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Knowledge Representation Using Fuzzy Petri Nets
September 1990 (vol. 2 no. 3)
pp. 311-319

A fuzzy Petri net model (FPN) is presented to represent the fuzzy production rule of a rule-based system in which a fuzzy production rule describes the fuzzy relation between two propositions. Based on the fuzzy Petri net model, an efficient algorithm is proposed to perform fuzzy reasoning automatically. It can determine whether an antecedent-consequence relationship exists from proposition d/sub s/ to proposition d/sub j/, where d/sub s/ not=d/sub j/. If the degree of truth of proposition d/sub s/ is given, then the degrees of truth of proposition d/sub j/ can be evaluated. The formal description of the model and the fuzzy reasoning algorithm are shown in detail. The upper bound of the time complexity of the fuzzy reasoning algorithm is O(nm), where n is the number of places and m is the number of transitions. Its execution time is proportional to the number of nodes in a sprouting tree generated by the algorithm only generates necessary reasoning paths from a starting place to a goal place, it can be executed very efficiently.

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Index Terms:
fuzzy Petri nets; fuzzy production rule; rule-based system; fuzzy relation; fuzzy reasoning; formal description; upper bound; time complexity; execution time; sprouting tree; computational complexity; knowledge representation; Petri nets
S.-M. Chen, J.-S. Ke, J.-F. Chang, "Knowledge Representation Using Fuzzy Petri Nets," IEEE Transactions on Knowledge and Data Engineering, vol. 2, no. 3, pp. 311-319, Sept. 1990, doi:10.1109/69.60794
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