Weakly Regular Semigroups Characterized in Terms of Neutrosophic Bipolar-Valued Fuzzy Ideals

Abstract

In this paper, we introduce several new concepts of neutrosophic bipolar valued fuzzy structures in semigroups, specifically focusing on neutrosophic bipolar valued fuzzy bi-ideals, generalized bi-ideals, ideals, and interior ideals. We investigate the fundamental properties of these notions in detail. Furthermore, we establish several characterizations of weakly regular semigroups in terms of these newly defined fuzzy ideals. Our results extend existing studies on bipolar fuzzy sets and neutrosophic structures and provide a more robust framework for managing uncertainty within algebraic systems.