The period of powers of a fuzzy matrix

A fuzzy matrix plays an important role in system models based on a fuzzy re lation, 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 fi nite period. Many properties about convergence have been investigated, for example, sufficient conditions for convergence are shown. Moreover, a lot o f 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-mi n composition. (C) 2000 Elsevier Science B.V. All rights reserved.