Eventual periodicity of the fuzzy max-difference equation xn=max{C,xn−m−kxn−m}

In this paper, we study the eventual periodicity of the fuzzy max-type difference equation x n = max { C , x n − m − k x n − m } , n ∈ { 0 , 1 , … } , where m and k are positive integers, C and the initial values are positive fuzzy numbers. Let the support supp C = { t : C ( t ) > 0 } ‾ = [ C 1 , C 2 ] of C . We show that: (1) if C 1 > 1 , then every positive solution of this equation equals C eventually; (2) there exists a positive fuzzy number C with C 1 = 1 such that this equation has a positive solution which is not eventually periodic; (3) if C 2 ≤ 1 , then this equation has a positive solution which is not eventually periodic; (4) if C 1 < 1 < C 2 , then every positive solution of the above equation is not eventually periodic.