# Fuzzy logic

## Introduction

### Basiccontent

Fuzzylogicreferstotheuncertaintyconceptjudgmentandreasoningthinkingmodethatimitatesthehumanbrain.Forthedescriptionsystemofunknownoruncertainmodel,Aswellascontrolobjectswithstrongnonlinearityandlargelag,usefuzzysetsandfuzzyrulesforreasoning,expresstransitionalboundariesorqualitativeknowledgeandexperience,simulatehumanbrainmethods,implementfuzzycomprehensivejudgments,andreasontosolveregularfuzzyinformationthatisdifficulttodealwithbyconventionalmethods.problem.Fuzzylogicisgoodatexpressingqualitativeknowledgeandexperiencewithunclearboundaries.Itusestheconceptofmembershipfunctiontodistinguishfuzzysets,processfuzzyrelationships,simulatethehumanbraintoimplementrule-basedreasoning,andsolvethevariousproblemscausedbythelogicalfailureofthe"lawofexcludedmiddle".Identifytheproblem.

### Historicaldevelopment

Themainsignificanceofestablishingandresearchingfuzzylogicis:

(1)Usenewideasandnewtheoriessuchasfuzzylogicvariables,fuzzylogicfunctionsandlikelihoodinferencetofindsolutionstofuzzylogic.Thebreakthroughofsexualproblemslaidatheoreticalfoundationandpointedoutthedirectionforstudyingfuzzyobjectsfromalogicalpointofview.

(2)FuzzylogicisuniqueintheautomaticcontrolprocessthatisdifficulttodescribeandprocesswiththeoriginalBooleanalgebra,binarylogicandothermathematicsandlogictools,thediagnosisofdifficultdiseases,theresearchoflarge-scalesystems,etc.Place.

### Basictheory

Fuzzylogicisatautologyofbinarylogic:inmulti-valuedlogic,givenanMV-algebraA,anA-evaluationiscalculatedfromthepropositionThesetofformulasinMV-algebraicfunctions.Ifthisfunctionmapsaformulato1(or0)forallA-evaluations,thentheformulaisanA-tautology.Therefore,forinfinite-valuedlogic(suchasfuzzylogicandVukasevichlogic),weset[0,1]tobethelowersetofAtoobtain[0,1]-evaluationand[0,1]-tautology(oftenIt'scalledevaluationandtautology).ChanginventedMV-algebratostudythemulti-valuedlogicthatPolishmathematicianJan?ukasiewicz(Janukasiewicz)intervenedin1920.Chang'scompletenesstheorem(1958,1959)statesthatanyMV-algebraequationthatholdsintheinterval[0,1]alsoholdsinallMV-algebras.Throughthistheorem,itisprovedthattheinfinite-valuedVukaseviclogiccanbedescribedbyMV-algebra.Laterthesameappliestofuzzylogic.ThisissimilartotheBooleanalgebraequationthatholdsin{0,1}andholdsinanyBooleanalgebra.Booleanalgebrathereforecharacterizesstandardtwo-valuedlogic.

## Application

Basicapplicationscanbecharacterizedassubrangesofcontinuousvariables,oftentriangularortrapezoidalinshape.Forexample,thetemperaturemeasurementofananti-lockbrakecanhavemultipleindependentmembershipfunctions(membershipfunction)thatdefineaspecifictemperaturerangethatarerequiredtocorrectlycontrolthebrake.Eachfunctionmapsthesametemperaturetoatruevalueintherangeof0to1andisanon-concavefunction(otherwiseitmaybeclassifiedascolderifthetemperatureishigherinacertainpart).Thesetruevalues​​canthenbeusedtodeterminehowthebrakesshouldbecontrolled.

InFigure1,cold,warm,andhotarefunctionsofthemappedtemperaturerange.Apointonthisscalehasthree"truthvalues"—oneforeachfunction.Forthespecifictemperatureshown,thesethreetruevalues​​canbeinterpretedasdescribingthetemperatureas"quitecold","somewhatwarm"and"nothot".

Fuzzylogic(4photos)

FuzzylogicusuallyusesIF/THENrules,orconstructsequivalentthingssuchasfuzzyincidencematrix.

Theruleisusuallyexpressedinthefollowingform:

IFfuzzyvariableISfuzzysetTHENaction

Forexample,averysimpletemperatureregulatorusingafan:

IFtemperatureISverycoldTHENstopthefan

IFtemperatureIScoldTHENdecelerationfan

IFtemperatureISnormalTHENkeepthecurrentlevel

IFtemperatureISHotTHENaccelerationfan

Notethatthereisno"ELSE".Allrulesareevaluatedbecausethetemperaturecanbe"cold"and"normal"atthesametimetovaryingdegrees.

## Programminglanguage

Inapplication,theprogramminglanguageProLogisverysuitableforimplementingfuzzylogicduetoitsdatabasefacilitythatsetsup"rules"thatareinterrogatedbydeductivelogic.Thiskindofprogrammingiscalledlogicprogramming.

## Researchobject

(1)Logicisthestudyofthinking;

(2)Logicisthestudyoftheobjectiveworld;

(3)Logicisthestudyoflanguage;

(4)Logicisthestudyofthevalidityoftheformofreasoning."

(1)Thebackgroundoffuzzylogic.Human'sunderstandingofnaturecanberoughlydividedintotwocategories.Oneisprecisephenomena,whichcanbedescribedinpreciselanguage.Forexample,2+2=4;GuiyangCityisthecapitalofGuizhouProvince;MoutaiisChina’snationalliquor,andsoon.Itcanbeseenthatthesephenomenaallhaveprecisedefinitionsandproperties.However,intherealworld,thereisanotherphenomenonthatisdifficulttoaccuratelydescribeanddefine.Forexample,Huaxiisabeautifulplace(whatexactlyisbeautifulscenery?):Hisfatherisatallman(howtallisatallman?);TeacherZhangisamiddle-agedperson(howoldisamiddle-agedpersondefinedas?)?),andmanymore.Therearecountlesssuchphenomena.Correspondingtothe"precisionphenomenon"wecallitthe"fuzzyphenomenon".Inordertouserigorousscientificmethodstostudyfuzzyphenomenaandanalyzefuzzyproperties,fuzzymathematicscameintobeing.Andfuzzylogicisoneofthebranchdisciplinesderivedfromfuzzymathematics.

(2)Theresearchobjectoffuzzylogic.Asmentionedearlier,theresearchobjectoflogicisthevalidityoftheformofreasoning,andwhenitcomestofuzzylogic,itsresearchobjectisthevalidityoffuzzyreasoning.Sowhatisfuzzyreasoning?Whatisthedifferenceandconnectionbetweenfuzzyreasoningandprecisereasoning?Theseissueswillbediscussedbelow.

(1)Ifthefoodyoueatisrichinnutrients,yourbodywillbegood;thenifthefoodyoueatisrichinnutrients,whatwillyourbodybelike?

(2)IfChinawasverystronginthelateQingDynasty,itwouldnotbebulliedbytheimperialistcountries;thenifChinawasnotverystronginthelateQingDynasty,itwouldnotbebulliedbytheimperialistcountries?

## Thesignificanceofcreatingandresearchingfuzzylogic

(1)Usingnewideasandnewtheoriessuchasfuzzylogicvariables,fuzzylogicfunctions,andlikelihoodThebreakthroughlaidthetheoreticalfoundationandpointedoutthedirectionforthestudyoffuzzyobjectsfromthelogicalpointofview.

(2)FuzzylogicisuniqueintheautomaticcontrolprocessthatisdifficulttodescribeandprocesswiththeoriginalBooleanalgebra,binarylogicandothermathematicsandlogictools,thediagnosisofdifficultdiseases,theresearchoflarge-scalesystems,etc.Place.

(3)Intermsofmethodology,itprovidescorrectresearchmethodsforhumanresearchfromaccuracytovagueness,andfromcertaintytouncertainty.

## Otherexamples

Ifaperson’sheightis1.8meters,considerhimastall:

IFmaleIStrueANDheight>=1.8THENis_tallIStrue

IFmaleIStrueANDheight>=1.8THENis_shortISfalse

Buttheabovedefinitionisunrealistic.Therefore,underthefuzzyrules,thereisnoobviousdistinctionbetweentallandshort:

IFheight>=mediummaleTHENis_shortISagreesomehow

IFheight>=mediummaleTHENis_tallISagreesomehow

Inthecaseofblur,thereisnoheightlike1,83meters,onlytheblurvalue,suchasthefollowingassignment:

dwarfmale=[0,1.3]

msmallmale=(1.3,1.5)

mediummale=(1.5,1.8)

tallmale=(1.8,2.0)

giantmale>2.0mFortheconclusion,therearenotjusttwovalues,butfive:

agreenot=0

agreelittle=1

agreenot=0

agreelittle=1

p>

agreesomehow=2

agreealot=3

agreefully=4

Inabinaryor"fragile"situation,theheightApersonwhois1.79metersmaybeconsideredshort.Iftheheightofanotherpersonis1.8metersor2.25meters,thesepeopleareconsideredtall.

ThisfragileexampleisdeliberatelydifferentfromthevagueExample.Wecan’tputinthepremise

IFmale>=agreesomehowAND...becausegenderisoftenconsideredtobebinaryinformation.Soit’snotascomplicatedasheight.

Related Articles