Fuzzy hybrid systems modeling

A hybrid system is a system containing a mixture of discrete event components and continuous variable components. The existing hybrid system modeling methods are effective to handle crisp cases but difficult to represent deterministic uncertainties and subjectivity inherent in many real-world applications, especially those in biomedicine. We recently extended the framework of discrete event systems to a framework of fuzzy discrete systems. In the present paper, we generalize the crisp hybrid system framework to a fuzzy hybrid system framework by using fuzzy set theory. The former contains the latter as a special case. Membership grades of fuzzy sets are utilized to represent vague system's states and variables. We have also developed a computational algorithm to calculate fuzzy states and state transitions.