A Comprehensive Study of Fuzzy Quasi-Ideals in Ordered Semigroups

초록

In this work, we introduce the concept of (is an element of, is an element of boolean OR (k(& lowast;), q(k)))-fuzzy quasi-ideals in ordered semigroups. We provide several equivalent conditions of these fuzzy quasi-ideals and demonstrate that the intersection of any collection of these fuzzy quasi-ideals is of the same type, but their union is not. We also discuss how these novel fuzzy quasi-ideals connect to previously studying fuzzy quasi-ideal notions in the literature. Additionally, we provide characterizations of (is an element of, is an element of boolean OR (k(& lowast;), q(k)))-fuzzy quasi-ideals in terms of (k(& lowast;), k)-upper part of fuzzy sets. We further introduce the notion of completely semiprime (is an element of, is an element of boolean OR (k(& lowast;), q(k)))-fuzzy quasi-ideals and establish several equivalent conditions for them in terms of (k(& lowast;), k)-upper parts of fuzzy sets and ordered fuzzy points. Finally, we characterize the left and right regularities of ordered semigroups by using completely semiprime (is an element of, is an element of boolean OR (k(& lowast;), q(k)))-fuzzy quasi-ideals.

키워드