On Generalized Transitive Matrices

[摘要] Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, anddistributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitiveincline matrices is considered. Some properties of compositions of incline matrices are alsogiven, and a new transitive incline matrix is constructed from given incline matrices. Finally,the issue of the canonical form of a transitive incline matrix is discussed. The results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shownin the references.

[学科分类] 应用数学