Javad Ghasemian

This paper deals with Tikhonov-type regularization of fuzzy nonparametric regression models using quasi-Gaussian and quadratic fuzzy numbers. Implementing Tikhonov regularization in the Lagragian dual space, this estimation method is obtained. The distance measure for fuzzy numbers that suggested by Xu [27] is used and the local linear smoothing technique with the k–fold cross-validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit the presented model. Some simulation experiments are then presented which indicate the performance of the proposed method. © 2015 Institute of Advanced Scientific Research.

In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression modelsusingfuzzynumbersandGaussianbasisfunctions. Shrinkageregularizationmethodsare used in linear and nonlinear regression models to yield consistent estimators. Here, we propose a weighted ridge penalty on a fuzzy nonlinear regression model, then select the number of basis functions and smoothing parameter. In order to select tuning parameters in the regularization method, we use the Hausdorff distance for fuzzy numbers which was first suggested by Dubois and Prade [8]. The cross-validation procedure for selecting the optimal value of the smoothing parameterandthenumberofbasisfunctionsarefuzzifiedtofitthepresentedmodel. Thesimulation results show that our fuzzy nonlinear modelling performs well in various situations. © 2012 SBMAC.

This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the Lagrangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit the presented model. Some simulation experiments are then presented which indicate the performance of the proposed method.