HIGH-LEVEL FUZZY PETRI NETS AS A BASIS FOR MANAGING SYMBOLIC AND NUMERICAL INFORMATION

The focus of this paper is on an attempt towards a unified formalism to manage both symbolic and numerical information based on high-level fuzzy Petri nets (HLFPN). Fuzzy functions, fuzzy reasoning, and fuzzy neural networks are integrated in HLFPN In HLFPN model, a fuzzy place carries information to describe the fuzzy variable and the fuzzy set of a fuzzy condition. An arc is labeled with a fuzzy weight to represent the strength of connection between places and transitions. A fuzzy set and a fuzzy truth-value are attached to an uncertain fuzzy token to model imprecision and uncertainty. We have identified six types of uncertain transition: calculation transitions to compute functions with uncertain fuzzy inputs; inference transitions to perform fuzzy reasoning; neuron transitions to execute computations in neural networks; duplication transitions to duplicate an uncertain fuzzy token to several tokens carrying the same fuzzy sets and fuzzy truth values; aggregation transitions to combine several uncertain fuzzy tokens with the same fuzzy variable; and aggregation-duplication transitions to amalgamate aggregation transitions and duplication transitions. To guide the computation inside the HLFPN, an algorithm is developed and an example is used to illustrate the proposed approach.