On transitivity of generalized fuzzy matrices

In this paper, generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra. Some elementary properties and characterizations for transitive generalized fuzzy matrices are established and transitivity of powers of a generalized fuzzy matrix is discussed. Also, the transitive closure of a generalized fuzzy matrix is considered and some properties of the transitive closures are obtained. Partial results obtained in this paper generalize the corresponding ones on nilpotent matrices and on matrices with periods.