In order to distinguish with effect different intuitionistic fuzzy sets (IFSs), we generalize the asymmetrical relative entropy between IFSs as distance measure for higher discernment. Next, the formula of attribute weights is derived via an optimal model according to TOPSIS from the relative closeness degree constructed by the discerning relative entropy. Then, we propose a similarity formula with strong discernibility and two co-correlation degree formulas from the viewpoint of probability theory and prove their similar traits to the traditional correlation coefficient. To make full use of the three similarity measures presented in this paper, we consider aggregating those similarity measures and derive the synthetical similarity formula. Finally, the derived formula is used for clustering analysis under intuitionistic fuzzy (IF) information and the effectiveness and superiority are verified through a detailed comparison analysis of clustering results obtained by other clustering algorithms.
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