A fuzzy penalized regression model with variable selection

In the classical multiple regression modeling, there might be some insignificant input variables. These variables can be eliminated by automatic selectors, known as penalized methods. We propose a penalized estimation method for the coefficients of a linear regression model for studying the dependence of a LR fuzzy response (output) variable on a set of crisp explanatory (input) variables. To show the performances of the proposed model a simulation study was utilized under three scenarios of multicollinear and sparse data. The model demonstrates better performances in comparison to another three models on the basis of specified goodness of fit measures, under three variants of the penalty function. Evaluation of the method has been conducted on real data. The results demonstrate superior performances in terms of the goodness of fit measures in comparison to the other models. To take into account the imprecision due to the lack of knowledge about the data generation process, in the applications to real data bootstrap-t confidence intervals were also utilized.