Estimation Nonparametric Fuzzy Regression model using simulation

Abstract

In this research, three techniques of smoothing were used, local linear smoothing, kernel smoothing, k-Nearest Neighbor to estimate the model of the Fuzzy nonparametric regression. A dependent variable was represented by using Fuzzy Triangular Numbers . Based on the distance measure for the Fuzzy numbers which proposed by (Diamond) and we used the normal optimal smoothing method to select the optimal value of the smoothing parameter (h) where it was Fuzzified  to fit the Fuzzy  nonparametric model .

   In order to demonstrate the best technique of smoothing, the simulation was used to compare these techniques using the (bias) criterion to determine the best estimate of the data generated by the simulation method and at the approved and proposed kernel functions. The comparison criterion showed that the lowest value of this criterion was when using the k- nearest neighbor technique at kernel functions (Gaussian).