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Knowledge representation and reasoning with industrial application using interval-valued intuitionistic fuzzy Petri nets and extended TOPSIS

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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.

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Acknowledgements

Supported by the National Natural Science Foundation of China (61621062 and 61725306).

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Weichao Yue & Sanyi Li

  2. Department of Transportation Information Engineering, Henan College of Transportation, Zhengzhou, 450002, China

    Xiao Liu

  3. School of Automation, Central South University, Changsha, 410083, China

    Weihua Gui & Yongfang Xie

Authors
  1. Weichao Yue
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  2. Xiao Liu
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  3. Sanyi Li
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  4. Weihua Gui
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  5. Yongfang Xie
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Correspondence to Xiao Liu or Sanyi Li.

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Yue, W., Liu, X., Li, S. et al. Knowledge representation and reasoning with industrial application using interval-valued intuitionistic fuzzy Petri nets and extended TOPSIS. Int. J. Mach. Learn. & Cyber. 12, 987–1013 (2021). https://doi.org/10.1007/s13042-020-01216-1

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  • DOI: https://doi.org/10.1007/s13042-020-01216-1

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