Grey Reasoning Petri Nets for Large Group Knowledge Representation and Reasoning

Abstract

In previous studies, fuzzy Petri nets (FPNs) have been used for knowledge representation and reasoning in various areas. However, the traditional FPNs have limited abilities in representing uncertain knowledge and conducting approximate reasoning when applied in practical situations. In addition, the knowledge parameters in existing FPNs are usually given by a small number of experts. To address these issues, a grey reasoning Petri net (GRPN) model is proposed in this article for knowledge representation and reasoning under large group environment. In this model, grey production rules in an expert system are modeled by the GRPNs, where grey numbers are used to represent the truth degrees of places, certainty values, and the thresholds on output arcs of transitions. The grey weighted Bonferroni mean operator is adopted as a substitute of the classical min and max operators in the developed grey reasoning algorithm to capture the interrelationships of input places and the interrelationships between transitions. Furthermore, a large group decision-making method is introduced for obtaining the knowledge parameters of GRPNs based on the grey correlation analysis. Finally, the usefulness and effectiveness of the proposed GRPN model is demonstrated by a real-world risk evaluation example.