Controllability And Observability Of Fuzzy Discrete Event Systems

In this paper,we first discuss the observability of fuzzy discrete event systems: we extend the degree of uncontrollability from?0,1?to the interval[0,1] and redefine the observability of a fuzzy language.Also,it is proved that the observable fuzzy sublanguages are closed under intersection.Next,we prove that there exists a partially observable fuzzy supervisor if and only if the desired fuzzy language is controllable and observable.When the desired fuzzy language is uncontrollable and unobservable,we study the existence of infimal controllable and observable fuzzy superlanguage.Last,the controllability and observability definition of a fuzzy language generated by composition of some fuzzy discrete event systems is given.In this new sense,we present a necessary and sufficient condition for the desired fuzzy language to be controllable and observable.