Sumea logiikka - techintroduce

Esittely

Perustiedot

FuzzylogicreferstoteheuncvartyConceptJudgmentAndReasoningThinkingModeThatimitatShehehumanbrain.ForedescriptionsystemofunknownoruncettureModel, Aswellascontrolobjectswithstrongnonlinearityandlargelag, Usefuzzytsandfuzzyyrulesforreasoning, expressTransitionalboundesorqualitativedgeanDexperience.ongelma.Fuzzylogicisgoodatexpressingqualitatiiviset tietämykset.Itusestheconceptofmembershipfunctiontodistinguishfuzzysets,processfuzzyrelationships,simulatethehumanbraintoimplementrule-basedreasoning,andsolvethevariousongelmascausedbythelogicalfailureofthe"lawofexcludedmiddle".Identifytheongelma.

Historiallinen kehitys

Vuonna 1965 amerikkalainen matemaatikko.ZadehFirstProPotedTheConceptoffUzzySet, merkitsemällä.TeoriginallogicandmathematicsbasedonbinaryLogicarediffultodescribeandDealwithmanyVagueObjectSintherealworld.FuzzymathematicsandfuzzylogicessessentiallydescribeandprocessfuzzyobjectSaccurated.

IndertoestablishamathematicalModeloffuzzyobjects, L.Zadehextendedtheconceptofordinarysetsthatonlytakethebinaryvaluesof0and1totheconceptoffuzzysetsthattakeinfinitelymanyvaluesontheinterval[0,1]."DegreefMembership" andusethEconcept of "DegreefMembership" TOACCURESTYDESCRIBOBECHONSHICHBETBETIESSILESSILLESSIFUZZYSS -sovellukset.Preciselybecausefuzzysetsarebasedoncontinuousinfinitelymanyvalues,fuzzylogiccanberegardedasthescienceofusingfuzzysetsofinfinitecontinuousvaluestostudyfuzzyobjects.SomebasicconceptsandMethodsoffuzzyMathematicsarApiedToTheFieldOflogic, tuloksena oleva.Vastaavat ComparativerESearchisAnSomadeOnfuzzyConnectiesdandfuzzytruthtables.ChadalsocriedoutresearchonlikeliOnferencesuchasfuzzyhypothesisInference ja.

Theinainsignicancefestablishingdresearchingfuzzylogicis:

(1) UsenewideasandNewtheoriessuchasfuzzylogicvariables, fuzzylogicfunctionsandlikelIOnInferencetofindSolutionStofuzzyLogic.Thebreakthroughofsexualongelmaslaidatheoreticalfoundationandpointedoutthedirectionforstudyingfuzzyobjectsfromalogicalpointofview.

(2) fuzzylogicisUniqueintheautomaticcontrolprocessThatisdiffultOnTodescribeandprocesswiththeoriginalBooleanalgebra, binaryLogicandothermathematicsandLogictools, theediagnosisofiffultdiseases, theesearchoflarge-scalesytems, jne..Paikka.

(3) Intermethodologia, It ProvididesCorrectResearchMethodsforHumanresearchFromaccuracyToVagueness and FromcaneTouncancety.Lisäksi matematiikan tutkimuksen mukaan fuzzylogiccanhelpsolvesomeParadoxes.Theestudyofdialekticallogicwillalsohaveaprofoundimpact.Tietysti, fuzzylogictheoryitelfneedstobefurthersystematisoitu, täydellinen ja standardoitu.

