Alzheimer's disease can be diagnosed through various clinical methods. Among them, electroencephalography has proven to be a powerful, non-invasive, affordable, and painless tool for its diagnosis. In this study, eight machine learning (ML) approaches, including SVM, BLDA, DT, GNB, KNN, RF, and deep learning (DL) methods such as RNN and RBF, were employed to classify Alzheimer's disease into two stages: moderate Alzheimer's disease (ADM) and advanced Alzheimer's disease (ADA). To this aim, electroencephalography data collected from five different hospitals over a decade has been used. A novel method based on neural networks has been proposed to increase accuracy and obtain fast classification times. Results show that deep neuronal networks based on radial basis functions initialized with fuzzy means achieved the best balanced accuracy with 96.66% accuracy in ADA classification and 93.31% accuracy in ADM classification. Apart from improving accuracy, it is noteworthy that this algorithm had never been used before to classify patients with Alzheimer's disease. • The dataset employed has the highest number of subjects compared to other works. • 668 patients from five different hospitals have been considered in the analysis. • The proposed method has fast training and classification. • The algorithm integrates fuzzy initialization improving optimization procedures. • First study classifying Alzheimer Disease with RBF neural networks and fuzzy means. [ABSTRACT FROM AUTHOR]