<p>This study aims to investigate the rheological and thermal properties of Carreau hybrid fuzzy nanofluid composed of copper and alumina nanoparticles (Al₂O₃ and Cu) dispersed in engine oil over stretching/shrinking Riga wedge. Variability in nanoparticle properties was addressed using fuzzy logic. This method facilitated the identification of the optimal copper and alumina nanoparticle combination for peak performance. By examining nanoparticle concentrations within the range of [0%, 5%, and 10%] using triangular fuzzy numbers, the analysis demonstrated that these hybrid nanofluids can improve heat transfer rates by 20–30% in comparison to conventional nanofluids. An “artificial neural network” (ANN) was utilized to predict the fluid’s performance. A comparison of two ANN training methods—the Levenberg–Marquardt Scheme and the Bayesian regularization scheme—analyzed the predictive capability of the initial data for key performance indicators. Visualizations, including error histograms and performance plots for training, testing, and validation, were employed to assess the accuracy of the ANN models. The ANN, trained with LMS and BRS, achieved low gradient values (9.89e-08, 2.85e-08, 9.31e-08, and 1.89e-08) at epochs 180, 10, 92, and 6, respectively. Best validation performance yielded low mean squared errors (2.23e-08, 2.32e-10, 6.27e-08, and 2.82e-09) at corresponding epochs. These results indicate significant enhancements in thermal conductivity and heat transfer for hybrid nanofluid applications. The integration of fuzzy logic and ANN offers a robust framework for nanofluid property optimization, proposing practical strategies for thermal management.</p>