New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering

A similarity measure is a useful tool for determining the similarity between two objects. Although there are many different similarity measures among the intuitionistic fuzzy sets (IFSs) proposed in the literature, the Jaccard index has yet to be considered as way to define them. The Jaccard index is a statistic used for comparing the similarity and diversity of sample sets. In this study, we propose a new similarity measure for IFSs induced by the Jaccard index. According to our results, proposed similarity measures between IFSs based on the Jaccard index present better properties. Several examples are used to compare the proposed approach with several existing methods. Numerical results show that the proposed measures are more reasonable than these existing measures. On the other hand, measuring the similarity between IFSs is also important in clustering. Thus, we also propose a clustering procedure by combining the proposed similarity measure with a robust clustering method for analyzing IFS data sets. We also compare the proposed clustering procedure with two clustering methods for IFS data sets.