Fuzzy Lasso regression model with exact explanatory variables and fuzzy responses

Abstract

Fuzzy multivariate regression analysis is aimed to model the relationship between a set of fuzzy responses and a set of non-fuzzy or fuzzy explanatory variables. This paper extended the Lasso method for multiple linear regression model possessing non-fuzzy explanatory variables and fuzzy responses. The fuzzy Lasso method is able to increase the interpretability of the model by eliminating the variables irrelevant to the fuzzy response variables. For this purpose, a fuzzy penalized method was introduced to estimate unknown fuzzy regression coefficients and tuning constant. Some common goodness-of-fit criteria were also employed to examine the performance of the proposed method. The effectiveness of the proposed method was also assessed through two applied examples and a simulation study. Moreover, the proposed method was compared with several common fuzzy multiple regression models. The numerical results clearly showed higher accuracy of the proposed fuzzy Lasso method compared to the other existing fuzzy multiple regression models in determination of the noninformative explanatory variables. Thus, the proposed fuzzy Lasso regression model can be successfully applied to improve the prediction accuracy and interpretability of the fuzzy multiple regression models for real life applications in expert systems.