Accurately estimating swelling ratios and drug kinetic model parameters under controlled experimental conditions is crucial for identifying optimal production processes. Fuzzy modelling approaches are particularly valuable for the analysis of complex systems, such as drug delivery systems, owing to their capacity to effectively manage uncertainty and data complexity. This study focuses on introducing a fuzzy-hybrid methodology to model the swelling behavior of poly(1-vinyl-1,2,4-triazole) (PVTAz) hydrogels and the drug release profile of PVTAz hydrogels loaded with 5-Fluorouracil. The proposed fuzzy-hybrid approach was utilized in modeling swelling behavior of the PVTAz hydrogels as a fuzzy function of time, temperature, pH, and the drug release behavior as a fuzzy function of time only. All the obtained models were illustrated with respect to the experimental data, showing their effectiveness and applicability. The performance metrics ARE, RMSE, and R2 were evaluated for the central tendency of each model to statistically prove the models’ validity. This research contributes significantly to advancing our understanding of hydrogel behaviors in drug delivery systems, showcasing the interdisciplinary synergy that enhances research outcomes.