A Novel Intuitionistic Fuzzy Set for Decision‐Making

Abstract

Intuitionistic fuzzy sets have been extensively employed to manage uncertainty in expert systems and decision‐making domains. Recently, to address more sophisticated real‐world problems involving multidimensional uncertainty, several theoretical frameworks have been extended into the complex domain. However, existing complex intuitionistic fuzzy sets (CIFSs) model the magnitude and phase as independent components, reducing them to isolated dimensions rather than a unified entity. This separation disrupts the coupled magnitude‐phase relationship, limiting the model's ability to capture the unique interference phenomena and rich uncertainty characterizations. Therefore, we propose a novel CIFS framework grounded in the intrinsic algebraic structure of complex numbers. The proposed framework integrates magnitude and phase into a unified representation, ensuring consistency with the fundamental rules of complex arithmetic. To support this framework, we define several fundamental CIFS operations directly based on complex arithmetic. Furthermore, to address conflicting evaluations from diverse sources, we introduce a new aggregation operator capable of integrating multiple CIFSs while mitigating conflicts in expert decision‐making and develop a corresponding intelligent decision‐making algorithm. The effectiveness and robustness of the proposed algorithm are validated through medical diagnosis and software selection, demonstrating its practical utility in expert systems.