Decentralized supervisory control of fuzzy discrete event systems

Fuzzy discrete event systems (FDESs), proposed recently by Lin Feng and Ying Hao, are possible to effectively cope with some problems having fuzziness, impreciseness, and subjectivity. Qiu, and 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, both the observability and the controllability of events in Cao and Ying´s work are crisp. In this work, both the observability and the controllability of events are considered to be fuzzy. We set up the decentralized supervisory control theorem of FDESs in the more generic framework. In particular, based on 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. As well, this computing method can be applied to check the existence of the decentralized supervisors in classical discrete event systems.