Combining similarity and divergence measures for intuitionistic fuzzy information clustering

Abstract

In the study of intuitionistic fuzzy clustering, the construction of an intuitionistic fuzzy similarity matrix (IFSM) is a fundamental and important issue in the direct clustering analysis, since it determines clustering results and computational efforts. Many methods based on the axioms of intuitionistic fuzzy similarity relations are applicable to IFSM construction. However, most of existing methods may yield a “counterintuitive result” in some cases and consume much computational time. In this paper, we propose a novel intuitionistic fuzzy clustering method to deal with such problems. First, based on the normalized Hamming distance, we define a similarity measure between intuitionistic fuzzy numbers (IFNs), by which a similarity measure between intuitionistic fuzzy sets (IFSs) is induced. Second, a divergence measure between IFSs is obtained by extending the dissimilarity of IFNs. Third, we construct an IFSM by using together the similarity and divergence measures so as to cluster the intuitionistic fuzzy information. Finally, two examples are presented to show the effectiveness and advantages of our method.