In order to distinguish with effect different hesitant fuzzy elements (HFEs), we introduce the asymmetrical relative entropy between HFEs as a 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 the concept of cocorrelation degree from the viewpoint of probability theory and develop another new formula of hesitant fuzzy correlation coefficient, and prove their similar properties to the traditional correlation coefficient. To make full use of the existing similarity measures including the ones presented by us, we consider aggregation of similarity measures for hesitant fuzzy sets and derive the synthetical similarity formula. Finally, the derived formula is used for netting clustering analysis under hesitant fuzzy information and the effectiveness and superiority are verified through a comparison analysis of clustering results obtained by other clustering algorithms.
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