Safe Diagnosability of Fuzzy Discrete-Event Systems and a Polynomial-Time Verification

Since fuzzy discrete-event systems (FDESs) were significantly brought forward, the study of FDESs has received increasing attention recently. This paper addresses the safe diagnosability under the framework of FDESs. The contributions are threefold. First, the notion of safe diagnosability for fuzzy systems is formalized. A safe diagnosable FDES means that not only each failure can be detected in terms of fuzziness, as well as the detection must be completed before any unsafe operation is executed. Then, a necessary and sufficient condition of safe diagnosability of FDESs is proposed by constructing the safe diagnoser. Finally, we present an algorithm for verifying the safe diagnosability of FDESs based on a constructive nondeterministic automaton, namely verifier. It is worth noting that both constructing the verifier and verifying the safe diagnosability of FDESs can be realized with a polynomial complexity.