A New Decision-Making Approach Using Bipolar Interval-Valued Fuzzy Soft Matrices (European Journal of Pure and Applied Mathematics, 2025)
Based on what the fuzzy set theory has earned a lot of significant interest from researchers and has led to several important extensions. The bipolar fuzzy sets (BFSs) have gained a lot of applications in different fields. The BFS includes extensions such as interval bipolar fuzzy sets, which are BFS but in an interval form. In this article, we introduce a new hypermodel called bipolar interval fuzzy soft sets (BIVFSSs) in matrix form when we extend the bipolar fuzzy soft matrix to effectively and flexibly represent and manipulate uncertain information with increased flexibility. The matrix form gives BIVFSSs more freedom and accuracy in handling data and performing more algebraic operations. Therefore, the present study coined the notion of determinant on a bipolar interval-valued fuzzy soft matrix (BIVFSM) and its properties. Then we presented all the mathematical properties of this form, supported by numerical examples and representations, to explain the mechanism of operation of these tools accurately. Finally, these tools have been applied to solve a multi-attribute decision-making problem by proposing a multi-step algorithm.
Keywords: fuzzy matrices, interval fuzzy matrices, soft set, decision-making, bipolar fuzzy soft matrices