On the Monotone Matrices over Distributive Lattices

Since lattice matrices are useful tools in various domains like cluster analysis, computer network, traffic control, logistics and so on, the study of the properties of lattice matrices is valuable. A lattice matrix is called monotone if is transitive or is monotone increasing. In this paper, the transitivity of powers and the properties of a transitive lattice matrix are studied. Also, the proper- tyes of a monotone increasing lattice matrix are considered.