncentyConceptJudgmentAndReasoningThinkingModeThatiMitatestheHumanbrain.Forthedescriptionsystemofunknownoruncertainmodel,Aswellascontrolobjectswithstrongnonlinearityandlargelag,usefuzzysetsandfuzzyrulesforreasoning,expresstransitionalboundariesorqualitativeknowledgeandexperience,simulatehumanbrainmethods,implementfuzzycomprehensivejudgments,andreasontosolveregularfuzzyinformationthatisdifficulttodealwithbyconventionalmethods.problém.FuzzlogicicisgoodatexpressingqualitativenowledgedgeandexperienceWithUnclearboundaries.Itusestheconceptofmembershipfunctiontodistinguishfuzzysets,processfuzzyrelationships,simulatethehumanbraintoimplementrule-basedreasoning,andsolvethevariousproblémscausedbythelogicalfailureofthe"lawofexcludedmiddle".Identifytheproblém.
Historický vývoj
V roce 1965 americký matematik.ZadehfirstProposedTheConceceptofFuzzyset, MarkingThebirthofFuzZymathematics.TheoriginalLogicAndMathematicsBasenBinaryLogiCaredifiCutICultScreatDealwithManyvagueObjectsintherealworld.Fuzzomathematicsand afuzzlogicesensiallydescribeandProcessfuzzyObjectSacasately.
INorderToestablishaMathematicalModeloffuzzyObjects, l.Zadehextendedtheconceptofordinarysetsthatonlytakethebinaryvaluesof0and1totheconceptoffuzzysetsthattakeinfinitelymanyvaluesontheinterval[0,1].ANDUSETHECTONCEPTOF „Stupence ofMembership“.Preciselybecausefuzzysetsarebasedoncontinuousinfinitelymanyvalues,fuzzylogiccanberegardedasthescienceofusingfuzzysetsofinfinitecontinuousvaluestostudyfuzzyobjects.SomeBasicConceptSandMethodsofUzZymathematicsareApliedTothefieldOfLogic, výsledkem výsledek sekundySuchAsfuzzalogicvariables afuzzylogicfunctions.Odpovídající komparativeresearchAssalsoMadeonFuzzyConnectivesAnd afuzzytuthTables.ChadalsOcarriedOdouresearchOnLikelikeLohoodInferencesuchasfuzzyhypothesisInference, andomeoftheresultsHaveEndiRectlypliedTothedevelofFuzzyControllers.
ThatisIgnIficancefestabilishingandResearchingFuzzlogicis:
(1) UsenewideasandNewtheoriessuchAsfuzzylogicvariables, fuzzalogicfunctionsAndLikelioHoHinHinferencetofindSolutionStofuzzylogic.Thebreakthroughofsexualproblémslaidatheoreticalfoundationandpointedoutthedirectionforstudyingfuzzyobjectsfromalogicalpointofview.
(2) FuzzlogicisuniqueintheautomaticControlProcessthisDifficultToDescreaneadProcesswiththeriginalBoolaNeanalgebra, binaryLogicandotherMathematicsAndLogicToLools, theEresearchoflarge, atd..Místo.
(3) IntermsOfMethodology, ItProvidesCorreCerecreSearchMethodsforhumanresearchFomaccuracyTovagueness a frompeartyTounCelety.Kromě toho, inthebasic výzkum matematiky, fuzzalogiccanhelpsolvesomeparadoxes.TheStudyofDialecticalLogicwilLALSOHAVEAPROFUNDIMPACT.Samozřejmě, fuzzlogictheoryitSelfneedStobefurtherSystematizovaná, úplná a nestandardizovaná.
Základní teorie
FuzzlogicisatautologyofBinaryLogic: inmulti-vauedLogic, dánAnMv-algebraa, ana-evaluationIscalculatedFopositionTheSetofformlasinmv-algebraicfunctions.IfThisFunctionMapsaformulato1 (OR0) foralla-evaluace, thentheformulaisana-tautologie.ForInfinite-valuedLogic (takovýsfuzzologicandvukasevichLogic), Weset [0,1] tobethelowerSoFatoObtain [0,1] -evaluation a [0,1] -Tautologie (často se svlékne acalledevaluation attautology)).Changinvententmv-algebratostudythemulti-ValuedLogicthatpolishMathematianjan? UKASIEWICZ (Janukasiewicz) zasahující.Chang'sCompletenessTheorem (1958,1959) Statesthatanymv-algebraequationtholdsintheinterval [0,1] také holdsinallmv-algebras.Prostřednictvím thisTheorema, itisprovelthettheinfinite-varedVukasevicLeDedescrippedBymv-algebra.Nocalthesameappliestofuzzalogic.ThissisiMilartotheBoolaNeaNebraequationthatholdsin {0,1} aldsinanyboolaNeanalgebra.Booleanalgebrathereforecharacterizesstandardtwo-varedLogic.
