Convergence of max-arithmetic mean powers of a fuzzy matrix

Fuzzy matrices provide convenient representations for fuzzy relations on finite universes. In the literature, the powers of a fuzzy matrix with max–min/max-product/max-Archimedean t-norm compositions have been studied. It turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved. In this paper, the max-arithmetic mean composition is considered for the fuzzy relations. We show that the max-arithmetic mean powers of a fuzzy matrix always are convergent.