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Although an intuitionistic fuzzy twin support vector machines (IFTSVM) can reduce the impact of noise and outliers in classification problems, it is sensitive to noise, is unstable in resampling and lacks sparsity. To challenge these issues, the truncated pinball loss and the intra-class weight technique are introduced into the IFTSVM model and a weighted IFTSVM with truncated pinball loss (Tpin-WIFTSVM) is proposed. Firstly, the Tpin-WIFTSVM fully takes into account the quantile distance and punishes both correctly and incorrectly classified instances by truncated pinball loss function that maintains a balance between noise insensitivity and model sparsity. Besides, to adjust the importance of the data in the model training, we employ both membership and non-membership weights and the local neighborhood information between the data points to reduce the impact of noise and outliers effectively. Finally, successive overrelaxation (SOR) is used to improve the computational efficiency of the proposed model. The experimental results and corresponding statistical analyses validate the effectiveness of the proposed Tpin-WIFTSVM.