On Selected Properties of Uninorm Petri Nets and Their Application in Modeling Knowledge-Based Systems - Suraj, Zbigniew (Procedia computer science, 2023)
In this paper, we analyze selected structural and dynamic properties of uninorm Petri nets in terms of their use in modeling knowledge-based systems operating in an uncertain environment. The uninorm Petri nets use uninorms to describe their behavior. Uninorms are a special type of aggregation functions that generalize both t-norms and s-norms. This generalization is that in the case of a uninorm, the neutral element can take any value in the unit interval, in contrast to triangular norms, for which the neutral element is equal to 1 or 0 depending on whether the triangular norm is a t-norm or an s-norm. Thanks to this, by manipulating the neutral element in the unit interval, it is possible to better match the behavior of the used net to the requirements of the modeled system. When modeling systems using uninorm Petri nets, as well as nets using triangular norms, the following questions are important for the designer of such models: (1) What properties of the net affect the uniqueness of the model's decisions? (2) How to choose uninorms assigned to net transitions so that the behavior of the net model is deterministic? This work provides answers to these two questions above. The subject of this paper is a continuation of the author's earlier research on generalized fuzzy Petri nets based on triangular norms. This also falls within the range of challenges outlined in a review article on the state of research on the theory and applications of fuzzy Petri nets, developed by Zhou & Zain authors and published in Artificial Intelligence Review, 45, 405–446, 2016.