Diagnosability of Fuzzy Discrete Event Systems

TL;DR

This paper introduces a formal framework for diagnosing failures in fuzzy discrete event systems (FDESs), accounting for uncertainty in event observability and failure likelihood, and provides conditions for diagnosability.

Contribution

It formalizes diagnosability in FDESs with fuzzy observability and failure sets, and establishes necessary and sufficient conditions for diagnosis.

Findings

Defined diagnosability for FDESs with fuzzy event sets

Developed observability-based diagnosers for FDESs

Provided a necessary and sufficient condition for FDES diagnosability

Abstract

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.