Circular intuitionistic fuzzy Hamacher aggregation operators for multi-attribute decision-making

Decision-making in uncertain and imprecise environments often requires robust mathematical frameworks capable of effectively representing and aggregating conflicting information. Circular Intuitionistic Fuzzy Sets (C-IFSs) are powerful tools for modeling such complexities by combining intuitionistic and cubic fuzzy set properties. In this study, we extend the applicability of C-IFSs by integrating them with the Hamacher operational framework, offering a more flexible and adaptive approach to aggregation. To this end, we propose six novel aggregation operators: Circular Intuitionistic Fuzzy Hamacher Weighted Average (CIFHWA), Circular Intuitionistic Fuzzy Hamacher Ordered Weighted Average (CIFHOWA), Circular Intuitionistic Fuzzy Hamacher Hybrid Weighted Average (CIFHHWA), Circular Intuitionistic Fuzzy Hamacher Weighted Geometric (CIFHWG), Circular Intuitionistic Fuzzy Hamacher Ordered Weighted Geometric (CIFHOWG), and Circular Intuitionistic Fuzzy Hamacher Hybrid Weighted Geometric (CIFHHWG). These operators are designed to address multi-criteria decision-making challenges with improved precision. We further develop score and accuracy functions to rank C-IFSs and propose a neural-based scheme employing cubic correlation coefficients to enhance computational efficiency. A detailed numerical example validates the framework's effectiveness, illustrating its practical utility. Additionally, comparative analyses with existing techniques and sensitivity and robustness examinations demonstrate its superiority in handling complex decision-making scenarios. The findings underscore the advantages of using Hamacher-based operations with C-IFSs, offering a novel contribution to fuzzy decision-making and opening avenues for future research in uncertain data analysis.