Fuzzy support vector regression

The epsilon-SVR has two limitations. Firstly, the tube radius (epsilon) or noise rate along the y-axis must be already specified. Secondly, this method is suitable for function estimation according to training data in which noise is independent of input x (is constant). To resolving these limitations, in approaches like v-SVIRN, the tube radius or the radius of estimated interval function which can be variable with respect to input x, is determined automatically. Then, for the test sample x, the centre of interval function is reported as the most probable value of output according to training samples. This method is useful when the noise of data along the y-axis has a symmetric distribution. In such situation, the centre of interval function and the most probable value of function are identical. In practice, the noise of data along the y-axis may be from an asymmetric distribution. In this paper, we propose a novel approach which estimates simultaneously an interval function and a triangular fuzzy function. The estimated interval function of our proposed method is similar to the estimated function of v-SVIRN. The center of triangular fuzzy function is the most probable value of function according to training samples which is important when the noise of training data along the y-axis is from an asymmetric distribution.