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.
Highlights
Fuzzy Petri nets (FPNs), as a graphical and mathematical modeling methodology, are an important tool for knowledge representation and reasoning in expert systems [1]–[3]
Motivated by the aforementioned analyses, we propose the q-rung orthopair fuzzy linguistic reasoning Petri net (q-ROFLRPN) model by using q-rung orthopair fuzzy linguistic set (q-ROFLS) and weighted ordered weighted averaging (WOWA) operator
According to the sensitivity analysis and comparative study above, we can obtain that the q-ROFLRPN model can overcome the deficiencies in conventional FPN models and the knowledge representation and reasoning of expert system conducted by the proposed q-ROFLRPN model is more flexible, intelligent and reliable
Summary
Fuzzy Petri nets (FPNs), as a graphical and mathematical modeling methodology, are an important tool for knowledge representation and reasoning in expert systems [1]–[3]. The linguistic scale functions (LSFs) [32] can assign different semantic values to the linguistic term to deal with balanced LTSs and unbalanced LTSs. On the other hand, the knowledge reasoning power of FPNs based on traditional reasoning operators, such as max, min and algebraic product, is limited, due to the increasing complexity of expert systems [33]. The proposed q-ROFLRPN model has the following advantages: 1) It can model the membership degrees of LVs and hesitancy of experts and express the knowledge representation parameters from both qualitative and quantitative perspectives It can expand the space of accepted information of fuzzy set by adjusting the parameter of q-ROFLSs. 2) It provides the new operational laws of q-ROFLSs, which guarantee the operations are closed to overcome the drawbacks of the reasoning result in granularity and logic.
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