Multi-Q Cubic Bipolar Fuzzy Soft Sets and Cosine Similarity Methods for Multi-Criteria Decision Making

This study introduces a novel mathematical tool for representing imprecise and ambiguous data: the multi-q cubic bipolar fuzzy soft set. Building upon established bipolar fuzzy sets and soft sets, this paper fist defines the concept of multi-q cubic bipolar fuzzy sets and their fundamental properties. Mathematical operations such as complement, union, and intersection are then developed for these sets. The core contribution lies in the introduction of multi-q cubic bipolar fuzzy soft sets. This new tool allows for a more nuanced representation of imprecise data compared to existing approaches. Key operations for manipulating these sets, including complement, restriction, and expansion, are defined. The applicability of multi-q cubic bipolar fuzzy soft sets extends to various domains, including multi-criteria decision making and problem solving. Illustrative examples demonstrate the practical utility of this innovative concept.