On the max-generalized f-mean powers of a fuzzy matrix

Let f be a strictly monotonic and continuous function from a connected subset S of [0, 1]. Let λ ∈ (0, 1) be given. The f-mean of two numbers a, b ∈ S is defined by a ⊗ b = f^-1(λf(a) + (1 - λ)f(b)). Let M_n×n(S) be the set of all n × n matrices with all entries are in S. The max-generalized f-mean powers of A,B ∈ M_n×n(S) is defined by [A ⊗ B]_ij = max_1≤k≤n a_ik ⊗ b_kj. In this paper, we consider the powers of a fuzzy matrix with max-generalized f-mean operations. We show that the powers of such a fuzzy matrix are always convergent.