On the power sequence of a fuzzy matrix with convex combination of max-product and max-min operations

Abstract

In the literature, the powers of a fuzzy matrix with max-min/max-product/max Archimedean t-norm/max t-norm/max-arithmetic mean 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, we consider the powers of a fuzzy matrix with convex combination of max-product and max-min operations. We show that the powers of a fuzzy matrix A with such operations are asymptotical p-period if and only if the powers of an associated Boolean matrix A¯ are p-periodic. Moreover, necessary and sufficient conditions for such a fuzzy matrix to be nilpotent are proposed.