Decision-making under uncertainty is often complex and involves incomplete and imprecise information on several criteria. To address these challenges, this study introduces a graded soft set framework by incorporating membership and complementary inverse membership functions into soft set theory. Basic set operations and their algebraic properties are set up. Three algorithms are developed to solve the alternative selection problem, the weighted ranking problem and the parameter reduction problem. The proposed approaches use criterion weights and the grading scores for the evaluation of the alternatives and the determination of the less significant parameters. Applications to supplier selection and symptom-based assessment illustrate the framework's practical utility. The suggested methodology provides a straightforward and interpretable decision-supporting tool for multi-criteria decision-making, which needs to be validated in sensitivity analysis and compared to other existing methodologies