Periodicity of A Four-order Maximum Fuzzy Difference Equation.

Abstract-In this article, we investigate the periodicity of a four-order maximum fuzzy difference equation with the positive fuzzy numbers for the initial values and the parameter. Firstly, we transform the maximum fuzzy difference equation into a corresponding maximum ordinary difference equations with parameters by utilizing the fuzzy set theory. Secondly, we obtain the expressions of the eventual periodic solutions for the maximum ordinary difference equations by the inequality technique, the iteration method and the mathematical induction. Finally, we achieve the expressions of the eventual periodic solutions for the maximum fuzzy difference equation. In addition, we give some numerical simulations to verify the effectiveness of our theoretical analysis. [ABSTRACT FROM AUTHOR]