The Gaussian AHP(AHP-GS) is a decision-making method that uses quantitative inputs and dispersion measures to calculate criteria weights. As a variation of the Analytic Hierarchy Process (AHP), it reduces the subjectivity of traditional AHP and efficiently handles large sets of alternatives. Data normalization is crucial in multi-criteria decision-making (MCDM) methods, ensuring comparability across criteria with different units and scales. In AHP-GS, which integrates Gaussian functions to model uncertainties, the choice of normalization technique significantly impacts prioritization results, affecting decision accuracy and robustness. The study examines whether varying normalization methods change the rankings produced by AHP-GS. Methods like min-max scaling, Euclidean normalization, and max normalization are applied to two datasets from Ceará (Brazil): the Municipal Human Development Index (MHDI) and urbanization data. Ranking similarity coefficient is calculated to assess the relationship between MHDI and urbanization rankings. Using simulated and real-world scenarios, performance metrics such as consistency, sensitivity to input changes, and robustness under uncertainty are evaluated. Results show notable variations in rankings and stability depending on the normalization method, emphasizing the importance of choosing a technique suited to the problem and data. This work enhances MCDM precision and provides practical insights for applying AHP-GS in complex decision-making contexts.