Bipolar fuzzy Petri nets for knowledge representation and acquisition considering non-cooperative behaviors
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ORIGINAL ARTICLE
Bipolar fuzzy Petri nets for knowledge representation and acquisition considering non-cooperative behaviors Xue-Guo Xu1 • Yun Xiong1 • Dong-Hui Xu1 • Hu-Chen Liu2,3 Received: 5 May 2019 / Accepted: 22 March 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Fuzzy Petri nets (FPNs) are a promising modeling tool for knowledge representation and reasoning. As a new type of FPNs, bipolar fuzzy Petri nets (BFPNs) are developed in this article to overcome the shortcomings and improve the performance of traditional FPNs. In order to depict expert knowledge more accurately, the BFPN model adopts bipolar fuzzy sets (BFSs), which are characterized by the satisfaction degree to property and the satisfaction degree to its counter property, to represent knowledge parameters. Because of the increasing scale of expert systems, a concurrent hierarchical reasoning algorithm is introduced to simplify the structure of BFPNs and reduce the computation complexity of knowledge reasoning algorithm. In addition, a large group expert weighting method is proposed for knowledge acquisition by taking experts’ non-cooperative behaviors into account. A realistic case of risk index evaluation system is presented to show the effectiveness and practicality of the proposed BFPNs. The result shows that the new BFPN model is feasible and efficient for knowledge representation and acquisition. Keywords Fuzzy Petri net (FPN) Bipolar fuzzy set (BFS) Knowledge acquisition Knowledge representation Expert system
1 Introduction An expert system is an intellectual programming system which can solve problems in relevant fields with expert level, use the experience and knowledge that domain experts accumulated for many years, and simulate the thought process of human experts [1, 2]. The expert system has been characterized by capturing expert knowledge in such a way that it is possible for nonexperts to address a given problem through the knowledge captured and stored in computer [3, 4]. The most important phases of developing an expert system are the acquisition of experts’ professional knowledge and the representation of the identified knowledge rules. The knowledge & Dong-Hui Xu [email protected] 1
School of Management, Shanghai University, 99 Shangda Road, Shanghai 200444, People’s Republic of China
2
College of Economics and Management, China Jiliang University, Hangzhou 310018, People’s Republic of China
3
School of Economics and Management, Tongji University, Shanghai 200092, People’s Republic of China
acquisition refers to how elicit domain knowledge through interactions with experts. The knowledge representation is to transform the abstract knowledge within the domain into a system conceptual framework that can be processed [5]. Fuzzy Petri nets (FPNs) are a powerful modeling tool to deal with imprecise and fuzzy knowledge information of rulebased systems [6, 7]. Combining fuzzy sets and Petri nets, the FPNs have strong ability of knowledge representation and reasoning and are suitable to mo
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