Modeling uncertainty reasoning with possibilistic petri nets

Abstract

Manipulation of perceptions is a remarkable human capability in a wide variety of physical and mental tasks under fuzzy or uncertain surroundings. Possibilistic reasoning can be treated as a mechanism that mimics human inference mechanisms with uncertain information. Petri nets are a graphical and mathematical modeling tool with powerful modeling and analytical ability. The focus of this paper is on the integration of Petri nets with possibilistic reasoning to reap the benefits of both formalisms. This integration leads to a possibilistic Petri nets model (PPN) with the following features. A possibilistic token carries information to describe an object and its corresponding possibility and necessity measures. Possibilistic transitions are classified into four types: inference transitions, duplication transitions, aggregation transitions, and aggregation-duplication transitions. A reasoning algorithm, based on possibilistic Petri nets, is also presented to improve the efficiency of possibilistic reasoning and an example related to diagnosis of cracks in reinforced concrete structures is used to illustrate the proposed approach.