Cardiovascular diseases (CVDs) remain a leading global cause of mortality, highlighting the critical need for accurate, interpretable, and robust diagnostic tools. This study introduces two innovative graph-based fuzzy learning frameworks: the Fuzzy Graph Neural Network (FGNN) and the Fuzzy Graph Attention Network (FGAT), designed to enhance CVD risk prediction and clinical decision support. By integrating fuzzy set theory with a standard fuzzy inference system (FIS), these models effectively address uncertainty and imprecision in medical data, while graph neural networks (GNNs) capture complex inter-feature relationships by representing patients as nodes and clinical attributes as edges. FGNN combines fuzzy logic with a standard FIS to model feature interactions, using membership functions and rule-based reasoning to ensure robustness against noisy or incomplete data. FGAT builds on this by incorporating an attention mechanism to prioritize critical features, enhancing prediction accuracy. Both models leverage the strengths of fuzzy logic to handle uncertainty and GNNs to model relational data, offering scalable and high-performing solutions. Evaluated on a benchmark CVD dataset, FGNN and FGAT outperform traditional machine learning baselines in accuracy, precision, recall, and F1-score, demonstrating their potential for personalized CVD risk assessment and decision support in healthcare.