Interval Valued Intuitionistic Fuzzy Set Theoretic Approach for Decision Making Problem using a New Score Function

The interval valued intuitionistic fuzzy set (IVIFS) serves as a powerful and effective framework for representing the genuine preferences of decision makers (DMs) and managing imprecise information. The objective of this study is twofold. First, a novel score function is developed to defuzzify interval valued intuitionistic fuzzy numbers (IVIFNs), and its fundamental properties are examined. Second, two methods are proposed to address multiple attribute decision making (MADM) problems based on the IVIFS framework, where the performance ratings of alternatives with respect to various attributes are expressed in terms of IVIFNs. The proposed methods assign different degrees of importance to each attribute and incorporate a demand function that reflects the satisfaction requirements of the DM. Using this demand function, the DM can determine the most suitable alternative or establish a ranking among the available alternatives. Finally, three test-based validity criteria and a numerical example are presented to demonstrate the rationality and effectiveness of the proposed methods.