Supervisory control of bi-fuzzy discrete event systems under partial observations

Fuzzy discrete event systems (FDESs) have been proposed based on type-1 fuzzy sets (T1 FSs) theory. However, for some cases, T1 FSs have limited capabilities to handle data uncertainties directly. Hence, FDESs might not be satisfactory models to characterize some high-uncertainty DESs. In order to characterize high-uncertainty DESs precisely, in this paper, we present a new model, called as bi-fuzzy discrete event systems (BFDESs), by combining DESs theory with type-2 fuzzy sets (T2 FSs) theory. Then, we consider the supervisory control problem of BFDESs under partial observations, and thus obtain the necessary and sufficient conditions for the existence of bi-fuzzy supervisors. In addition, we present a method to check the conditions.