A New Similarity Measure for Picture Fuzzy Sets and Its Various Applications

Similarity measures offer a useful way to assess how similar two collections of things are to one another. They are also useful tools for handling cognitively inspired decision-making problems. Compared to intuitionistic fuzzy sets, the picture fuzzy set theory offers advantages for representing ambiguous and uncertain concepts in practical contexts. This is because picture fuzzy sets take into account the degree of neutrality of a factor that is crucial in many different decision-making scenarios, such as human voting, personnel selection, and medical diagnosis. The similarity measurements are crucial when comparing two picture fuzzy sets. Numerous studies on picture fuzzy sets' similarity measurements are available in the literature. All these similarity measures, however, produce irrational outcomes in the majority of the issues such as satisfying the axiomatic requirements, computation of similarity between different picture fuzzy sets, and classifying an unknown pattern into one of the known patterns. Therefore, we propose a novel similarity measure based on the inverse tangent function for picture fuzzy sets in this study that is more efficient than all existing similarity measures. We also demonstrate its utility in classification and medical diagnostic problems and contrast its performance with the available ones. At last, we suggest a new decision-making technique in a picture fuzzy setting that is more robust than the technique for order preference by similarity to the ideal solution.