Prediction of Fuzzy Nonparametric Regression Function: A Comparative Study of a New Hybrid Method and Smoothing Methods

Abstract

In this paper, the fuzzy regression model is considered with crisp inputs and symmetric triangular fuzzy output. This study aims to formulate the fuzzy inference system based on the Sugeno inference model for the fuzzy regression function prediction by the fuzzy least-squares problem-based on Diamond's distance. In this study, the fuzzy least-squares problem is used to optimize consequent parameters, and the results are derived based on the V-fold cross-validation, so that the validity and quality of the proposed method can be guaranteed. The proposed method is used to reduce the bias and the boundary effect of the estimated underlying regression function. Also, a comparative study of the fuzzy nonparametric regression function prediction is carried out between the proposed model and smoothing methods, such as k-nearest neighbor (k-NN), kernel smoothing (KS), and local linear smoothing (LLS). Different approaches are illustrated by some examples and the results are compared. Comparing the results indicates that, among the various prediction models, the proposed model is the best, decreasing the boundary effect significantly. Also, in comparison with different methods, in both one-dimensional and two-dimensional inputs, it may be considered the best candidate for the prediction.