Recent advances in Artificial Intelligence have yielded significant progress in developing medical and clinical diagnosis techniques. Machine learning algorithms are among the most promising methods for detection and classification problems. Despite their inherent robustness, the primary challenge in employing these approaches lies in their opaque behaviour, a critical factor in medical diagnosis. Establishing trust between clinicians and patients requires an explainable model. This paper presents a two-stage approach to improving explainability: the first stage, Grammatical Feature Construction (GFC), uses Grammatical Evolution (GE) to perform feature construction. These features are interpretable as they are generated from the original features by applying simple arithmetic operations to the original data. These features are independent of the model/algorithm that will be used for classification, so any classification algorithm could be used in the second stage; we focus here on Linear Discriminant Analysis (LDA) to create GFC/LDA, which provides greater explainability than using LDA alone while maintaining comparable performance. To evaluate the effectiveness of GFC/LDA, we conducted a comprehensive comparative analysis against methods including GE as a classifier and LDA using all original features in two Breast Cancer datasets, the Digital Database for Screening Mammography and the Wisconsin Breast Cancer dataset. The results demonstrate that the GFC/LDA approach yields comparable with the other methods but produces more interpretable models.