Document Type
Article
Source of Publication
European Journal of Pure and Applied Mathematics
Publication Date
10-1-2024
Abstract
The numerous extensions of fuzzy groups (FG) and fuzzy subgroups are complicated. Several results depending on different approaches of FG theory were introduced. This study introduces a novel extension, named bipolar-valued fuzzy groups (BVF-groups), which are based on bipolar-valued fuzzy space (BVF-space) and are created using Dib’s methodology. The BVF-space replaces the universal set in conventional set theory. The BVF-space generalizes the notion of fuzzy space (F-space) from [0, 1] to [−1, 0] × [0, 1] for the range of membership function. The novel theory of BVF-group is achieved through the BVF-space and bipolar valued binary operation (BVFBO) to build a new algebraic structure in a natural way, which satisfies four axioms as in classical group and FG theory. The challenges associated with the lack of a bipolar valued fuzzy universal set may also be resolved using this approach. This generalization highlights how to present and explore the BVF-groupoid, BVF-monoid, and BVF-group based on BVF-space. Also, as a connection result, we proved that every intuitionistic fuzzy groupoid (group) is a bipolar valued fuzzy groupoid (group), but the inverse is not true. Some theorems support the relations between BVF-group as a generalization of the classical (fuzzy) group are illustrated in detail.
DOI Link
ISSN
Volume
17
Issue
4
First Page
2898
Last Page
2914
Disciplines
Mathematics
Keywords
bipolar valued fuzzy binary operation, bipolar valued fuzzy function, bipolar valued fuzzy group subgroup, bipolar valued fuzzy space, fuzzy binary operation, fuzzy function, fuzzy group, Fuzzy space
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Recommended Citation
Al-Zu’bi, Fadi; Ahmad, Abdul Ghaffur; Alkouri, Abd Ulazeez; and Darus, Maslina, "A Novel Bipolar Valued Fuzzy Group based on Dib’s approach" (2024). All Works. 6910.
https://zuscholars.zu.ac.ae/works/6910
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Gold: This publication is openly available in an open access journal/series