On the design of similarity measures based on fuzzy integral

Similarity measure for fuzzy sets is designed with the help of a conventional fuzzy measure and integral. Similarity measure based on fuzzy integral not only evaluates similarity but also captures the characteristics occurring between various data sets. Compared to a conventional approach based on a distance measure, the proposed similarity measure based on fuzzy integral delivers additional information that convergence in similarity value provides data comparison structure between data sets. The properties of the proposed similarity measure are analyzed and demonstrated with illustrative examples. The degree of each data set and its distribution plays a crucial role in discriminating data characteristics. The designed similarity measure shows its convergence. Comparison with random data is carried out, and its similarity value and convergence properties are analyzed with the use of the similarity measure.