Perusteoria

FuzzylogicisatautologyfaryLogic: inmulti-arvoinenloginen, annettavaanMv-AlgebraA, ana-arvioitujavaltiottujafromthepropositionTheTeTofformulasinmv-Algebraicfunctions.IFTHIFICUNCHUONMAPSAFORMULATO1 (OR0) FORALLA-arvioinnit, ThentHeformulaisana-tautologia.Siksi forInfinite-arvoinenloginen (sucasfuzzylogicandVukasevichLogic), weset [0,1] tobethelowersetofatoobtain [0,1] -valmiuation ja 0,1] -tautologia (useinScalleDeVauationandtautology).ChanginTentedMV-AlgebratoStudyThemult-arvoinenLogicThatPolishMathematicianJan? Ukasiewicz (Janukasiewicz) Intervenedin1920.Chang'scompleenessTheOorem (1958, 1959) Statesthatanymv-algebraequationthatholdsinTheintHinterval [0,1] myös.Tämän läpi tämän läpi.Myöhemmä.Tämä.SimilarToTheBooleanalgebraequationThatholdsin {0,1} AndholdsinyBooleanalgebra.Booleanalgebrathereforecharacterizesstandardtwo-arvoinenloginen.

Soveltaminen

FuzzylogiccanbeUnedTocontrolhouseHoldApplianCessuchaswashingMachines (sensestHeloaDandDetergentConcentrationAdJustsheirwashingcycleaccordingy) jairconditions.

BasicSoveltaminensCanbeCharacterizedAssubranesOfcontuleSVariables, usein.Exexances, theTemperaturemeasurementofananti-lockbrakecanhavemultipleIndedentMembershipfunctions (Jäsenfunktio), jotka antavat mahdollisuudet.Jokainen functionmapsTheSametEMperatureToAValueintherangeOf0To1andisanon-ConCaveFunction (muuten.Thesetruevaluescanthenbeusedtodeterminehowthebrakesshouldbecontrolled.

InFigure1,cold,warm,andhotarefunctionsofthemappedtemperaturerange.ApointonThisscalehasthree "totuusarvot" - yksi foreachfunction.Forthespecifictemperatureshown,thesethreetruevaluescanbeinterpretedasdescribingthetemperatureas"quitecold","somewhatwarm"and"nothot".

Yleensä trapezoidisoitu, buttheatributionfunctionftRIngleSUsedforfuzzyRegressionanalysis.

Sumuinen logiikka (4 kuvaa)

FuzzylogicusuallyusesIF/THENrules,orconstructsequivalentthingssuchasfuzzyincidencematrix.

TheruleisusuuruuruuredInThefollowingForm:

IffuzzyVariableSfuzzyTHenaction

Esimerkiksi Averyn yksinkertainen lämpötilan säädin tuulettimen avulla:

IftemperatureSverycoldTheNstopthefan

IftemperatureSiscoldTheDeCelerationFan

IftemperatureisnormalTheKeepTheCurrentLevelvel

IftemperatureishtHenaccelationFan

MotthatThereisno "else".AllrulesareAVAILEDBECAUSETETEMPERATECANBE "Kylmä" ja "Normaali" AtthesametimeTovaryingDegrees.

Siellä olevat ja ja, ja ei -operatorsInBooleanLogInfuzzyLogic.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 "erittäin" tai "pienen" kanusematemaattinen formulastoMoDifyTheConnoTationofaset.

Ohjelmointikieli

Soveltaminen, ProgramminganganguagePrologisverySitbleForimplementfuzzyLogicDueTootsDataBasefacelityTetsetsUp "Säännöt", jotka.Tämä.

ResearchObject

ToclarifyTheSearchObjectoffuzzylogic, youmustfirstnowthelogibalReseartObject, becausefuzzylogicisonlyadevelopmentbasedonClassicallogic.Haaran kurinalaisuus.AslongastheresearchobjectOfLogicisclarfief, TheentheresearchObjectoffuzzylogicWillbeEasyToundernsand.SowhatexActLESTherESearchObjectOfLogic? ThereareVarioSanswerstohisquestion."

Fuzzy logic

TheObjectSofLogicCanbedIivideToThOtHowingViewPointSFromabroadPerspektive:

(1) LogicisthestudyoftHinking;

(2) LogicisthestudyofTheObjectiveWorld;

(3) LogicisthestudyofLanguage;

(4) LogicisthestudyfThit -valmityformOfreasoning."

