Optimization of Market Risk via Maclaurin Symmetric Mean Aggregation Operators: An Application of Interval-Valued Intuitionistic Fuzzy Sets in Multi-Attribute Group Decision-Making

New aggregation operators (AOs) for interval-valued intuitionistic fuzzy sets (IVIFS) have been developed, offering advancements in multi-attribute group decision-making (MAGDM). IVIFS employs intervals for membership and non-membership grades, providing a robust framework to handle uncertainties inherent in real-world scenarios. This study introduces operational laws for interval-valued intuitionistic fuzzy values (IVIFVs), formulated on the Frank T-norm and T-conorm, and presents a generalization of the Maclaurin symmetric mean (MSM) operator tailored for these values. Named the interval-valued intuitionistic fuzzy Frank weighted MSM (IVIFFWMSM) and interval-valued intuitionistic fuzzy Frank MSM (IVIFFMSM), these operators incorporate new operational principles that enhance the aggregation process. The effectiveness of these operators is demonstrated through their application to a MAGDM problem, where they are compared with existing operators. This approach not only enriches the theoretical landscape of fuzzy decision-making models but also provides practical insights into the optimization of market risk.