基于元模型的模糊Petri网反向传播学习算法

BP Learning Algorithm for Fuzzy Petri Nets Based on Metal Model

模糊Petri网是知识表达与并行推理的重要工具,但拓扑为非严格分层的结构。为在不增加虚节点的情况下实现模糊Petri网的反向传播学习,提出模糊Petri网元模型的概念,统一四种基本产生式规则对应的模糊Petri网模型。并建立元模型的结论置信度关于条件置信度的连续映射,给出了正向推理算法。为提高收敛速率,先通过基于回溯策略的反向推理算法,计算元模型结论置信度对条件置信度的梯度函数,最后采用Levenberg-Marquardt算法实现权值优化。

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 couM 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.