A Novel Bipolar Valued Fuzzy Group based on Dib's approach

Authors

  • Fadi Al-Zu’bi Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
  • Abdul Ghaffur Ahmad Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia.
  • Abd Ulazeez Alkouri Department of Mathematics, Faculty of Science, Ajloun National University, P.O. 43, Ajloun- 26810, Jordan.
  • Maslina Darus Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5473

Keywords:

Fuzzy space, bipolar valued fuzzy space, fuzzy binary operation, bipolar valued fuzzy binary operation, fuzzy function, bipolar valued fuzzy function, fuzzy group and bipolar valued fuzzy group subgroup.

Abstract

The numerous extensions of fuzzy groups (FG) and fuzzy subgroups are a complicated issue. Several results depending on different approaches of FG theory were introduced. In this research, we introduce a novel extension created to represent the bipolar valued fuzzy groups (BVF-groups) based on bipolar valued fuzzy space (BVF-space), which replaces the universal set in conventional set theory. The BVF-space generalizes the notion of fuzzy space (F-space) from to  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 the way 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.

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Published

2024-10-31

Issue

Vol. 17 No. 4: (October 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 Fadi Al-Zu’bi, Abdul Ghaffur Ahmad, Abd Ulazeez Alkouri, Maslina Darus

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How to Cite

A Novel Bipolar Valued Fuzzy Group based on Dib’s approach. (2024). European Journal of Pure and Applied Mathematics, 17(4), 2898-2914. https://doi.org/10.29020/nybg.ejpam.v17i4.5473