Characterizations of ordered semihypergroups via (M, N)-int-soft bi-hyperideals

The aim of this article is to study ordered semihypergroups in the framework of ( {M, N})-int-soft bi-hyperideals. In this paper, we introduce the notion of (M, N) -int-soft bi-hyperideals\ of ordered semihypergroups. Some properties of ({M, N})-int-soft bi-hyperideals in ordered semihypergroups are provided. We show that every int-soft bi-hyperideal is an ({M, N})-int-soft bi-hyperideals of S over U but the converse is not true which is shown with help of an example. We characterize left ({M, N}) simple and completely regular ordered semihypergroups by means of ({M, N})-int-soft bi-hyperideals.The aim of this article is to study ordered semihypergroups in the framework of \left( {M, N}\right)-int-soft bi-hyperideals. In this paper, we introduce the notion of \left( {M, N}\right)-int-soft bi-hyperideals of ordered semihypergroups. Some properties of \left( {M, N}\right)-int-soft bi-hyperideals in ordered semihypergroups are provided. We show that every int-soft bi-hyperideal is an \left( {M, N}\right)-int-soft bi-hyperideals of S over U but the converse is not true which is shown with help of an example. We characterize left \left( \text{resp. right}\right) simple and completely regular ordered semihypergroups by means of \left( {M, N}\right)-int-soft bi-hyperideals.

Keywords:

Int-soft hyperideal , int-soft bi-hyperideal , (M , N)-int-soft bi-hyperideal