Application of a Novel Interval-Valued Intuitionistic Fuzzy Correlation Coefficient to the Supplier Selection Problem

The connection between two or more factors plays a key role in many choices in industry where data often lacks clarity or completeness. Classical correlation coefficients, however, fail to fully capture a complete measure of the delicate balance between membership and non-membership information in fuzzy data. Existing interval-valued intuitionistic fuzzy measures also show inconsistency in handling negative relationships, complementary patterns, and structured linguistic variability, and thus underscore the need for a more generalized and reliable correlation framework to manage uncertainty effectively. In this paper, we propose a generalized correlation coefficient specifically formulated for interval-valued intuitionistic fuzzy data. It uniquely represents uncertainty through interval-based membership and non-membership degrees. The proposed coefficient gives a better picture of unclear relationships. The performance of the coefficient is illustrated through numerical examples and through its application in a multicriteria group decision-making problem focused on supplier selection. A detailed comparative study with existing methods is conducted to highlight the superiority of the proposed approach in terms of robustness and reliability. A sensitivity analysis is also performed to examine the impact of an adjustable parameter in the proposed measure. It reveals that the proposed measure remains consistent and produces dependable results even under varying decision conditions.