Improved ordering and aggregation operators for circular intuitionistic fuzzy sets in multi-criteria decision-making

The Circular Intuitionistic Fuzzy Set (CIFS) is an extension of the Intuitionistic Fuzzy Set (IFS), developed to represent information with distributed uncertainty through a circular uncertainty region. Each CIFS element is defined by a centre, representing membership ($$\mathcal {M}$$) and non-membership ($$\mathcal {N}$$) degrees, and a radius r, indicating the maximum dispersion. While recent studies have proposed aggregation operators and score and accuracy functions for CIFS, inconsistencies remain, particularly regarding the interpretation of radius, where smaller values should be preferred. This paper addresses these issues by first categorizing dispersion in CIFS as either homogeneous or heterogeneous, thereby aligning the score and accuracy functions with the radius condition. New functions are then introduced for consistent ordering of CIF values. Additionally, novel aggregation operators: CIF Weighted Averaging (CIFWA), CIF Ordered Weighted Averaging (CIFOWA), and CIF Hybrid Weighted Averaging (CIFHWA) are proposed and analysed using algebraic sums and products. An algorithm is also developed for solving Multi-Criteria Decision-Making (MCDM) problems within the CIFS framework, supported by simulations and comparative analyses with existing IFS and CIFS-based methods.