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Petri nets and Fuzzy Petri nets as modeling formalism are not adaptable according to the changes of the arc weight. Weights are the parameters that represent the new incoming data of the system modeled by a (Fuzzy) Petri net. The weight changes meet the system changes in a variety of application domains (e.g. Intelligent E-learning, Computer Numerical Control, Weather Forecasting, and Expert Systems). In this paper, we introduce a new class of Fuzzy Petri nets that takes into account the weight changes of the arc in the Fuzzy reasoning process. We give the formal description of the model, an algorithm for learning the weights without the need to transfer into a neural network, an algorithm for the fuzzy reasoning, the algebraic forms of the new state equation, and the stability analysis. Finally, we introduce a weather forecasting application as a real example. [ABSTRACT FROM AUTHOR]

Abstract: Neuro-fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems. In this paper, a modified gradient-based neuro-fuzzy learning algorithm is proposed for zero-order Takagi–Sugeno inference systems. This modified algorithm, compared with conventional gradient-based neuro-fuzzy learning algorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. Some weak and strong convergence results for this algorithm are proved, indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value, respectively. A constant learning rate is used. Some conditions for the constant learning rate to guarantee the convergence are specified. Numerical examples are provided to support the theoretical findings. [Copyright &y& Elsevier]