Predictability of fuzzy discrete event systems

Abstract

This paper studies the problem of predictability in fuzzy discrete event systems (FDESs). FDESs combine fuzzy set theory with discrete events systems (DESs). They are proposed in Lin and Ying (2001) to cope with vagueness, impreciseness, and subjectivity in real-world problems. In this work: (1) We propose a fuzzy approach for predictability by introducing fuzzy predictability functions to characterize the predictability degree of a prefix, a faulty trace as well as a faulty event in a fuzzy DES. These functions take values in the interval [0, 1]. The degree of predictability gives a valuable measure to refine the decision about fault predictability. (2) We show that the degree of predictability of a faulty event is always at most equal to its degree of diagnosability. This captures the idea that predictability is stronger than diagnosability. (3) For checking predictability in FDESs, we propose an approach based on the so-called verifier. This approach results in a polynomial (in the number of states) complexity test for the verification of predictability. Our results generalize those of predictability for crisp DESs and allow one to deal with the problem of predictability for both crisp DESs and FDESs.