Intuitionistic fuzzy twin support vector machines with the insensitive pinball loss

Due to the use of membership and nonmembership functions of samples from intuitionistic fuzzy sets(IFSs), intuitionistic fuzzy twin support vector machines (IFTSVMs) can effectively suppress noise in the data. However, the objective function of IFTSVMs partially considers score values of samples and employs the hinge loss function which leads to the sensitivity to feature noise and instability to re-sampling. To enhance the performance of IFTSVMs, we propose novel IFTSVMs with the insensitive pinball loss function. In the proposed convex optimization models, a simple strategy is devised to achieve the score value of each training sample and score values of samples in both classes are defined by using IFSs. Unlike previous methods, we introduce two groups of slack variables to derive the dual formulations of convex models which make them have compact representations. Some properties of the proposed models including geometric properties and noise insensitivity are theoretically analyzed. We also explain the proposed models in terms of the idea of the weighted scatter minimization, which provides theoretical foundations for the proposed models. Experiments on a series of data sets are performed and experimental results demonstrate that the proposed convex models are superior to some existing learning models in the presence of feature noise or label noise.