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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]