Elastic Net Oriented to Fuzzy Semiparametric Regression Model With Fuzzy Explanatory Variables and Fuzzy Responses

In the multivariate linear regression model, it is desirable to include the important explanatory variables to achieve maximal prediction. In this context, the present paper is an attempt to extend the conventional elastic net multiple linear regression model adopted with a semiparametric method to fuzzy predictors and responses. For this purpose, kernel smoothing and elastic net penalized methods were combined to construct a novel variable-selection method in a fuzzy multiple regression model. Some common goodness-of-fit criteria were also included to examine the performance of the proposed method. The effectiveness of the proposed method was illustrated through three numerical examples including a simulation study and two practical cases. The proposed method was also compared with several common fuzzy multiple regression models. The numerical results clearly indicated that the proposed method is capable of providing sufficiently accurate results in cases where noninformative explanatory variables are removed from the model.