Neural Architectures of Fuzzy Petri Nets

In this chapter, we discuss a novel approach to pattern classification using a concept of fuzzy Petri nets. In contrast to the commonly encountered Petri nets with their inherently Boolean character of processing tokens and firing transitions, the proposed generalization involves continuous variables. This extension makes the nets to be fully in rapport with the panoply of the real-world classification problems. The introduced model of the fuzzy Petri net hinges on the logic nature of the operations governing its underlying behavior. The logic-driven effect in these nets becomes especially apparent when we are concerned with the modeling of its transitions and expressing pertinent mechanisms of a continuous rather than an on-off firing phenomenon. An interpretation of fuzzy Petri nets in the setting of pattern classification is provided. This interpretation helps us gain a better insight into the mechanisms of the overall classification process. Input places correspond to the features of the patterns. Transitions build aggregates of the generic features giving rise to their logical summarization. The output places map themselves onto the classes of the patterns while the marking of the places correspond to the class of membership values. Details of the learning algorithm are also provided along with an illustrative numeric experiment.