Introduction: Over the past decade Heart and diabetes disease prediction are major research works in the past decade. For prediction of the Heart and Diabetes diseases, a model using an approach based on rough sets for reducing the attributes and for classification, fuzzy logic system is proposed in this paper. Methods: The overall process of prediction is split into two main steps, 1) Using rough set theory and hybrid firefly and BAT algorithms, feature reduction is done 2) Fuzzy logic system classifies the disease datasets. Reduction of attributes is carried out by rough sets and Hybrid BAT and Firefly optimization algorithm. Results & Discussion: Then the classification of datasets is carried out by the fuzzy system which is based on the membership function and fuzzy rules. The experimentation is performed on several heart disease datasets available in UCI Machine learning repository like datasets of Hungarian, Cleveland, and Switzerland and diabetes dataset collected from a hospital in India. The experimentation results show that the proposed prediction algorithm outperforms existing approaches by achieving better accuracy, specificity, and sensitivity. © 2021 Bentham Science Publishers.