Toward Optimization of Reasoning Using Generalized Fuzzy Petri Nets

Abstract

Recently, generalized fuzzy Petri nets have been proposed. This paper describes a modified class of generalized fuzzy Petri nets called optimized generalized fuzzy Petri nets. The main difference between the current net model and the previous one is the definition of the operator binding function $\delta$. This function, like in the previous net model, combines transitions with triples of operators $(In,Out_1,Out_2)$ in the form of appropriate triangular norms. The operator In refers to the way in which all input places are connected to a given transition (or more precisely, the statements corresponding to these places) and affects the aggregation power of truth degrees associated with the input places of the transition. However, the operators $Out_1$ and $Out_2$ refer to the way in which the new markings of output places of the transition are calculated after firing the transaction. For the operator In, it is assumed that it can belong to one of two classes, i.e., t or s-norms, while the operator $Out_1$ belongs to the class of t-norms, and the operator $Out_2$ to the class of s-norms. The meaning of these three operators in the current net model is the same as in the previous one. However, the new net model has been extended to include external knowledge about the partial order between the triangle norms used in the model. In addition, it is assumed that the new net model works in the steps mode. The paper also shows how to use this net model in the fuzzy reasoning algorithm. The tangible benefit of this approach compared to the previous one lies in the fact that the user can now more precisely adapt his model to the real life situation and use it more effectively by choosing the appropriate triples of operators for net transitions. This paper also presents an example of a small rule-based decision support system in the field of control, illustrating the described approach.