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Integrating ridge-type regularization in fuzzy nonlinear regression. (English) Zbl 1318.62254
Summary: 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 D. Dubois and H. Prade [in: Analysis of fuzzy information, Vol. 1: Math. logic. Boca Raton, Florida: CRC Press, Inc. 3–39 (1987; Zbl 0663.94028)]. 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.

MSC:
62J86 Fuzziness, and linear inference and regression
62J07 Ridge regression; shrinkage estimators (Lasso)
Software:
nlmdl; SemiPar
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