ThisisasumarymadebyThefamousdomcICSCHOLARCHENBO.Kirja, ChenboanalyzedTheAboveFourviewPointSonebyOne, jaPlotOutTheadVanTagesandDisadvantagesOfVariousViewPoints.Lopuksi, heputforwardhisownview, hebelievedthattheresearchobjectOflogicistHevalidityOfreasoningForm.Tämä katselujen tunnistaminen.Inlayman'sterms: TheObjectOfLogicresearchisthECorcectnessOfreasoning.Tiukasti luona (moreacademical), theObjectofLogicresearchisTheValiditySformOfreasoning.

TheViewTHatTheObjectOfLogICResearchisTheValitydSForMorMoFreasoninghasbeenRecognezedBySCholarSandExperts.JälkikäsittelyTheSearchObjectOfLogic, iCanenterThequestionIWanTToTalkABout.WhatShereSearchObjectoffuzzyLogic? Täällä, IwantToDiscussFromThefowingaspects:

(1) The BackgroundoffuzzyLogic.Ihmisen tuntemus.Yksiprecisephenomena, joka on kirjoittanut.Esimerkiksi 2+2 = 4; GuiyangcitySTheCapital of Guizhoun maakunta; Moutaiischina'snationAlliquor, Andsoon.ItCanbesenthatthesephenomenaAllHaveRecisedFinitionSandProperties.Intherealworld, sensanotherfenomenononthatisdiffulttoAccuraalyDescribean jadefine.Forexample, Huaxiisabeautifulplace (whatexactlyisbeautifulscenery?).ThereAreCountlessSuchphenomena.Vastaava "tarkkuusfenomenoni" WecallitThe "fuzzyphenomenon".InorderTouserigorousscientificmethodstostodyfuzzyphenomena jaanalyzefuzzyproperties, fuzzymathematicsCameObeing.AndfuzzylogicisONOftheBranchDiciplinesDerivedfromfuzzymathematics.

(2) TheresearchObjectoffuzzyLogic.ATENTIONTIONEWLIER, TheresearchObjectOfLogicisThevalidididsFTheformOfreasoning -.SOWHATISFUZZYRACING? WHITESTHEDIFERENCEANDCONNECTIONBETWEENFUZZYRAsoningAndPreciser -mauste? Nämä ohjeet.

Ensinnäkin, Let'stakealookatwhatfuzzyreasoningis.KutenExactrasening, fuzzyreasoningisalsocomposedofOfbasiclogicalelementssuchasconceptsandJudgments, butfuzzyreasoninghasitsowniquewayofreasoning.Theconclusionsdervedbyfuzzyreasoningarenotabsolutelytrueandfalse.ITSClusionsCanonlybedescrededByMembershipDegree.Forexample, theTeacherzhanginThePreViousexampleisamiddle-appersson.ThishAveryTypicalfuzzyJudgmentsence.Täällä.Forexample, 40-vuotias keski-ikäisille ihmisille.Isittruethat41-vuotiaanaddle-agedandisregardedasfalse? Koska.Forthispowerlessongelmainbinarylogicbutcanbeeasilysolvedinfuzzylogic,weuseChadnotationtodescribethiscase.ChadNotationExpressesAllTheelementsInThefuzzySetHrughTheMoffRactions.AnditDegreeOfMembership, WherethedenominArreRePresentsTheelement ja ThenumeraRrEpresentsTheDegreeOfMembership.Intheaboveexample, wecanexpressitas (a) = (0.5/MR.Zhang), joka merkitsee.Zhangisamiddle-agePersonandly0.5IntermSofDegree.HerraPutasidetheabsoluteTruthandfalseuthe.Kuitenkin thefuzzyphenomenonhasalsobeenAccuraalyDescraded.ThereasonFortheaccuracyOfthefuzzyphenomenonismainlyforthefuzzyReasoningtoberealizedonthemachine.

