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High-level fuzzy Petri nets as a basis for managing symbolic and numerical information.

Liu, K.F.R.; Lee, J.; Chiang, W.

In: International Journal of Artificial Intelligence, Tools, Architectures, Languages, and Algorithms, Vol. 9, No. 4, pages 569-588. 2000.

Abstract: 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 (HLFPNs). Fuzzy functions, fuzzy reasoning, and fuzzy neural networks are integrated in HLFPNs. In the 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 connections between places and transitions. A fuzzy set and a fuzzy truth value are attached to an uncertain fuzzy token to model imprecision and uncertainty. Six types of uncertain transitions are identified: calculation transitions to compare 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 to combine several uncertain fuzzy tokens with the same fuzzy variable; and aggregation-duplication transitions to amalgamate aggregation transitions with duplication transitions. To guide the computation inside the HLFPN, an algorithms is developed and an example is used to illustrate the proposed approach.

Keywords: fuzzy reasoning, high-level fuzzy Petri nets.

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