FUZZY NONPARAMETRIC REGRESSION BASED ON K-NEAREST NEIGHBORS AND THE R-NEIGHBORHOOD RADIUS

Abstract

In this paper, we present four nonparametric methods to fit some fuzzy regression models, when both the explanatory and response variables are fuzzy quantities. In this approach, we first introduced a distance between triangular fuzzy numbers. Then, two fuzzy nonparametric regression models are presented based on the extended version of K-nearest neighbors (KNN) method on fuzzy data (with the same/modified weights). In addition, a new method is investigated to fit two fuzzy non-parametric regression models based on the R-neighborhood radius (RNR) method on fuzzy data (with the same/modified weights). Among these methods, the two methods of KNN and RNR with the modified weights have the better performances than the methods with the same weights. To evaluate the proposed fuzzy nonparametric regression models, two measures of goodness of fit are presented. The application of the proposed methods are studied in modelling some data sets.