BP learning algorithm for fuzzy Petri nets based on metal model

Fuzzy Petri nets (FPN) are widely used for their advantages of fuzzy knowledge representation and concurrent reasoning. Back propagation (BP) algorithm used in learning of ANN seems inapplicable to FPN without add virtual nodes. To overcome the drawback, a metal fuzzy Petri nets (MFPN) model was proposed. As a result, FPN mapped from four elementary production rules could be uniformed by MFPN. A continuous function mapping from certainty factor of antecedent propositions to that of consequent ones in MFPN was defined, based on which, a forward continuous reasoning algorithm was proposed. To improve convergence speed, a reverse reasoning algorithm based on retrospective strategy was introduced, then the gradient function of certainty factor of consequent propositions was given. Levenberg-Marquardt algorithm was adopted to weight optimization.