Fuzzy N-Bipolar Soft Sets for Multi-Criteria Decision-Making: Theory and Application

Sagvan Y. Musa^1,2, Baravan A. Asaad^3,4,*, Hanan Alohali⁵, Zanyar A. Ameen⁶, Mesfer H. Alqahtani⁷
1 Department of Mathematics, College of Education, University of Zakho, Zakho, 42002, Iraq
2 Department of Computer Science, College of Science, Knowledge University, Erbil, 44001, Iraq
3 Department of Mathematics, College of Science, University of Zakho, Zakho, 42002, Iraq
4 Department of Computer Science, College of Science, Cihan University-Duhok, Duhok, 42001, Iraq
5 Department of Mathematics, College of Science, King Saud University, Riyadh, 11451, Saudi Arabia
6 Department of Mathematics, College of Science, University of Duhok, Duhok, 42001, Iraq
7 Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk, 48322, Saudi Arabia
* Corresponding Author: Baravan A. Asaad. Email: email
(This article belongs to the Special Issue: Algorithms, Models, and Applications of Fuzzy Optimization and Decision Making)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2025.062524

Received 20 December 2024; Accepted 28 February 2025; Published online 02 April 2025

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Abstract

This paper introduces fuzzy N-bipolar soft (FN-BS) sets, a novel mathematical framework designed to enhance multi-criteria decision-making (MCDM) processes under uncertainty. The study addresses a significant limitation in existing models by unifying fuzzy logic, the consideration of bipolarity, and the ability to evaluate attributes on a multinary scale. The specific contributions of the FN-BS framework include: (1) a formal definition and set-theoretic foundation, (2) the development of two innovative algorithms for solving decision-making (DM) problems, and (3) a comparative analysis demonstrating its superiority over established models. The proposed framework is applied to a real-world case study on selecting vaccination programs across multiple countries, showcasing consistent DM outcomes and exceptional adaptability to complex and uncertain scenarios. These results position FN-BS sets as a versatile and powerful tool for addressing dynamic DM challenges.