Optimizing Decision-Making with Aggregation Operators for Generalized Intuitionistic Fuzzy Sets and Their Applications in the Tech Industry

Abstract Intuitionistic fuzzy sets (IFSs) extend the principles of fuzzy set (FS) theory by incorporating dual-degree attributes, encompassing both membership and non-membership degrees constrained within unity. IFSs find versatile applications across various domains, effectively addressing complex decision-making challenges. This study advances IFS theory to Generalized Intuitionistic Fuzzy Sets (GIFSBs) and introduces novel operators GIFWAA, GIFWGA, GIFOWAA, and GIFOWGA, tailored for GIFSBs. The primary aim is to enhance decision-making capabilities by introducing aggregation operators within the GIFSB framework that align with preferences for optimal outcomes. The article introduces new operators for GIFSBs characterized by attributes like Idempotency, Boundedness, Monotonicity and Commutativity, resulting in aggregated values aligned with GIFNs. A comprehensive analysis of the relationships among these operations is conducted, offering a thorough understanding of their applicability. These operators are practically demonstrated in a multiple-criteria decision-making process for evaluating startup success in the Tech Industry, broadening their utility for decision-makers, and aligning with existing ranking formulas for IFSs and Pythagorean fuzzy sets under specific conditions.