Proposing a method for regression based on feature extraction and hesitant fuzzy sets

In this paper, an effective method for regression is presented in which a variety of fuzzy clustering methods and concepts of Hesitant fuzzy sets are used. First, the fuzzy clustering algorithm is applied to the data, and after projecting the cluster membership function on different features, the number of clusters of fuzzy sets is obtained on each dimension (or feature). We then consider these fuzzy sets as a hesitant fuzzy set on each feature, and we obtain the Hesitant Fuzzy Correlation Coefficient Matrix (HFCCM) for the attributes. Subsequently, a nonlinear mapping based on the principal components analysis of the HFCCM is used to convert the dataset's features into new features. Finally, the new extracted features are assigned to the fuzzy clustering algorithm and a Sugeno fuzzy regression system is fitted. The proposed method was compared with some other methods to several regression datasets. The results of the experiments indicate that the proposed method is successful in extracting and reducing the characteristics, as well as increasing the regression accuracy. Also, the number of rules of the fuzzy regression model in the proposed method is fairly low.