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The extensive adoption of artificial intelligence in clinical decision support systems necessitates a significant presence of interpretable machine learning models. Therefore, we develop a recurrent neural network-based interpretable method, combining the fuzzy concepts and recurrent units, to train accurate and explainable models on high-dimensional longitudinal electronic health records data. Through supervised learning, our method allows the identification of variable encoding functions and significant rules. To demonstrate performance and capabilities in classification and rule discovery, we first test our method on a simulated dataset. The proposed methods achieve the best model performance compared to other methods, and the rules learned are almost identical to what we used to generate the synthetic data. Furthermore, we showcase a pilot application that proved its potential in the early detection of cardiac event onset. Our proposed algorithm obtains a comparable model performance to vanilla GRU models and remains relatively stable when the prediction window size changes. Examining the rules generated by our EvolveFNN model with the GRU unit, we find that the extracted rules not only align with clinical practices and existing literature but also provide potential risk factors not explored before in the population. The additional experiments on the MIMIC-III benchmark dataset show the algorithm's generalizability. In conclusion, our approach, EvolveFNN, can effectively train accurate, interpretable, and reliable models using large longitudinal electronic health records, thereby offering valuable insights for clinicians.