On the asymptotic period of powers of a fuzzy matrix

In our prior study, we have examined in depth the notion of an asymptotic period of the power sequence of an n×nn×n fuzzy matrix with max-Archimedean-tt-norms, and established a characterization for the power sequence of an n×nn×n fuzzy matrix with an asymptotic period using analytical-decomposition methods. In this paper, by using graph-theoretical tools, we further give an alternative proof for this characterization. With the notion of an asymptotic period using graph-theoretical tools, we additionally show a new characterization for the limit behaviour, and then derive some results for the power sequence of an n×nn×n fuzzy matrix with an asymptotic period.