A Closeness‐Driven Decision Evaluation Framework With Radius‐Augmented Divergence in Circular Intuitionistic Fuzzy Contexts

Divergence measures constitute a fundamental mechanism for quantifying informational discrepancies in uncertainty‐aware decision analytics. Nevertheless, divergence‐based approaches have only recently been explored to circular intuitionistic fuzzy (CIF) environments, and existing studies remain largely confined to specific divergence formulations and decision models. In particular, Tsallis‐type divergence has not been systematically developed to jointly characterize CIF evaluation centers and uncertainty dispersion. In response to this research gap, a closeness‐driven decision evaluation framework is established based on a novel radius‐augmented CIF–Tsallis divergence. The proposed divergence integrates an ε ‐regularized center‐based Tsallis divergence with a radius‐aware discrepancy component, enabling simultaneous modeling of central disagreement and uncertainty dispersion. The resulting formulation is analytically shown to be well defined, finite, and continuous, ensuring theoretical consistency and numerical stability. Building upon this divergence, a CIF–Tsallis closeness indexing procedure is developed by combining divergence‐based proximity with both optimistic and pessimistic CIF reference profiles. The proposed framework transforms CIF evaluations into interpretable closeness indices for alternative ranking while improving discrimination capability through explicit consideration of uncertainty dispersion. An industrial case study on Generative Artificial Intelligence and cloud service provider selection validates the effectiveness of the developed framework in practical settings. The results, supported by extensive sensitivity analyses and comparative evaluations with representative CIF divergence–based decision frameworks, indicate that the proposed framework produces stable and interpretable ranking outcomes and provides an effective decision‐support tool for complex group decision‐making under uncertainty.