ON ORDERED HYPERSTRUCTURES

Abstract

In this paper we study a (semi)hypergroup ( , ) H besides a binary relation ≤ , where ≤ is a partial preorder or a partial order such that satisfies the monotone condition. This structure is called a partially preordered (ordered) (semi)hypergroup. Also, we consider some well-known hypergroups and define a binary relation on them such that to become partially preordered (ordered) hypergroups. Finally, we associate a semihypergroup to a Γ -semigroup and prove some properties.