Periodicity of the Positive Solutions of a Fuzzy Max-Difference Equation

Abstract

We investigate the periodic nature of the positive solutions of the fuzzy max-difference equation $x_{n+1}=\text{max}\left\{A_n/x_{n-m},x_{n-k}\right\},n=\mathrm{0,1},\dots$, where $k,m\in \{\mathrm{1,2},\dots \}$, $A_n$ is a periodic sequence of fuzzy numbers, and $x_{-d},x_{-d+1},\dots ,x_0$ are positive fuzzy numbers with $d=\left\{m,k\right\}$. We show that every positive solution of this equation is eventually periodic with period $k+1$.