In this study, we present a novel clinical decision support system and discuss its interpretability-related properties. It combines a decision set of rules with a machine learning scheme to offer global and local interpretability. More specifically, machine learning is used to predict the likelihood of each of those rules to be correct for a particular patient, which may also contribute to better predictive performances. Moreover, the reliability analysis of individual predictions is also addressed, contributing to further personalized interpretability. The combination of these several elements may be crucial to obtain the clinical stakeholders' trust, leading to a better assessment of patients' conditions and improvement of the physicians' decision-making.