aplikace
FuzzlogiccanbeusedtoControlhouseholdAppliancessuchasswashingMachines (ITSesestheLoaDandDetergentConcentrationAdstheIrshingcycleaccordinly) aircondonditions.
BasicaplikacescanbecharacterizedAssubrangesofContinuousvariables, oftentriangulartrapezoidilinshape.FORMAPLEC, thetempereMereMurementOnfananti-lockbrakecanhavemultiplindependent-functionshiptions (členství), které jsou defineaspecificteRanangeThatareRectArectlyControlthebrake.Každá FunctionMapsheSetemperatureToatRueValueValuerangeof0To1andisanon-ConcaveFunction (jinak..Thesetruevaluescanthenbeusedtodeterminehowthebrakesshouldbecontrolled.
InFigure1,cold,warm,andhotarefunctionsofthemappedtemperaturerange.Apointonthisscalehasthree "TruthValues" - OneForEachFunction.Forthespecifictemperatureshown,thesethreetruevaluescanbeinterpretedasdescribingthetemperatureas"quitecold","somewhatwarm"and"nothot".
Obvykle, lichoběžník, buttheattributionfunctionOftriangleisusedforfuzzyregressionAnalysis.
Fuzzy Logic (4 fotografie)
FuzzylogicusuallyusesIF/THENrules,orconstructsequivalentthingssuchasfuzzyincidencematrix.TheruleisusUsUsExpressintEfollowlingForm:
IFFUZZZYVariableIsFuzzysetThenaction
Například jednoduchý regulátor teploty Avery pomocí ventilátoru:
IfteMperatureSveryColdThenstopThefan
IfteMPeratureSiscoldThendeCelerationFan
IfteMperaturesNormalTheepTeeptheCurrentlevel
IfteMPeratureSishotThenaccelerationFan
Nothatthereisno "else".AllrulesareeValuatedBecauseTheTemperaturecanbe "studený" a "normální" atthesametimetovaryingdegrees.
Nebo, nebo, a bez antoperatorsinbooleanlogicinfuzzalogic.Theyareusuallydefinedasminimum,maximum,andcomplement;whentheyaredefinedinthisway,theyarecalledZadehoperatorsbecausetheywerefirstdefinedinZadeh'soriginalpaper.Forfuzzyvariablesxandy:
NOTx=(1-truth(x))xANDy=minimum(truth(x),truth(y))xORy=maximum(truth(x),truth(y))canalsouseotheroperatorscalledhedgeswhichareclosertonaturallanguage.GeneralAdverbssuchas „velmi“ nebo „alittle“ canusemathematicalFormulastoModifyThonnotationOnOfaset.
Programovací jazyk
Nepřipsalice, TheprogrammingLanguagePrologisverySeableForImplementingFuzZylogicDueToitsDatabasefacilalityThesetSup „pravidla“.ThisIndofProgrammingIsCalledLogicprogramming.
ResearchObject
ToclarifteresearchObjectOffuzzLogic, yous mustfirstKnowtheLogicalResearchObject, protože FuzZylogicisonlyAdevelopmentBasenClassclassicalLogic.Disciplína pobočky.AslongastheresearchObjectjectOfLogicisClarified, ThenTheresearchObjectOfzofuzZyLogicWillbeeasyTounderSard.SowhatexactlyisteresearchObjectOfLogic? ThereArevariousanswerstothisquestion."
TheObjectSofLogicCanBedIdIndotheFollingViewPointsFromabRoadPerspective:
(1) LogicTheStudyofthinking;
(2) LogicTheStudyofTheObjectiveWorld;
(3) LogicTheStudyoflanguage;
(4) LogicisthestudyofTheValidityofTheformOfReasoning."
