Bipolar Fuzzy Algebraic Structures: Theory, Isomorphisms, and Decision-Making Applications

Authors

  • Om Alkhear Salem Blebalu Department of mathematics, Faculty of science, University of zawia, Alajelat, Libya

Keywords:

Bipolar fuzzy set, Abstract algebra, Bipolar fuzzy group, Bipolar fuzzy semiring, Dombi aggregation operator, multi-criteria decision making (MCDM), Fuzzy homomorphism, Isomorphism theorems, Fuzzy Decision Matrix

Abstract

This research presents a comprehensive study of bipolar fuzzy algebraic structures, an emerging field at the intersection of classical abstract algebra and bipolar fuzzy set theory. Unlike traditional fuzzy sets operating in [0,1], bipolar fuzzy sets operate in [-1,1], capturing both positive membership (satisfaction degree) and negative membership (satisfaction degree of the counter-property). This research develops a unified framework for bipolar fuzzy groups and bipolar fuzzy semirings, establishes fundamental isomorphism theorems, introduces novel aggregation operators based on Dombi operations, and presents practical applications in multi-criteria decision-making (MCDM). All results are aligned with the latest developments published in 2024-2025.

Downloads

Published

2026-04-04

How to Cite

Om Alkhear Salem Blebalu. (2026). Bipolar Fuzzy Algebraic Structures: Theory, Isomorphisms, and Decision-Making Applications. North African Journal of Scientific Publishing (NAJSP), 4(2), 39–44. Retrieved from https://najsp.com/index.php/home/article/view/817

Issue

Volume 4, Issue 2, 2026

Section

Applied and Natural Sciences

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.