On generalized fuzzy matrices with periods

In this paper, generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra. Some properties and characterizations for generalized fuzzy matrices with periods are established and an expression for the transitive closure of a generalized fuzzy matrix with a period as a sum of its powers is shown. Reduction of generalized fuzzy matrices is defined and some properties for reduction of generalized fuzzy matrices with periods are obtained. Also, the structure of all standard eigenvectors for a generalized fuzzy matrix with a period is determined.