Fuzzy support vector regression machine with penalizing Gaussian noises on triangular fuzzy number space

In view of the shortage of ε-insensitive loss function for Gaussian noise, this paper presents a new version of fuzzy support vector machine (SVM) which can penalize Gaussian noise to forecast fuzzy nonlinear system. Since there exist some problems of finite samples and uncertain data in many forecasting problem, the input variables are described as crisp numbers by fuzzy comprehensive evaluation. To represent the fuzzy degree of these input variables, the symmetric triangular fuzzy technique is adopted. Then by the integration of the fuzzy theory, ν-SVM and Gaussian loss function theory, the fuzzy ν-SVM with Gaussian loss function (F g-SVM) which can penalize Gaussian noise is proposed. To seek the optimal parameters of F g-SVM, genetic algorithm is also proposed to optimize the unknown parameters of F g-SVM. The results of the application in sale system forecasts confirm the feasibility and the validity of the F g-SVM model. Compared with the traditional model, F g-SVM method requires fewer samples and has better generalization capability for Gaussian noise.