Fuzzy multimodel of timed Petri nets

This paper deals with discrete event systems (DES) modeled either by discrete timed Petri nets without conflict or by continuous Petri nets. A fuzzy rule-based multimodel is developed for this kind of system. The behavior of each Petri net transition is described by the combination of two linear local fuzzy models. Using the Takagi-Sugemo model in a systematic way, we define the exact modeling for both classes of timed Petri nets. As a result, we notice that classical sets result in the exact description of discrete timed Petri nets. On the contrary, only fuzzy sets are suitable to describe continuous Petri nets exactly. The proposed fuzzy multimodels are very interesting from a control point of view. In that sense, general results such as convergence for timed Petri nets are given.