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

Document Type : Research Paper

Authors

1 Government Higher Secondary School, Mohib Banda, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.

2 Department of mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.

3 Department of mathematics, Government Degree College Garhi Kapura, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.

10.29252/as.2021.2051

Abstract

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

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