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On the Periodicity of a Max-type Fuzzy Difference Equations
American Journal of Electromagnetics and Applications
Volume 7, Issue 2, December 2019, Pages: 13-18
Received: Nov. 17, 2019; Accepted: Dec. 2, 2019; Published: Dec. 11, 2019
Authors
Changyou Wang, 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
Wei Wei, College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Qiang Yang, College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, P. R. China
Yonghong Li, College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Article Tools Abstract PDF (220KB)
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.
Keywords
Fuzzy Difference Equation, Max-Type, Cut Theory, Periodicity, Boundedness
Changyou Wang, Wei Wei, Qiang Yang, Yonghong Li, On the Periodicity of a Max-type Fuzzy Difference Equations, American Journal of Electromagnetics and Applications. Vol. 7, No. 2, 2019, pp. 13-18. doi: 10.11648/j.ajea.20190702.11
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