关键词: 犹豫模糊集, 交叉熵, 离差最大化, 协相关度, 聚类分析

Abstract: For the multi-attribute clustering problem that decision information is hesitant fuzzy set (HFS) and the attribute weights are completely unknown, this paper proposes a co-correlation degree based on hesitant fuzzy cross-entropy and clustering method. In order to distinguish different HFSs, this paper defines the cross-entropy between two hesitant fuzzy elements (HFEs), and verifies the validity and rationality in comparison with the results obtained by other distance formulas. Next, this paper derives the formula of attribute weights according to the maximizing deviation algorithm from the hesitant fuzzy cross-entropy. Then, this paper proposes the concept of co-correlation degree, proves its similar properties with the traditional correlation coefficient, and considers different attributes' weight at the same time, which is determined by the formula of attribute weights. Finally, this paper uses the weighted formula of co-correlation degree for clustering analysis under hesitant fuzzy information, and verifies the feasibility and effectiveness through the comparison analysis of clustering results of diverse literature.

Key words: hesitant fuzzy set, cross-entropy, maximizing deviation, co-correlation degree, clustering analysis