Modeling and control of fuzzy discrete event systems

In order to make it possible to effectively represent deterministic uncertainties and vagueness as well as the human subjective observation and judgement inherent to many real-world problems, especially those in biomedicine, we introduce, in this paper, fuzzy states and fuzzy events and generalize (crisp) discrete event systems (DES) to fuzzy DES. The largely graph-based current framework of the crisp DES is unsuitable for the expansion, and we have thus reformulated it using state vectors and event transition matrices which can be extended to fuzzy vectors and matrices by allowing their elements to take values between 0 and 1. To measure information related to fuzzy DES, we generalize the crisp DES observability. The new observability allows one to determine whether or not the system output observed is sufficient for decision making. Finally, we extend the optimal control of DES to fuzzy DES. The new fuzzy DES theory is consistent with the existing theory, both at the conceptual and the computation levels, in that the former contains the latter as a special case when the memberships must be either 0 or 1. Numerical examples are provided to illustrate the theoretical development.