Tripolar Fuzzy (m, n)-Quasi-Ideals of Ordered Semigroups

Paper Details

Authors: Phukhaengsi A.; Khamrot P.; Gaketem T.

DOI: 10.28924/2291-8639-24-2026-156

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

In 2009, M. A. Ansari et al. introduced the concept of (m, n)-quasi-ideals in semigroup theory. Nearly a decade later, in 2018, Rao proposed the framework of tripolar fuzzy sets, which generalizes the classical fuzzy, bipolar fuzzy, and intuitionistic fuzzy set theories. Building upon these developments, this paper introduces and studies the notion of tripolar fuzzy (m, n)-quasi-ideals in semigroups. We explore their fundamental characteristics, analyze their connections with conventional (m, n)-quasi-ideals, and establish relationships between these two structures. In addition, we investigate the notions of minimality, primeness, and semiprimeness within this newly defined framework. © 2026 the author(s).

Keywords

ordered semigroups; semigroups; tripoar fuzzy ideals; tripolar fuzzy (m, n)-quasi-ideals

Read Paper Back to Search