A fuzzy nonlinear univariate regression model with exact predictors and fuzzy responses

Abstract

In this paper, a fuzzy nonlinear univariate regression model with nonfuzzy predictors and fuzzy responses is proposed. For this purpose, both nonlinear parametric and nonparametric methods were utilized. The left and right spreads of unknown fuzzy smooth function were estimated via a popular kernel-based curve-fitting method, while the center was estimated using both parametric and nonparametric curve-fitting methods. In fact, two techniques were suggested and compared in terms of estimating the center of fuzzy smooth function: (1) nonparametric method (similar to the left and right spreads) and (2) parametric method adopted with a common nonlinear regression model called truncated spline regression. Each stage was separately estimated the unknown components were addressed via the conventional statistical regression methods. The proposed method managed to provide a simple and fast estimation/prediction approach for the fuzzy univariate regression analysis for any types of LR-fuzzy numbers. Some common goodness-of-fit criteria were also employed to evaluate the performance of the proposed method. The effectiveness of the developed method was further illustrated through three numerical examples including a simulation study based on a common kernel. The proposed method was also compared with several common fuzzy linear/nonlinear regression models. The numerical evaluations indicated that the proposed parametric method for centers exhibited more accurate results as compared with the nonparametric method.