Novel similarity measures between picture fuzzy sets and their applications to pattern recognition and medical diagnosis

Similarity measures provide an efficient tool to analyze the degree of closeness between two sets of objects. The picture fuzzy set theory has advantages over intuitionistic fuzzy sets to represent uncertain and vague concepts in real-life situations. This paper proposes some novel similarity measures between two picture fuzzy sets (PFSs). First, the paper defines two new distance measures (DMs) based on Chi-square and Canberra DMs under the picture fuzzy environment. Using the relationship between distance and similarity measures, we introduce Chi-square picture fuzzy similarity and Canberra picture fuzzy similarity measures between PFSs. Further, the work proposes the weighted version of the developed picture fuzzy similarity measures (PFSMs) and demonstrates several properties associated with them. We also extend the proposed PFSMs from the discrete domain to a continuous domain. Then, the paper develops applications of the proposed PFSMs in pattern recognition and medical diagnosis problems. Several numerical examples are considered to illustrate the performance of the developed measures in real-life situations. A comparative study with existing PFSMs is also included, showing that our proposed measures performance is better than previous ones.