Background Timely referral for advanced therapies (i.e., heart transplantation, left ventricular assist device) is critical for ensuring optimal outcomes for heart failure patients. Using electronic health records, our goal was to use data from a single hospitalization to develop an interpretable clinical decision-making system for predicting the need for advanced therapies at the subsequent hospitalization. Methods Michigan Medicine heart failure patients from 2013–2021 with a left ventricular ejection fraction ≤ 35% and at least two heart failure hospitalizations within one year were used to train an interpretable machine learning model constructed using fuzzy logic and tropical geometry. Clinical knowledge was used to initialize the model. The performance and robustness of the model were evaluated with the mean and standard deviation of the area under the receiver operating curve (AUC), the area under the precision-recall curve (AUPRC), and the F1 score of the ensemble. We inferred membership functions from the model for continuous clinical variables, extracted decision rules, and then evaluated their relative importance. Results The model was trained and validated using data from 557 heart failure hospitalizations from 300 patients, of whom 193 received advanced therapies. The mean (standard deviation) of AUC, AUPRC, and F1 scores of the proposed model initialized with clinical knowledge was 0.747 (0.080), 0.642 (0.080), and 0.569 (0.067), respectively, showing superior predictive performance or increased interpretability over other machine learning methods. The model learned critical risk factors predicting the need for advanced therapies in the subsequent hospitalization. Furthermore, our model displayed transparent rule sets composed of these critical concepts to justify the prediction. Conclusion These results demonstrate the ability to successfully predict the need for advanced heart failure therapies by generating transparent and accessible clinical rules although further research is needed to prospectively validate the risk factors identified by the model.