<p>The time-varying (TV) Yang-Baxter-like matrix equation (YBLME) is of significant importance in physics, mathematics, and dynamic system modeling. However, traditional methods for solving the TVYBLME often suffer from high computational complexity and poor real-time performance. Although existing zeroing neural network (ZNN) models for solving the TVYBLME achieve fixed-time convergence (FxTC), their loose upper bounds on the convergence time (UBCTs) limit their applicability in rapidly evolving dynamic systems. To overcome these issues, this paper proposes an improved noise-tolerant ZNN (INTZNN) model, which incorporates a nonlinear activation function with an exponential gain factor. This enables the INTZNN model to achieve FxTC with a tighter UBCT than existing ZNN models, while maintaining strong robustness against different types of noise. The proposed model is also extended to solve the time-invariant YBLME, demonstrating similar advantages. Numerical experiments validate the rapid convergence and noise tolerance of the INTZNN model, highlighting its superiority over existing ZNN models across different scenarios.</p>