Multi-Criteria Group Decision-Making in Circular Intuitionistic Fuzzy Environment via a Geometric Linguistic Transformation Mechanism

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Abstract
Circular Intuitionistic Fuzzy Sets (C-IFSs) provide a robust geometric framework for capturing uncertainty in Multi-Criteria Group Decision-Making (MCGDM). Nevertheless, current approaches often suffer from information loss during the linguistic term transformation and lack effective mechanisms to handle outlier opinions in the consensus process.To overcome these limitations, this paper proposes a novel consensus-driven MCGDM framework based on geometrically interpretable mappings.First, distinct from rigid static tables, we construct a parametric transformation mechanism using geometric curves within the Intuitionistic Fuzzy Interpretation Triangle (IFIT). This approach flexibly encodes experts' risk attitudes while maintaining monotonic semantic consistency.Second, we redefine the radius of C-IFVs as a consensus measure to develop a dynamic outlier detection algorithm. By iteratively filtering extreme deviations, this method prevents the erroneous expansion of uncertainty regions and ensures the aggregation result reflects the true majority preference. Third, an improved defuzzification function is introduced to align with the proposed aggregation logic, enhancing the distinguishability of ranking results.Finally, a supplier selection case study validates that our framework significantly improves decision stability and effectively preserves semantic integrity in complex environments.

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