A novel parameter similarity measure between interval-valued picture fuzzy sets with its app-lication in pattern recognition.

The article focuses on developing a novel similarity measure for interval-valued picture fuzzy sets (IVPFSs) to better handle incomplete, indeterminate, and inconsistent information in pattern recognition and medical diagnosis. IVPFSs extend picture fuzzy sets by representing membership degrees as intervals, capturing uncertainty more effectively. The proposed similarity measure transforms interval-valued picture fuzzy numbers into right-angled triangular pyramids in a spatial coordinate system and calculates distances based on their centers of gravity, incorporating a parameter to adjust the effect of refusal membership degree margins. Comparative analyses demonstrate that this new measure overcomes limitations of existing methods—such as division-by-zero issues, failure to satisfy similarity axioms, and counterintuitive results—and performs well in practical applications including mineral field classification and medical diagnosis. The study concludes that the proposed similarity measure provides more reasonable, reliable, and discriminative results in IVPFS environments, suggesting its potential for broader applications in uncertain information processing.