Fuzzy discrete event systems and their observability

We generalize discrete event systems to fuzzy discrete event systems. We introduce fuzzy states and fuzzy events to discrete event systems to describe deterministic uncertainties often existing in some practical applications such as medical applications. This is done by first reformulating crisp discrete event systems in terms of state vectors and transition matrices and then introducing fuzziness in these vectors and matrices. To measure information related to discrete event systems, we modify observability introduced in supervisory control. The modified observability allows us to determine if the output observed is sufficient for decision making. It can be used in both crisp discrete event systems and fuzzy discrete event systems