Using fuzzy places and hypertokens to reduce the number of states in stochastic Petri nets

A difficulty often encountered when using the Petri net approach to stochastic modeling is a proliferation in the number of states in the associated Markov chain. In this paper we present a solution to this proliferation problem by introducing the concept of a fuzzy stochastic Petri net. This paper then focuses on the problem of finding the stationary probability of reaching some selected output nodes, starting from selected input nodes when using a fuzzy set approach to modeling with stochastic Petri nets.