A New Linguistic Petri Net for Complex Knowledge Representation and Reasoning

Fuzzy Petri nets (FPNs) are a useful instrument for modelling expert systems to conduct knowledge representation and reasoning. Many studies have been carried out for improving the performance of FPNs in terms of their accurate representation of knowledge and power of approximate reasoning. Nevertheless, the current representation methods with FPNs are unable to handle the uncertain linguistic knowledge given by domain experts and the reliability of their judgments. In addition, the existing reasoning algorithms have no way to capture the interrelationship of the propositions with the same output transition. Therefore, we present a new type of FPNs, called 2-dimensional uncertain linguistic Petri nets (2DULPNs). The 2-dimensional uncertain linguistic variables (2DULVs) and Choquet integral are combined for knowledge representation and reasoning for the first time. The truth degrees of propositions, thresholds and certainty values of linguistic production rules are denoted as 2DULVs. Some new aggregated operators based on Choquet integral are proposed and used in the approximate reasoning to capture the interactions among antecedent propositions. Finally, an equipment fault diagnosis example is provided to illustrate the correctness and effectiveness of the proposed 2DULPN model.