This study addresses the World Health Organization's recommendation for vaccination, It is firmly supported by studies demonstrating its important effect in lowering childhood diseases and mortality. Specifically, we focus on rotavirus, aiming to deepen our understanding of its transmission dynamics through the development and analysis of a specialized SIR epidemic model. This model divides the child populations into three key compartments are susceptible, infected and recovered. To improve the model's accuracy, we further distinguish between vaccinated and unvaccinated susceptible children, as well as infectious and non-infectious infected individuals. This refined categorization allows for a more detailed exploration of rotavirus dynamics transmission. The model looks at both endemic and disease-free equilibria. It determines local and global stability conditions that depend on the fuzzy fundamental reproduction number ( \(R_{0}\) ). The centroid approach is used to carry out the defuzzification procedure. Additionally, we perform a local stability study for the endemic equilibrium for \(R_{0}\)  > 1 and a global stability evaluation using Lyapunov theory under specific conditions. Numerical simulations using Python software verify our analytical results and provide a thorough evaluation of the model's effectiveness in lowering child rotavirus spread.