T. Razzaghnia - Department of Statistics, North Tehran Branch, Islamic Azad University, Tehran, Iran
S. Danesh - Young Researchers and Elite Club, East Tehran Branch, Islamic Azad university, Tehran, Iran.
A. Maleki - Department of Statistics, West tehran Branch, Islamic Azad University, Tehran, Iran

In this paper, three methods of nonparametric fuzzy regression with crisp input and asymmetric trapezoidal fuzzy output, are compared. It analyzes the three nonparametric techniques in statistics, namely local linear smoothing (L-L-S), K- nearest neighbor Smoothing (K-NN) and kernel smoothing (K-S) with trapezoidal fuzzy data to obtain the best smoothing parameters. In addition, it makes an analysis on three real-world datasets and calculates the goodness of fit to illustrate the application of the proposed method.In this paper, we propose to analyze the three nonparametric regression techniques in statistical regression, namely local linear smoothing (L-L-S), the K- nearest neighbor smoothing (K-NN) and the kernel smoothing techniques (K-S) with trapezoidal fuzzy data.This article is organized as follows: In section ۲, we have some preliminaries about fuzzy nonparametric regression and trapezoidal fuzzy data. In section ۳, smoothing methods for trapezoidal fuzzy numbers are proposed and in section ۴, two numerical examples are solved.

Local Linear Smoothing (L-L-S), K-Nearest Neighbor Smoothing (K-NN), Kernel Smoothing (K-S)