Abstract
A fuzzy matrix plays an important role in system models based on a fuzzy relation, and the performance of such a system depends on forming powers of a fuzzy matrix. The powers of a general fuzzy matrix either converge or oscillate with a finite period. Many properties about convergence have been investigated, for example, sufficient conditions for convergence are shown. Moreover, a lot of properties about convergence of powers of a transitive fuzzy matrix have been considered. However, few investigations about the period have been made. In this paper, we consider the period of the powers of a general fuzzy matrix by a graph theoretical viewpoint, and show conditions for convergence under the max–min composition.
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