On Similarity Measures of Complex Picture Fuzzy Sets With Applications in the Field of Pattern Recognition

Despite the significant advancements in fuzzy set theory, existing similarity measures for complex picture fuzzy sets (CPFSs) often result in impractical results in real-world scenarios. This presents a critical gap in accurately modeling and analyzing CPFSs, particularly in applications like pattern recognition and medical diagnosis. The present work addresses this problem by introducing various novel similarity measures for CPFSs, accompanied by rigorous axiomatic validation and a thorough discussion of their properties. Different sets of CPFSs have been empirically evaluated using both existing and proposed similarity measures, demonstrating the practical applicability and superiority of the latter. Based on the principle of maximum similarity, a comprehensive methodology involving these proposed measures has been illustrated, along with their implementation in solving different problems in pattern recognition and medical diagnosis. Additionally, a comparative analysis has been conducted to provide better clarity and understanding of the effectiveness of these measures. The results indicate that the proposed similarity measures offer significant advantages and improved accuracy for pattern recognition and medical diagnosis problems.