Decentralized supervisory control of fuzzy discrete event systems

In order to more effectively cope with the real-world problems of fuzziness and impreciseness, fuzzy discrete event systems (FDESs) were proposed by Lin and Ying. Qiu, and then, Cao and Ying independently developed supervisory control theory of FDESs. We note that the controllability of events in Qiu's work is fuzzy but the observability of events is crisp, and, the observability of events in Cao and Ying's work is also crisp although the controllability is not completely crisp. Motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in real-life world, in this work, both the observability and the controllability of events are considered to be fuzzy. As a continuation of the centralized supervisory control of FDESs proposed by Qiu and Liu, this paper investigates the decentralized supervisory control of FDESs in the more generic framework. In particular, on the basis of Qiu's work, we present a detailed computing approach to verify whether the controllability and co-observability conditions hold, and this method can decide the existence of the decentralized supervisors. Also, this computing method can be applied to check the existence of the decentralized supervisors in classical discrete event systems.