Diagnosability of Fuzzy Discrete Event Systems
  In order to more effectively cope with the real-world problems of vagueness,
{\it fuzzy discrete event systems} (FDESs) were proposed recently, and the
supervisory control theory of FDESs was developed. In view of the importance of
failure diagnosis, in this paper, we present an approach of the failure
diagnosis in the framework of FDESs. More specifically: (1) We formalize the
definition of diagnosability for FDESs, in which the observable set and failure
set of events are {\it fuzzy}, that is, each event has certain degree to be
observable and unobservable, and, also, each event may possess different
possibility of failure occurring. (2) Through the construction of
observability-based diagnosers of FDESs, we investigate its some basic
properties. In particular, we present a necessary and sufficient condition for
diagnosability of FDESs. (3) Some examples serving to illuminate the
applications of the diagnosability of FDESs are described. To conclude, some
related issues are raised for further consideration.
