Fuzzy robust ν-support vector machine with penalizing hybrid noises on symmetric triangular fuzzy number space

In view of the shortage of ε-insensitive loss function for hybrid noises such as singularity points, biggish magnitude noises and Gaussian noises, this paper presents a new version of fuzzy support vector machine (SVM) which can penalize those hybrid noises to forecast fuzzy nonlinear system. Since there exist some problems of hybrid noises and uncertain data in many actual forecasting problem, the input variables are described as fuzzy numbers by fuzzy comprehensive evaluation. Then by the integration of the triangular fuzzy theory, ν-SVM and loss function theory, the fuzzy robust ν-SVM with robust loss function (FRν-SVM) which can penalize those hybrid noises is proposed. To seek the optimal parameters of FRν-SVM, particle swarm optimization is also proposed to optimize the unknown parameters of FRν-SVM. The results of the application in fuzzy sale system forecasts confirm the feasibility and the validity of the FRν-SVM model. Compared with the traditional model and other SVM methods, FRν-SVM method requires fewer samples and has better generalization capability for Gaussian noise.