Fuzzy (m,n)-Quasi-Hyperideals in Ordered Semihypergroups: A Novel Approach

Abstract

This paper presents a novel methodology for exploring the structure of ordered semihypergroups through the lens of fuzzy logic, with a particular focus on the classification and properties of fuzzy (m,n)-quasi-hyperideals. In this regard, we first explore some properties of (m,n)-quasi-hyperideals of ordered semihypergroups. Then we extend this notion to fuzzy (m,n)-quasi-hyperideals of ordered semihypergroups. More precisely, we investigate their properties, provide nontrivial examples, and connect them to (m,n)-quasi-hyperideals through level sets and characteristic function.

Keywords: (m,n) quasi-hyperideal, fuzzy (m,n) quasi-hyperideal, level set, Ordered semihypergroup