Document Type
Article
Source of Publication
European Journal of Pure and Applied Mathematics
Publication Date
11-5-2025
Abstract
Fuzzy group theory has evolved beyond single-valued memberships to account for dual polarity and uncertainty. Building on Dib’s fuzzy space and bipolar-valued fuzzy sets, we develop a unified algebraic theory of bipolar-valued fuzzy (BVF) subgroups, including BVF normal subgroups and BVF homomorphisms, via a BVF binary operation (BVFBO) on a BVF-space. We establish necessary and sufficient subgroup criteria, characterize normality through coset symmetry in BVF-space, and prove homomorphism properties that align BVF structures with their classical counterparts through correspondence theorems. The framework clarifies when associativity holds between subgroup elements and ambient BVF-group elements and provides constructive examples. This generalization resolves limitations tied to the absence of a bipolar fuzzy universal set and supports applications in polarity-sensitive decision systems and network analysis.
DOI Link
ISSN
Publisher
New York Business Global LLC
Volume
18
Issue
4
First Page
6761
Disciplines
Mathematics
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Recommended Citation
Al-Zu’bi, Fadi; Ahmad, Abd Ghafur; Alkouri, Abd Ulazeez; Darus, Maslina; and Damrah, Sadeq, "Bipolar-valued fuzzy subgroups, normal subgroups, and homomorphisms on Dib’s fuzzy space" (2025). All Works. 8366.
https://zuscholars.zu.ac.ae/works/8366
Indexed in Scopus
no
Open Access
yes
Open Access Type
Gold: This publication is openly available in an open access journal/series