FireGNN: Neuro-Symbolic Graph Neural Networks with Trainable Fuzzy Rules for Interpretable Medical Image Classification

Medical image classification requires not only high predictive performance but also interpretability to ensure clinical trust and adoption. Graph Neural Networks (GNNs) offer a powerful framework for modeling relational structures within datasets, however, standard GNNs often operate as black boxes, limiting transparency and usability particularly in clinical settings. In this work, we present an interpretable graph-based learning framework named FireGNN that integrates trainable fuzzy rules into GNNs for medical image classification. These rules embed topological descriptors - node degree, clustering coefficient, and label agreement - using learnable thresholds and sharpness parameters to enable intrinsic symbolic reasoning. Additionally, we explore auxiliary self-supervised tasks (e.g., homophily prediction, similarity entropy) as a benchmark to evaluate the contribution of topological learning. Our fuzzy-rule-enhanced model achieves strong performance across five MedMNIST benchmarks and the synthetic dataset MorphoMNIST, while also generating interpretable rule-based explanations. To our knowledge, this is the first integration of trainable fuzzy rules within a GNN.