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

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.