Computation of supremal controllable sublanguages and infimal controllable superlanguages for fuzzy discrete event systems

Recently, several approaches for the study of fuzzy discrete event systems (FDES) in a supervisory control context have been proposed. Although controllability of fuzzy languages and their implementation by a supervisor could be verified by algorithmic procedures, the problem of supervisor synthesis was only solved for the case of FDES with crisp states but fuzzy state transitions. In this paper, we present algorithms to compute the supremal controllable fuzzy sublanguage and the infimal controllable prefix-closed fuzzy superlanguage of a given fuzzy language for the general case of FDES with fuzzy states, fuzzy state transitions and fuzzy event controllability properties, and formally prove their correctness.