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<sup>−1</sup>(λf(a) + (1 − λ)f(b)). Let M<inf>n×n</inf>(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<inf>n×n</inf>(S) is defined by [A ⨂ B]<inf>ij</inf> = max<inf>1≤k≤n</inf> a<inf>ik</inf> ⨂ b<inf>kj</inf>. 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.

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