ThisISasmaryMadebythefAmousdomdomMoLogicscholarchenbo.Inthebook, ChenboanalyzedTheaBoveFourviewpointSoneByone, a bodnutí.Konečně, HeputForwardHisownview, hebeliedThereSearchObjectjectOfLogicistheValiditeFreasonFreamingform.ThisIewIsIsAlsoreCognizelizedIthefirstchapter "WhateISLogic" WasingBylixiaowUin "ninechaptersphilosophyoflogic" editedbyzhangqingyu.INLAYMAN'STERMS: TheObjectOfLogicResearcheStheCorectnessOfRaseaning.Strictlyspeaking (moreacademicky), theObjectOfLogicResearchEstralidityofTheformRasoning.
TheVIEWTHATHEOBjectOfLogicResearchIsTheValidityOfTheforMofReasoningHasBeenRecognizedByscholarsandexperts, AndihavenoobjectiontothisView.AfterclarifikaceThereSearchObjectOfLogic, icanenterthequestioniwantToTalkabout.WhatiSthereSearchObjectOfzofZuzzalogic? Tady, iWantTodiscussFromTheFollowingAsPects:
(1) ThebackgroundOfFuzzzylogic.Lidský poruchoundingofnatureCanberoughlyDividedIndotWocategories.OneIsprecisePhenomena, který je možné.Například 2+2 = 4; guiyangcityistheCapital of Guizhou provincie;.ItcanbeseentHattheSefenomenaallhavePreciseDefinitionSandProperties.Nicméně, v inntherealworld, thisIsnotherphenomenoNthatifIfficulttoAscretalyDescribeanddefine.Forexample, Huaxiisabeautifulplace (WhatexactlyIsBeautifulscenery?): HisfatherisaTallman (HowtallisaTallman?); Učitelzhangisamiddle-egentperson (Howoldisamiddle-egentperdondonsAs?).ThereCountlesssuchphenomena.Odpovídající "PrecisionPhenomenon" wecallitthe "fuzzyfenomenon".INORDORDOUSERIGORSSCIENTIFICKODSTOSTOSTUDYFUZZYPHENOMENAANDANALYZEFUZZZYPROPERTIES, FUZZAMATHEMATICSCAMEITOBEING.A FuzzlogicisoneofthebRanchDisciplinderinedFomFuzZymathematics.
(2) TheresearchObjectOfzofzuzzalogic.AsmentionedeDearlier, TheresearchObjectjectOfLogiciVevalidityofTheforMofreasoning, a když je to.SowhatisfuzZyreasoning? WhatIsTedifferenceAndConnectionbetween MewenSeasonsingand aprecisereasoning?.
Nejprve si můžete uskutečnit.LikexAcTreasong, FuzZyreasoningingIsAlsocomposedofBasicLogicalElementssuchasconceptSandjudgments, butfuzZyreasoningHasitSowNuniquewayofReasoning.TheConclusionsderivedByFuzZyreasoningingarenotabsolutelytrueandfalse.Jeho ConclusionsCanonlyBedeScriptedByMembershipDegree.Forexample, theteacherzhangintreviousexampleisamiddle-věku.TOTOSAVEYTYPICALFUZZZYJUDGMENTSENTENTE.Zde jeusttHeabsolutetrutHandFalsehoodInTraditionAlitionAlLogicCan neuseuseuseusedStodeScretheCecceptofMiddle-egentpeople.Forexample, čtyřicetiletá konstrukce pro lidi středního věku.ISITTRUETHAT41 LITERISMISDLE-AGEDANDISREDEDASFALSE?.Forthispowerlessprobléminbinarylogicbutcanbeeasilysolvedinfuzzylogic,weuseChadnotationtodescribethiscase.ChadnotationExpresseSeSalltheelementsIntheFuzZZeSeSetThroughThesumoffractions.AnditsDegreeofMembership, wherethethededenominateRrepresentsTheelement, andthenumeReRrepresentsthedegreeofMembershiphip.IntheaBoveExample, WeCanexPressitas (A) = (0.5/MR.Zhang), který je.Zhangisamiddle-AgederSernondonly0.5intermsOfDegree.HerewePutasideTheabsolutetututhandSfalsehood.Avšak FuzzyphyfenomenonhassalobeeenAccuralylylydscripted.ThereasovenfortheaccUracyofTheFuzzyphyfenomenonismainlyFotheFuzZyreasoningToberealizeLoNthemachine.
