Integrating Ridge-type regularization in fuzzy nonlinear regression

Abstract

Abstract. In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression models using fuzzy numbers and Gaussian basis functions. Shrinkage regularization methods are 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 parameter and the number of basis functions are fuzzified to fit the presented model. The simulation results show that our fuzzy nonlinear modelling performs well in various situations.Mathematical subject classification: Primary: 62J86; Secondary: 62J07.

Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers

“…Tateishi, Matsui and Konishi [16] constructed nonlinear regression models with Gaussian basis functions using weighted type regularization for analyzing data with complex structures. Farnoosh, Ghasemian and Fard [4] proposed a weighted ridge penalty on a fuzzy nonlinear regression model using fuzzy numbers and Gaussian basis functions. Jiang, Jiang and Song [7] developed weighted composite regression estimation and used the Adaptive Lasso and SCAD regularization to achieve a simultaneous parameter model estimation and selection.…”