Fuzzy logika

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.Zadehextendedtheconceptofordinarysetsthatonlytakethebinaryvalues​​of0and1totheconceptoffuzzysetsthattakeinfinitelymanyvalues​​ontheinterval[0,1].ANDUSETHECTONCEPTOF „Stupence ofMembership“.Preciselybecausefuzzysetsarebasedoncontinuousinfinitelymanyvalues,fuzzylogiccanberegardedasthescienceofusingfuzzysetsofinfinitecontinuousvalues​​tostudyfuzzyobjects.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..Thesetruevalues​​canthenbeusedtodeterminehowthebrakesshouldbecontrolled.

InFigure1,cold,warm,andhotarefunctionsofthemappedtemperaturerange.Apointonthisscalehasthree "TruthValues" - OneForEachFunction.Forthespecifictemperatureshown,thesethreetruevalues​​canbeinterpretedasdescribingthetemperatureas"quitecold","somewhatwarm"and"nothot".

Obvykle, lichoběžník, buttheattributionfunctionOftriangleisusedforfuzzyregressionAnalysis.

Fuzzy Logic (4 fotografie)

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

ANGRACESOWHOW = 2

engovialot = 3

souhlasím = 4

Inabinární „křehká“ situace, Theheighpersonwhois1.79MetersMayBeconsideredShort.IftheheightOnToterpersonis1.8Metersor2.25meters, ThesepeoplearEConsideredTall.

ThisFragileexampleIsDeliberelyDifferentFomThevagueexample.Wecan'tputinthepremise

IFmale>=agreesomehowAND...ProtožegenderisoftenconSideredTobeBanaryInformace.SOIT'SOTASCOMPLICELICESSASHEIGHT.