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On the Periodicity of a Max-type Fuzzy Difference Equations

Received: 17 November 2019     Accepted: 2 December 2019     Published: 11 December 2019
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Abstract

Our aim in this paper is to discuss the periodicity and boundedness of a max-type fuzzy difference equation. When studying the periodicity of the solution to the max-fuzzy difference equation, the equation is first converted into a difference system composed of two related difference equations through the cut set theory of the fuzzy number, then the periodicity of each solution sequence in the system is obtained by means of inequality technique, mathematical induction and other theoretical methods, thus the periodicity of the solution is proved. As researching the boundedness of the solution for the fuzzy difference equation, the difference system is also obtained through the cut set theory of the fuzzy number, then analyze the boundedness to each solution sequence according to the periodicity with the solution sequence, through examining the value of the finite subsequence in each solution sequence, the boundedness with these subsequences can be obtained, and then the boundedness for each solution sequence made up of complete subsequences can be known, thus the boundedness of the solution is proved. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, the numerical results not only show the dynamic behavior of the solutions to the fuzzy difference systems, but also verify the effectiveness of the theoretical results.

Published in American Journal of Electromagnetics and Applications (Volume 7, Issue 2)
DOI 10.11648/j.ajea.20190702.11
Page(s) 13-18
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), 2019. Published by Science Publishing Group

Keywords

Fuzzy Difference Equation, Max-Type, Cut Theory, Periodicity, Boundedness

References
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Cite This Article
  • APA Style

    Changyou Wang, Wei Wei, Qiang Yang, Yonghong Li. (2019). On the Periodicity of a Max-type Fuzzy Difference Equations. American Journal of Electromagnetics and Applications, 7(2), 13-18. https://doi.org/10.11648/j.ajea.20190702.11

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    ACS Style

    Changyou Wang; Wei Wei; Qiang Yang; Yonghong Li. On the Periodicity of a Max-type Fuzzy Difference Equations. Am. J. Electromagn. Appl. 2019, 7(2), 13-18. doi: 10.11648/j.ajea.20190702.11

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    AMA Style

    Changyou Wang, Wei Wei, Qiang Yang, Yonghong Li. On the Periodicity of a Max-type Fuzzy Difference Equations. Am J Electromagn Appl. 2019;7(2):13-18. doi: 10.11648/j.ajea.20190702.11

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  • @article{10.11648/j.ajea.20190702.11,
      author = {Changyou Wang and Wei Wei and Qiang Yang and Yonghong Li},
      title = {On the Periodicity of a Max-type Fuzzy Difference Equations},
      journal = {American Journal of Electromagnetics and Applications},
      volume = {7},
      number = {2},
      pages = {13-18},
      doi = {10.11648/j.ajea.20190702.11},
      url = {https://doi.org/10.11648/j.ajea.20190702.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajea.20190702.11},
      abstract = {Our aim in this paper is to discuss the periodicity and boundedness of a max-type fuzzy difference equation. When studying the periodicity of the solution to the max-fuzzy difference equation, the equation is first converted into a difference system composed of two related difference equations through the cut set theory of the fuzzy number, then the periodicity of each solution sequence in the system is obtained by means of inequality technique, mathematical induction and other theoretical methods, thus the periodicity of the solution is proved. As researching the boundedness of the solution for the fuzzy difference equation, the difference system is also obtained through the cut set theory of the fuzzy number, then analyze the boundedness to each solution sequence according to the periodicity with the solution sequence, through examining the value of the finite subsequence in each solution sequence, the boundedness with these subsequences can be obtained, and then the boundedness for each solution sequence made up of complete subsequences can be known, thus the boundedness of the solution is proved. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, the numerical results not only show the dynamic behavior of the solutions to the fuzzy difference systems, but also verify the effectiveness of the theoretical results.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - On the Periodicity of a Max-type Fuzzy Difference Equations
    AU  - Changyou Wang
    AU  - Wei Wei
    AU  - Qiang Yang
    AU  - Yonghong Li
    Y1  - 2019/12/11
    PY  - 2019
    N1  - https://doi.org/10.11648/j.ajea.20190702.11
    DO  - 10.11648/j.ajea.20190702.11
    T2  - American Journal of Electromagnetics and Applications
    JF  - American Journal of Electromagnetics and Applications
    JO  - American Journal of Electromagnetics and Applications
    SP  - 13
    EP  - 18
    PB  - Science Publishing Group
    SN  - 2376-5984
    UR  - https://doi.org/10.11648/j.ajea.20190702.11
    AB  - Our aim in this paper is to discuss the periodicity and boundedness of a max-type fuzzy difference equation. When studying the periodicity of the solution to the max-fuzzy difference equation, the equation is first converted into a difference system composed of two related difference equations through the cut set theory of the fuzzy number, then the periodicity of each solution sequence in the system is obtained by means of inequality technique, mathematical induction and other theoretical methods, thus the periodicity of the solution is proved. As researching the boundedness of the solution for the fuzzy difference equation, the difference system is also obtained through the cut set theory of the fuzzy number, then analyze the boundedness to each solution sequence according to the periodicity with the solution sequence, through examining the value of the finite subsequence in each solution sequence, the boundedness with these subsequences can be obtained, and then the boundedness for each solution sequence made up of complete subsequences can be known, thus the boundedness of the solution is proved. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, the numerical results not only show the dynamic behavior of the solutions to the fuzzy difference systems, but also verify the effectiveness of the theoretical results.
    VL  - 7
    IS  - 2
    ER  - 

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Author Information
  • College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

  • College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

  • College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, P. R. China

  • College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

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