THE COMPOSITION, CONVERGENCE AND TRANSITIVITY OF POWERS AND ADJOINT OF GENERALIZED FUZZY MATRICES

Abstract

Path algebras are additively idempotent semirings and generalize Boolean algebras, fuzzy algebras, distributive lattices and inclines.  Thus the Boolean matrices, the fuzzy matrices, the lattice matrices and the incline matrices are prototypical examples of matrices over path algebras.  In this paper, generalized fuzzy matrices are considered as matrices over path algebras.  Compositions of generalized
fuzzy matrices are discussed, and a new transitive matrix is constructed from given matrices.  Furthermore, the transitivity and the convergent index for powers of generalized fuzzy matrices are studied, some properties of powers are also established through adjoint matrix, and finally the invertibility of a matrix is investigated.  Some results obtained here generalize and develop the corresponding ones on fuzzy matrices, lattice matrices and incline matrices shown in the references.