  The supervisory control theory of fuzzy discrete event systems (FDESs) for
fuzzy language equivalence has been developed. However, in a way, language
equivalence has limited expressiveness. So if the given specification can not
be expressed by language equivalence, then the control for language equivalence
does not work. In this paper, we further establish the supervisory control
theory of FDESs for fuzzy simulation equivalence whose expressiveness is
stronger than that of fuzzy language equivalence. First, we formalize the
notions of fuzzy simulation and fuzzy simulation equivalence between two FDESs.
Then we present a method for deciding whether there is a fuzzy simulation or
not. In addition, we also show several basic properties of fuzzy simulation
relations. Afterwards, we put forward the notion of fuzzy simulation-based
controllability, and particularly show that it serves as a necessary and
sufficient condition for the existence of the fuzzy supervisors of FDESs.
Moreover, we study the "range" control problem of FDESs. Some examples are
given to illustrate the main results obtained.
