Domov technika Fuzzy relation equation

Fuzzy relation equation

Basicintroduction

Thefuzzyrelationequationoccupiesaveryimportantpositioninfuzzymathematicstheoryanditsapplication.SanchezofFrancehasdonepioneeringresearchinthisarea.Hefirstproposedthefuzzyrelationequationandgavethemaximumsolutionoftheequation.FollowingtheJapanesepoliticalelementtogiveaspecificsolutiontothefuzzyrelationequationonafiniteset,mycountry'sLuoChengzhong,XuWenli,CaoZhiqiang,LiBixiang,etc.gaveasimplifiedsolutiontotheequation.

Typesoffuzzyrelationequations

Therearetwotypesoffuzzyrelationequations.

TypeI

GiventhedomainU,V,W,thefuzzyrelationshipisknown

Findthefuzzyrelationship

Satisfytheequation:

TypeII

Knownfuzzyrelationship

Findthefuzzyrelationshipandsatisfytheequation:

InTypeII,let

,itsmembershipfunction:

iscalledasthetranspositionrelationshipof,anditalsostipulates

,thenTsatisfiestheequation:

Therefore,thetwotypesofequationscanbetransformedintoeachother.

Fuzzyrelationequationsolution

thatsatisfiesthefuzzyrelationequationiscalledthesolutionoftheequation,iftheequationIfthesection>hasasolution,theequationissaidtobecompatible,otherwisetheequationissaidtobeincompatible.Ifacertainsolutionoftheequation,foranyothersolution,thereisalways,theniscalledthemaximumoftheequationuntie.