Analysis of nonparametric fuzzy regression models

In this thesis, the nonparametric fuzzy regression models are examined. k-nearest neighbour, kernel smoothing and local polynomial smoothing models are expressed in fuzzy structure. Furthermore to these models, cross-validation and generalized cross-validation criteria are developed for bandwidth selection by using the hat matrix. The data used in the studies, the situation is taken into account as to be the response variable is valued fuzzy and the explanatory variable is valued crisp. The locpol package in R program is used for analysis. In applications especially the cases, that the degree of the polynomial is linear and cubic in fuzzy local polynomial regression model, are examined. The bandwidth for these models is selected by developed cross validation and generalized cross validation criteria, the performance of the models are compared using averaged squared error values. Studied on different types of data sets in order to be able to generalize the obtained results. In many applications it is observed that models, especially has more curvature, are expressed more smoothly (less fluctuating) although the fuzzy local cubic model's performance values are higher. Additionally, it is seen that steps of operation are reduced by selecting the higher bandwidth value than fuzzy local linear model, so it is concluded that the usage of fuzzy local cubic models gives better results.