The classification of images is of high importance in medicine. In this sense, Deep learning methodologies show excellent performance with regard to accuracy. The drawback of these methodologies is the fact that they are black boxes, so no explanation is given to users on the reasons underlying their choices. In the medical domain, this lack of transparency and information, typical of black box models, brings practitioners to raise concerns, and the result is a resistance to the use of deep learning tools. In order to overcome this problem, a different Machine Learning approach to image classification is used here that is based on interpretability concepts thanks to the use of an evolutionary algorithm. It relies on the application of two steps in succession. The first receives a set of images in the inut and performs image filtering on them so that a numerical data set is generated. The second is a classifier, the kernel of which is an evolutionary algorithm. This latter, at the same time, classifies and automatically extracts explicit knowledge as a set of IF–THEN rules. This method is investigated with respect to a data set of MRI brain imagery referring to Alzheimer’s disease. Namely, a two-class data set (non-demented and moderate demented) and a three-class data set (non-demented, mild demented, and moderate demented) are extracted. The methodology shows good results in terms of accuracy (100% for the best run over the two-class problem and 91.49% for the best run over the three-class one), (1.0000 and 0.9149, respectively), and Matthews Correlation Coefficient (1.0000 and 0.8763, respectively). To ascertain the quality of these results, they are contrasted against those from a wide set of well-known classifiers. The outcome of this comparison is that, in both problems, the methodology achieves the best results in terms of accuracy and , whereas, for the Matthews Correlation Coefficient, it has the best result over the two-class problem and the second over the three-class one.