Correlation coefficient of hesitant fuzzy sets

In this paper, we propose a variety of correlation coefficient measures for hesitant fuzzy sets (HFSs) and investigate their properties. Then, we define the concepts of correlation relation matrix, composition matrix and equivalent correlation relation matrix in the frame of HFSs. Furthermore, we propose a clustering method for HFSs. The method utilizes the correlation coefficient of HFSs to construct a correlation relation matrix, and utilizes an algorithm to transform it into an equivalent correlation relation matrix. The τ-cutting matrix of the equivalent correlation relation matrix is utilized to cluster the given HFSs. Finally, we utilize some pattern recognition numerical examples to validate a variety of correlation coefficient measures and the clustering method proposed in this paper.