Safe diagnosability of fuzzy discrete-event systems

Recently, safe diagnosability of discrete event systems (DESs) was investigated in the literature. This paper addresses the issue of safe diagnosability for fuzzy discrete event systems (FDESs). We formalize the notion of safe diagnosability for fuzzy automata, where the observability of fuzzy events is defined to be fuzzy instead of crisp. A safe diagnosable fuzzy automaton is required that not only faults can be detected with a certain degree but also fault detection must be completed before any forbidden string in the failed mode of system is executed. A fuzzy automaton called the recognizer is introduced to distinguish the forbidden strings from the illegal language. Then a safe diagnoser is constructed to perform safe diagnosis of FDESs. In particular, a necessary and sufficient condition of safe diagnosability for FDESs is derived, which extends the main results of safe diagnosability from crisp DESs to the setting of FDESs. Some illustrative examples are provided.