For time-varying delayed nonlinear systems with parameter uncertainties and persistent disturbances, an online and an offline robust fuzzy model predictive control algorithms are proposed in this article. Both methods guarantee the input-to-state stability of the system. Furthermore, a novel alternative optimization (AOP) approach and a dual-mode optimal control (OP)/AOP strategy are proposed to prevent the performance deterioration of the online OP approach due to the challenges in addressing the bilinear matrix inequality (BMI) constraints. With the established AOP and dual-mode OP/AOP techniques, the optimization problem constrained by BMIs is transformed into convex, and a significantly more precise approximation of the ellipsoidal minimal robust positively invariant set can be calculated. Besides, the system can eventually converge into a more compact ellipsoidal set. These two alternative optimization methods can be easily extended to various nonlinear systems. A numerical example and a continuous-time stirring tank example are provided to validate the effectiveness and advantages of the established methodologies.