The period of powers of a fuzzy matrix
An \(n{\times}n\) matrix \(A = (a_{ij})\) whose components are in the unit interval \([0,1]\) is called a fuzzy matrix. 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. The authors consider the period of the powers of a general fuzzy matrix by a graph theoretical viewpoint, and they state conditions for convergence under the max-min composition.
scientific article; zbMATH DE number 1423391