An Extension to the Theory of Fuzzy Discrete Event Systems

We originated theory of fuzzy discrete event systems (FDES) by generalizing the conventional discrete event systems so that vagueness and imprecision concerning the states and/or event transitions are more effectively dealt with. Through our experience in applying the FDES theory to HIV/AIDS prescription decision making, it become evident to us that an extended FDES theory is needed to cover diverse opinions from a group of experts and uncertainties on treatment regimens when forming state vectors and/or transition matrices. To address this problem, we now propose to use fuzzy number for each component of state vectors and/or transition matrices as opposed to a crisp number in the FDES theory. Operations of the fuzzy states and fuzzy transitions involving the fuzzy numbers are established, which is based on interval number operations. Furthermore, the parallel composition is also generalized such that a complex extended FDES can be synthesized from component models of the extended type. The extended FDES theory contains the FDES theory as a special case. A detailed numerical example is provided to illustrate the extended FDES.