Knowledge representation and reasoning with industrial application using interval-valued intuitionistic fuzzy Petri nets
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ORIGINAL ARTICLE
Knowledge representation and reasoning with industrial application using interval‑valued intuitionistic fuzzy Petri nets and extended TOPSIS Weichao Yue1 · Xiao Liu2 · Sanyi Li1 · Weihua Gui3 · Yongfang Xie3 Received: 28 October 2019 / Accepted: 22 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Fuzzy Petri nets (FPNs) have many successes in various applications as an important modeling technique for knowledge representation and reasoning. However, in the real world, the following conditions may make it difficult to precisely model knowledge based on current FPNs, including the cognitive nonconformity, fuzziness and uncertainty of experiential cognition of experts. In an effort to overcome the shortcomings of current FPNs, the interval-valued intuitionistic FPNs (IVIFPNs) are proposed based on interval-valued intuitionistic fuzzy sets (IVIFSs), IVIFSs hybrid averaging (IVIFSsHA) operator and extended TOPSIS (ETOPSIS). Combining with IVIFSsHA operator, an inference algorithm based on matrix operation is proposed to improve the efficiency of computing final truth values. In addition, an optimal alternative is determined based on the proposed ETOPSIS, in which intuitionistic information and fuzzy information can be considered simultaneously based on the proposed information collaborative entropy. Finally, a comparison test is presented to show the effectiveness of ETOPSIS. Moreover, a novel model for the identification of aluminum electrolysis cell condition is proposed based on IVIFPNs and ETOPSIS, and the application result shows that the proposed methods are efficient to deal with cognitive nonconformity and manage fuzziness and uncertainty of expert knowledge. These facts demonstrate the usefulness and advantages of the proposed methods in complex real-world applications. Keywords Fuzzy Petri nets · Interval-valued intuitionistic fuzzy sets · Extended TOPSIS · Knowledge representation · Identification of aluminum electrolysis cell condition
1 Introduction Knowledge representation and reasoning (KRR) are aimed at capturing and storing knowledge in a system to solve a particular problem for non-experts. KRR have always been received considerable attention, and have been widely used * Xiao Liu [email protected] * Sanyi Li [email protected] 1
School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China
2
Department of Transportation Information Engineering, Henan College of Transportation, Zhengzhou 450002, China
3
School of Automation, Central South University, Changsha 410083, China
in many fields, such as smart manufacturing [1], question answering system [2], etc. Fuzzy production rules (FPRs) [3], fuzzy cognitive maps [4], semantic knowledge network [5], fuzzy Petri nets (FPNs) [6] and so on are proposed for KRR over the past several years. FPNs, which contain the places representing propositions, transitions representing FPRs and directed arcs representing influence degrees between
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