A partial-robust-ridge-based regression model with fuzzy predictors-responses

Abstract

This paper extends the conventional semi-parametric partial linear regression model with fuzzy predictors and fuzzy response in cases where 1—outliers occur in data set, 2—multicollinearity exists in predictors. For this purpose, the classical kernel fitting method is first extended for estimating unknown fuzzy smooth function. Then, inspired by the conventional local linear smoothing method, a kernel-based weighted criterion is suggested for determining the exact coefficients on the basis of ridge methodology. Some common goodness-of-fit criteria are also used to examine the performance of the proposed method. The effectiveness of the proposed method is then illustrated through two numerical examples including a simulation study. The proposed method is also compared with some common fuzzy multiple regression models with fuzzy predictors and fuzzy responses. The numerical results clearly indicate that 1—the proposed method is not sensitive to the outliers, 2—the proposed method provides sufficiently accurate results in cases where multicollinearity happens among predictors and 3—comparing to existing fuzzy multiple regressions, the proposed model provides more efficient predictions. • A fuzzy semi-parametric regression model is proposed when multicollinearity and/or outliers occur. • The fuzzy model contains the fuzzy predictors-responses. • The ridge methodology and a novel robust method are applied to evaluate crisp coefficients. • The method is compared with several methods using various goodness-of-fit-measures.