Periodicity of the positive solutions of a fuzzy max-difference equation
Summary: We investigate the periodic nature of the positive solutions of the fuzzy max-difference equation \(x_{n + 1} = \text{max} \left\{A_n / x_{n - m}, x_{n - k}\right\}, n = 0,1, \ldots\), where \(k, m \in \{1,2, \ldots \}\), \(A_n\) is a periodic sequence of fuzzy numbers, and \(x_{- d}, x_{- d + 1}, \ldots, x_0\) are positive fuzzy numbers with \(d = \left\{m, k\right\}\). We show that every positive solution of this equation is eventually periodic with period \(k + 1\).
scientific article; zbMATH DE number 7023031
scientific article