A Novel Picture Fuzzy Similarity Measure: Theory and Practical Applications

Similarity metrics serve as valuable tools for evaluating the resemblance between two datasets. While intuitionistic fuzzy sets have been widely used, picture fuzzy sets present enhanced capabilities in capturing ambiguity and uncertainty within real-world applications. The role of similarity measures becomes pivotal when analyzing such sets, yet existing methodologies, despite extensive research, frequently generate illogical outcomes in various scenarios. Addressing this gap, our study introduces an advanced similarity measure tailored for picture fuzzy sets, demonstrating superior efficacy and reliability compared to conventional approaches. Through comprehensive benchmarking against established metrics, we validate its effectiveness in both classification tasks and diagnostic analyses. Furthermore, we propose a robust decision-making framework within the picture fuzzy domain, designed to surpass the limitations of the traditional TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method, offering improved accuracy in complex decision environments.