Analysis and control of fuzzy discrete event systems using bisimulation equivalence

In order to more effectively cope with the real-world problems of vagueness, impreciseness, and subjectivity, fuzzy discrete event systems (FDESs) were proposed recently. In this paper, we deal with the analysis and control of fuzzy discrete event systems by using bisimulation equivalence. In practice, we design a supervisor such that the controlled system is bisimilar to the specification. Also, a model theorem showing that a supervisor exists over a certain finite fuzzy state space is obtained. Furthermore, the notion of fuzzy state controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor.