Linguistic Reasoning Petri Nets Using q-Rung Orthopair Fuzzy Linguistic Sets and Weighted Ordered Weighted Averaging Operators

Abstract

Fuzzy Petri nets (FPNs) are an important tool for knowledge representation and reasoning in the rule-based expert system. Recently, various fuzzy sets and linguistic models have been introduced into FPNs to improve its ability in handling imprecise, fuzzy, and linguistic information. However, the existing FPN models still have the following two deficiencies: The first one is the incompatibility of the knowledge representation parameters in modeling the membership degrees of linguistic variables and hesitancy of experts when experts provide linguistic evaluations. Another one is that the reasoning operators in existing reasoning algorithm considering the local weights and ordered weights of propositions fail to guarantee the reasoning result satisfies the monotonicity, boundary, and idempotency. In this paper, we propose the q-rung orthopair fuzzy linguistic reasoning Petri nets (q-ROFLRPNs) by using the q-rung orthopair fuzzy linguistic sets (q-ROFLSs) to enhance the capability of conventional FPNs in dealing with fuzzy and linguistic knowledge. We define new closed operational laws of q-ROFLSs by linguistic scale functions (LSFs), which not only guarantee the validity and reliability of reasoning results but also handle different semantic situations of the linguistic term set. In addition, an enhanced reasoning algorithm based on weighted ordered weighted averaging (WOWA) operator is proposed by considering the weights of propositions themselves and their ordered weights, and the monotonicity, boundary, and idempotency of the results are satisfied. At last, a case study on fault diagnosis for metro door system is provided to demonstrate the effectiveness and advantages of the proposed model.

Keywords

• Fuzzy Petri net (FPN)
• knowledge representation
• q-rung orthopair fuzzy linguistic set
• weighted ordered weighted averaging (WOWA) operator