Affiliations: [a] Department of Mathematics, Abdul Wali Khan University Mardan, 23200, KP Pakistan
| [b] Department of Mathematics, University of Malakand, Lower Dir, KP Pakistan
Correspondence:
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Corresponding author. Asghar Khan, Department of Mathematics, Abdul Wali Khan University Mardan, 23200, KP, Pakistan. Tel.: +92 331 54 79 017; E-mail: asghar@awkum.edu.pk.
Abstract: The main goal of this paper is to study ordered semihypergroups in the framework of uni-soft left (right) hyperideals. The notions of uni-soft semihypergroups, uni-soft left (right) hyperideals are introduced, and the related properties are investigated. The concept of exclusive set is provided and the characterizations of ordered semihypergroups in terms of uni-soft left (right) hyperideals are studied. The notions of uni-soft product is considered and their properties related to uni-soft left (right) hyperideals are studied. Using the notions of uni-soft left (right) hyperideals, the main theorems for a regular and intra-regular ordered semihypergroups are investigated. The concepts of a concave soft set and critical soft point in ordered semihypergroups are provided and the basic properties of these notions are given.
Keywords: Uni-soft left (right) hyperideal, uni-soft semihypergroups, uni-soft product, concave soft set, critical soft point, regular and intra-regular ordered semihypergroup
