Mathematics and Computer Science

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Symmetric I* Restriction Method of Fuzzy Inference

Received: 12 November 2019    Accepted: 11 December 2019    Published: 24 December 2019
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Abstract

As one of important parts of fuzzy logic, fuzzy inference plays a vital role in the fields of fuzzy control, artificial intelligence, affective computing, image processing and so forth. Two key problems of fuzzy inference are FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens). How to get the ideal solution for FMP and FMT is a difficult problem in the area of fuzzy logic. Aiming at such problem, from the idea of symmetric implicational reasoning, triple I* method and restriction theory, we put forward and investigate the α-symmetric I* restriction method, and then generalize it to the α(x,y)-symmetric I* restriction method. To begin with, the α-symmetric I* restriction principle and the α(x,y)-symmetric I* restriction principle are established. Furthermore, the equivalent condition to let a basic restriction solution exist is given. Then the unified solutions of the α-symmetric I* restriction method and the α(x,y)-symmetric I* restriction method are achieved for R-implications and (S, N)-implications. Besides, some special cases of optimal solutions are shown. Finally, the corresponding conclusions are provided when the two methods degenerate into the α-triple I* restriction method and α(x,y)-triple I* restriction method. These research results would be an important improvement for the fields of fuzzy inference, fuzzy logic and related applications.

DOI 10.11648/j.mcs.20190406.14
Published in Mathematics and Computer Science (Volume 4, Issue 6, November 2019)
Page(s) 130-137
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fuzzy Inference, Fuzzy Implication, Triple I Method, Symmetric Implicational Method

References
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Author Information
  • School of Computer and Information, Hefei University of Technology, Hefei, China; Anhui Province Key Laboratory of Affective Computing & Advanced Intelligent Machine, Hefei University of Technology, Hefei, China; Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada

  • School of Computer and Information, Hefei University of Technology, Hefei, China; Anhui Province Key Laboratory of Affective Computing & Advanced Intelligent Machine, Hefei University of Technology, Hefei, China

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    Yiming Tang, Guangqing Bao. (2019). Symmetric I* Restriction Method of Fuzzy Inference. Mathematics and Computer Science, 4(6), 130-137. https://doi.org/10.11648/j.mcs.20190406.14

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    ACS Style

    Yiming Tang; Guangqing Bao. Symmetric I* Restriction Method of Fuzzy Inference. Math. Comput. Sci. 2019, 4(6), 130-137. doi: 10.11648/j.mcs.20190406.14

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    AMA Style

    Yiming Tang, Guangqing Bao. Symmetric I* Restriction Method of Fuzzy Inference. Math Comput Sci. 2019;4(6):130-137. doi: 10.11648/j.mcs.20190406.14

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  • @article{10.11648/j.mcs.20190406.14,
      author = {Yiming Tang and Guangqing Bao},
      title = {Symmetric I* Restriction Method of Fuzzy Inference},
      journal = {Mathematics and Computer Science},
      volume = {4},
      number = {6},
      pages = {130-137},
      doi = {10.11648/j.mcs.20190406.14},
      url = {https://doi.org/10.11648/j.mcs.20190406.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.mcs.20190406.14},
      abstract = {As one of important parts of fuzzy logic, fuzzy inference plays a vital role in the fields of fuzzy control, artificial intelligence, affective computing, image processing and so forth. Two key problems of fuzzy inference are FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens). How to get the ideal solution for FMP and FMT is a difficult problem in the area of fuzzy logic. Aiming at such problem, from the idea of symmetric implicational reasoning, triple I* method and restriction theory, we put forward and investigate the α-symmetric I* restriction method, and then generalize it to the α(x,y)-symmetric I* restriction method. To begin with, the α-symmetric I* restriction principle and the α(x,y)-symmetric I* restriction principle are established. Furthermore, the equivalent condition to let a basic restriction solution exist is given. Then the unified solutions of the α-symmetric I* restriction method and the α(x,y)-symmetric I* restriction method are achieved for R-implications and (S, N)-implications. Besides, some special cases of optimal solutions are shown. Finally, the corresponding conclusions are provided when the two methods degenerate into the α-triple I* restriction method and α(x,y)-triple I* restriction method. These research results would be an important improvement for the fields of fuzzy inference, fuzzy logic and related applications.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Symmetric I* Restriction Method of Fuzzy Inference
    AU  - Yiming Tang
    AU  - Guangqing Bao
    Y1  - 2019/12/24
    PY  - 2019
    N1  - https://doi.org/10.11648/j.mcs.20190406.14
    DO  - 10.11648/j.mcs.20190406.14
    T2  - Mathematics and Computer Science
    JF  - Mathematics and Computer Science
    JO  - Mathematics and Computer Science
    SP  - 130
    EP  - 137
    PB  - Science Publishing Group
    SN  - 2575-6028
    UR  - https://doi.org/10.11648/j.mcs.20190406.14
    AB  - As one of important parts of fuzzy logic, fuzzy inference plays a vital role in the fields of fuzzy control, artificial intelligence, affective computing, image processing and so forth. Two key problems of fuzzy inference are FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens). How to get the ideal solution for FMP and FMT is a difficult problem in the area of fuzzy logic. Aiming at such problem, from the idea of symmetric implicational reasoning, triple I* method and restriction theory, we put forward and investigate the α-symmetric I* restriction method, and then generalize it to the α(x,y)-symmetric I* restriction method. To begin with, the α-symmetric I* restriction principle and the α(x,y)-symmetric I* restriction principle are established. Furthermore, the equivalent condition to let a basic restriction solution exist is given. Then the unified solutions of the α-symmetric I* restriction method and the α(x,y)-symmetric I* restriction method are achieved for R-implications and (S, N)-implications. Besides, some special cases of optimal solutions are shown. Finally, the corresponding conclusions are provided when the two methods degenerate into the α-triple I* restriction method and α(x,y)-triple I* restriction method. These research results would be an important improvement for the fields of fuzzy inference, fuzzy logic and related applications.
    VL  - 4
    IS  - 6
    ER  - 

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