Extension of Bipolar Q-Intuitionistic Fuzzy Ideals to Lower Level Sets and Homomorphisms via Regular Ordered Semigroups

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DOI: https://doi.org/10.28924/2291-8639-24-2026-88
Published: Mar 19, 2026
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Murugan Palanikumar, Aiyared Iampan, Extension of Bipolar Q-Intuitionistic Fuzzy Ideals to Lower Level Sets and Homomorphisms via Regular Ordered Semigroups, Int. J. Anal. Appl., 24 (2026), 88.

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Murugan Palanikumar, Aiyared Iampan

Abstract

This paper investigates several (ς, ζ)-bipolar Q-intuitionistic fuzzy structures in an ordered semigroup S, including subsemigroups (GBQIFSSG), left ideals (GBQIFLId), right ideals (GBQIFRId), ideals (GBQIFId), and bi-ideals (GBQIFBId). We introduce a novel extension of GBQIFId, denoted (ς, ζ)-GBQIFI, and study its correspondence to lower level sets (FLId, FRId, FBId) within S. Several characterizations are established, showing conditions under which these fuzzy structures reduce to their crisp counterparts. Homomorphic and inverse images of GBQIFSSGs are analyzed, and the role of regularity in ordered semigroups is explored to derive equivalences between product and meet operations. Illustrative examples are provided to validate the proposed results and offer new insights into the interaction between bipolar fuzzy frameworks and algebraic structures.

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