Toiseksi keskustele.ChenbomadeaMoreAncisivesumaryfThevalididesOfreasoningandputForwardFiVere -tarkkailu.HebelievesthatMegeArterAceingiseffectivesHeultHeetThefollowingfivEconditionSatthesametime: (1) uskollisuus.(2) ContentRelevance.(3) itsenäisyys.(4) AiheNeutralityorUniversalAppliciability.(5) Yksinkertaisuus.Vaikka sechenboproposedsuchaframework, iTisimelimmanspsibleforykindifLogicalReasoningTometTheaboveFivekriteriatHesametimeMetime.TÄMÄNIONEXPRESSIMESIPLEVIEWSONTEEFCECTIVESTOFUZZYLOGIC.ThereingCommonlyUnedInfuzzyLogicinludesfuzzyhypoTheticiNreasoningandfuzzyconditionalreasoning.FuzzyhypoteticalReasoningisthemostrepresentative.Thedefinitionoffuzzyhypoteticierreasoningis: itisknownThatfuzzypropositio (Majorpremise) CononsionFuzzyPropositionb.Ifthereisafuzzypropositio1 (smallpremise) se, että.Wecallthisreasoningprocessfuzzyhypotheticalreasoning.Esimerkiksi:

(1) ifthefoodyoueatisrichinnitrients, sinunBudwillBegood; sienifthefoodyoueatisrichinnutrients, whatwillyourbodybelike?

(2) IFCHINAWASSSTONTONTHELATEQINGDYNASTY, ITWORDNOTBEBULIEDBYTHEIMPERIALISTCOUNTIES

DuetovaguehypothesestHelargeandsMallPremisesofreasoningarefuzzy, SiitsConclusionsarealSofUzzy.TämäScompleyDifferentFromtheaccuracyRequiredByTraditionalogic.NoowshouldfuzzyReasoningBeaccuraalyDescribedSothatitCanberecognedbyMachines? WecandiscussitFromtwoaspects: Humanexperienceandfuzzymathematics.

Theesignificanconcreatingandresearchingfuzzylogic

(1) KäyttämälläNewideasandNewtheoriessUchasfuzzylogICvariables-, fuzzylogicfunctions, andliKeliOntheBreakthroughLaidTheTheoreettfoundationdpointEDEDOutTheDirectionForthestudyoffuzzyobjectsfromthelogicalpointPointFView.

(3) Intermethodologia, It ProvididesCorrectResearchMethodsforHumanresearchFromaccuracyToVagueness and FromcaneTouncancety.

Lisäksi matematiikan tutkimuksen mukaan fuzzylogichelpstosolvesomeparadoxes.Theestudyofdialekticallogicwillalsohaveaprofoundimpact.Tietysti, fuzzylogictheoryitelfneedstobefurthersystematisoitu, täydellinen ja standardoitu.

Kyydysamples

Ifaperson'sheightis1.8 metriä, DatchHimastall:

IFmaleIStrueANDheight>=1.8Tenis_tallistrue

IFmaleIStrueANDheight>=1.8nthenis_shortisfalse

Buttheabovefinitionisunrealistinen.Siksi alustHefuzzyrules, seisnoobViousdistLanctionBetweLenDallandshort:

IFheight>=mediummaleTHENis_shortISagreesomehow

IFheight>=mediummaleTHENis_tallISagreesomehow

IntheCaseOfblur, siinä,

kääpiöt = [0,1.3]

msmallmale = (1.3,1.5)

keskinkertainen = (1.5,1.8)

Tallmale = (1.8,2.0)

giantmale>2.0MFORTHECONCLUSSION, THEREARENOTJUSTTWOVALUES, BUTFIVE:

agsenot = 0

agselittle = 1

agsenot = 0

agselittle = 1

Tooleileva = 2

acgealot = 3

Hyvästi = 4

Epätabinaarinen "hauras" tilanne, theHeightpersonwhois1.79 metersMayBeconsidedshort.Jos.8Metersor2.25 metriä, theesepLearConseredtall.

Tämä FragileExampleisDeLibery DefferentFromthevagueExample.Wecan’tputInThepremise

IFmale>=agreesomehowAND...Koska GenderisoftenConsidedTobebinaryInformation.Soit'sNotasComplitedAshEight.