On nilpotency 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 properties and characterizations for nilpotent generalized fuzzy matrices are established, reduction of generalized fuzzy matrices is defined and some properties of reduction of nilpotent generalized fuzzy matrices are obtained. Partial results obtained in this paper generalize the corresponding ones on fuzzy matrices, on lattice matrices and on incline matrices.