Modeling a flexible manufacturing cell using stochastic Petri nets with fuzzy parameters

In this paper, an approach for modeling and analysis of time critical, dynamic and complex systems using stochastic Petri nets together with fuzzy sets is presented. The presented method consists of two stages. The first stage is same as the conventional stochastic Petri nets with the difference that the steady-state probabilities are obtained parametrically in terms of transition firing rates. In the second stage, the transition firing rates are described by triangular fuzzy numbers and then by applying fuzzy mathematics, the fuzzy steady-state probabilities are calculated. A numerical example for modeling and analysis of a flexible manufacturing cell is given to show the applicability of proposed method. The importance of the proposed approach is that it can take into consideration both dimensions of uncertainty in system modeling, stochastic variability and imprecision.