Metal Model Based Fuzzy Petri Nets Back Propagation Learning Algorithm

In fuzzy production rule-based system, fuzzy Petri nets (FPN) is widely used for its advantage of fuzzy knowledge representation and concurrent reasoning. For the reason that back propagation (BP) algorithm can not be applied to learning of FPN directly without add virtual nodes. To overcome the drawback, a metal fuzzy Petri nets (MFPN) model is proposed. FPN mapped from four elementary production rules can be uniformed by MFPN. A continuous function maps from certainty factor of antecedent propositions to that of consequent ones in MFPN is defined, based on which, a forward continues reasoning algorithm is presented, then the gradient function of certainty factor of consequent propositions with respect to input arc weight is given. To improve convergence speed, Levenberg-Marquardt method is adopted to arc weight optimization.