Dynamics of the fuzzy difference equation zn = max {1/zn-m αn/zn-r}

In this paper, we study the eventual periodicity of the following fuzzy max-type difference equation zn = max {1/zn-m αn/zn-r},n = 0, 1, . . . , where {αn}n≥0 is a periodic sequence of positive fuzzy numbers and the initial values z−d,z−d+1,…,z−1 are positive fuzzy numbers with d = max { m , r } . We show that if max ( supp α n ) 1 , then every positive solution of this equation is eventually periodic with period 2 m .