Novel distance measures on complex picture fuzzy environment: applications in pattern recognition, medical diagnosis and clustering

Complex picture fuzzy sets (CPFSs) advance the fuzzy logic field, extending picture fuzzy sets (PFSs) and complex intuitionistic fuzzy sets (CIFSs) to model uncertain and ambiguous information more robustly. Distance and similarity measures are essential tools in fuzzy sets and their variants. Up to now, however, there is a significant gap and few studies on the distance measures of CPFSs. Thus, this work aims to introduce a series of new distance measures for CPFSs, drawing inspiration from Hellinger distance. All the proposed distance measures are validated, and their properties, including boundedness, non-degeneracy, symmetry and triangle inequality, are demonstrated. Moreover, the proposed measures exhibit superior performance compared to existing measures, as confirmed through numerical comparisons. Lastly, the proposed distance measures are applied in pattern recognition, medical diagnosis, and clustering, demonstrating that these measures possess a high level of confidence and can produce trustworthy and sensible results, particularly in comparable situations.