Behavior of the positive solutions of fuzzy max-difference equations (Q2495052)

The authors extend some results obtained by \textit{A. M. Amleh, J. Hoag}, and \textit{G. Lados} [Comput. Math. Appl. 36, No.~10--12, 401--404 (1998; Zbl 0933.39030)] and by \textit{I. Szalkai} [J. Difference Equ. Appl. 5, No.~1, 25--29 (1999; Zbl 0930.39011)] by studying the periodicity of the solutions of the fuzzy difference equations \[ \begin{aligned} x_{n+1} & =\max\{A/x_n,A/x_{n-1}\dots A/x_{n-k}\}\\ x_{n+1} & =\max\{A_0/x_n, A_1/x_{n-1}\}\end{aligned} \] where \(k\) is a positive integer, \(A,A_i,i=0,1\) are positive fuzzy numbers, and the initial values \(x_i\), \(i=-k,-k+1\dots 0\) (resp., \(i=-1,0)\) of the first (resp., second) equation are positive fuzzy numbers.