On the Max-geometric 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/ max-arithmetic mean composition 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-geometric mean composition is considered for the fuzzy relations. We proposed a simple and effective characterization for the limiting behavior with the notion of asymptotic period of a fuzzy matrix with the max-geometric mean composition. Moreover, if a fuzzy matrix A is primitive then we show that the max-geometric mean powers of A are always convergent.