Intuitionistic Fuzzy and Robust Loss Fused Framework for Stable and Efficient RVFL Learning

Random vector functional link (RVFL) networks have gained considerable attention as efficient randomized learning models due to their fast training and simple architecture. However, classical RVFL still suffers from three fundamental limitations: the reliance on the squared loss makes it highly vulnerable to noise and outliers; matrix inversion introduces substantial computational overhead; and the uniform treatment of all samples ignores the varying credibility present in real-world datasets. Existing extensions address these issues only partially, robust loss functions improve noise tolerance, and intuitionistic fuzzy (IF) schemes enhance credibility awareness, yet no framework integrates both perspectives within a unified formulation. In this work, we propose the intuitionistic fuzzy flexi guardian regularized RVFL (IF-XG-RVFL), a theoretically grounded framework that simultaneously addresses robustness, credibility modeling, and computational efficiency. The novelty of IF-XG-RVFL lies in the joint integration of 1) IF credibility scores, derived from both global and local uncertainty characteristics, and 2) a bounded, asymmetric, and smooth FleXi Guardian (XG) loss, which provides controlled asymmetry and robust error penalization. This dual integration yields a credibility-weighted and robust-loss RVFL formulation that remains smooth and fully differentiable. By leveraging this smoothness, the IF-XG-RVFL optimization problem is efficiently solved using a Nesterov accelerated gradient (NAG)-based algorithm, eliminating the need for matrix inversion and substantially reducing computational overhead. In addition, we provide a theoretical generalization error bound for the proposed IF-XG-RVFL framework using Rademacher complexity, establishing its learning guarantees. To the best of our knowledge, this is the first RVFL framework that simultaneously resolves the three key limitations of classical RVFL: robustness to noise, credibility-aware learning, and matrix-inversion-free scalability within a single unified model. Extensive experiments on UCI benchmark datasets and the BreakHis breast cancer histopathology dataset demonstrate that the proposed IF-XG-RVFL consistently outperforms several state-of-the-art randomized neural network variants in accuracy, stability, average rank, and statistical significance, as verified with the Friedman and Nemenyi tests. Furthermore, we conduct an additional evaluation on imbalanced KEEL datasets using the F1-score, where IF-XG-RVFL achieves the highest average F1-score and the best average rank among all compared methods. These results highlight the effectiveness of jointly modeling credibility and robust loss within a unified randomized neural framework.