Integrating ridge-type regularization in fuzzy nonlinear regression

Abstract

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.