Za druhé, diskutujte o polivu.ChenbomadeamoreincisissummaryofTheValidityOfRasonsing aputForwardFiveRequirements.HebelievesthatHathereasoningingiseffectivesHouldmeettheFollingFiveConditionSatthesametime: (1) věrnost.(2) ContentRelevance.(3) Nezávislost.(4) SubjectNeutralityoruniversalapplicability.(5) Jednoduchost.Ačkoli chenboproposedssuchaframework, iTiMaleimpOssible forOnanyKindoflogicalReasonTomeetTheaboveFiveCriteriaatthesametime.HeiselyExpressSomeSmpleViewSontEfEffectivefOfFuzZylogic.TheasoningComMonlyuseusedInfuzzalogicincludesfuzzyHypotheticalRasoningand afuzzyconditionalRasoning.Mezi FuzzyhypotheticalEasoningEmastrepresentative.TheDefinitionOfZyhypotheticalRasoningis: ITISKNOWNTHATTHATHUZZZYPROPOSIONA (MAJORPREMISE) obsahuje FuzzyPropositionB.IftereisafuzzypropositionA1 (SmallPremise), že.WecallthisReasonSProcessfuzzyHypotheticalEasoning.Například:
(1) IfTheFoodyoueatisrichinNutrients, yourbodywillbegood; pakFtHTHTHEFOOODYOUEatisrichinnutrients, Whatwillyourbodybelike?
(2) Ifchinawasverystronginthelateqingdynasty, itwotbebulliedbytheimperialistCountries; pakfchinawasnotverystronginthelateqingdynasty, itwotbebulliedbytheimperialistCountries?
DuetovaguehypotheSesthelargeandsMallpremisesOfRaseasoningarefuzzy, SoitsConcClusionsArealsofuzzy.ThisComPletelyDifferentFromTheacCuracyRequiredBytraditionAlLologic.SohowsHould FuzZyreasoningBeackalyDedScreatsSothatItCanberecognizedBymachines? WecandissitfromtwooSpects: humanexperienceandfuzzommathematics.
THESIGNIFICIFIKACECREATINGAND ASPEARKINGFUZZYLOGIC
(1)Usingnewideasandnewtheoriessuchasfuzzylogicvariables,fuzzylogicfunctions,andlikelihoodThebreakthroughlaidthetheoreticalfoundationandpointedoutthedirectionforthestudyoffuzzyobjectsfromthelogicalpointofview.
(2) FuzzlogicisuniqueintheautomaticControlProcessthisDifficultToDescreaneadProcesswiththeriginalBoolaNeanalgebra, binaryLogicandotherMathematicsAndLogicToLools, theEresearchoflarge, atd..Místo.
(3) IntermsOfMethodology, ItProvidesCorreCerecreSearchMethodsforhumanresearchFomaccuracyTovagueness a frompeartyTounCelety.
Kromě toho, inthebasic výzkum matematiky, fuzzlogichelpstosolvesomeparadoxes.TheStudyofDialecticalLogicwilLALSOHAVEAPROFUNDIMPACT.Samozřejmě, fuzzlogictheoryitSelfneedStobefurtherSystematizovaná, úplná a nestandardizovaná.
Otherexamples
Ifaperson'sheightis1.8meters, zvažte :himastall:
IFmaleIStrueANDheight>=1.8THenis_Tallistrue
IFmaleIStrueANDheight>=1.8thenis_shortisfalse
ButtheabovedefinitionisunRealistic.Proto, pod zkouškou, proto se neoBviousdistinctionBetweentalllandshort:
IFheight>=mediummaleTHENis_shortISagreesomehow
IFheight>=mediummaleTHENis_tallISagreesomehow
INTHECASEOFBLUR, ThisNoheightlike1,83meters, pouze theblurValue, sasthefollowlowingAssignment:
DWARFMALE = [0,1.3]
msmallmale = (1.3,1.5)
MIDDEMALE = (1.5,1.8)
Tallmale = (1.8,2.0)
giantmale>2.0mfortheConclusion, thereenotjusttwovalues, butfive:
congemnot = 0
AngoLeltle = 1
congemnot = 0
AngoLeltle = 1
p>ANGRACESOWHOW = 2
engovialot = 3
souhlasím = 4
Inabinární „křehká“ situace, Theheighpersonwhois1.79MetersMayBeconsideredShort.IftheheightOnToterpersonis1.8Metersor2.25meters, ThesepeoplearEConsideredTall.
ThisFragileexampleIsDeliberelyDifferentFomThevagueexample.Wecan'tputinthepremise
IFmale>=agreesomehowAND...ProtožegenderisoftenconSideredTobeBanaryInformace.SOIT'SOTASCOMPLICELICESSASHEIGHT.