Given the critical role of zeroing neural networks (ZNN) in various fields and the practical demand for models in effectively resisting real-time noise, this study introduces a novel anti-noise integral zeroing neural network (AN-IZNN) model alongside its enhanced counterpart (EAN-IZNN), for the applications of matrix problem solving. Theoretical analysis demonstrates their ability to achieve convergence even under different noise conditions. Both theoretical analyses and simulation validations highlight the superior performance of the proposed models over existing neural network models. Notably, the root mean square error of the proposed AN-IZNN and EAN-IZNN models is reduced by 92.6249% and 91.4178%, respectively, compared to scenarios without the proposed method, demonstrating the effectiveness of the solution.