A Novel Interval-Valued Intuitionistic Fuzzy Distance Measure Incorporating Min/Max Interaction Terms

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely employed in decision-making and pattern recognition, where distance measures serve as fundamental tools. However, many existing distance measures for IVIFSs have two limitations: one is the low discriminant ability, which usually produces the same value for different pairs; the second is the violation of the axiom of regularity, and the distance value is not within [0,1]. To overcome these shortcomings, this paper proposes a new distance measure, which integrates a non-linear transformation of endpoint differences with min/max interaction terms. In addition, it is proved that the proposed measure satisfies all four axioms of distance. Finally, comparative experiments show the effectiveness and superiority of the proposed measure. The results establish the proposed measure as a more discriminative and axiomatically sound tool for IVIFS-based analysis.