Hypersemilattice Strongly Regular Relations on Ordered Semihypergroups

Abstract

In this paper, we first consider the regular and strongly regular relations on ordered semihypergroups in detail. In particular, we introduce the concepts of the hypersemilattice strongly regular relations and complete hypersemilattice strongly regular relations on ordered semihypergroups, and investigate their related properties. Furthermore, the properties of hyperfilters of an ordered semihypergroup are studied, and several related applications are given. Especially, we prove that the equivalence relation ${\cal N}$ on an ordered semihypergroup $S$ is the least complete hypersemilattice strongly regular relation on $S$.