We describe a computer-aided diagnosis (CAD) system for discriminating patients suffering from Alzheimer’s disease (AD) and healthy patients. It is based on: 1) a clustering process to assess white matter, gray matter and cerebrospinal fluid volumes from noisy anatomical magnetic resonance (MR) and functional positron emission tomography (fPET) brain images; 2) a classification process that distinguishes the brain images of normal and AD patients. The clustering stage consists of three steps: First, the fuzzy c-mean (FCM) algorithm is used to provide a fuzzy partition of the initial centroids. Second, fuzzy tissue maps are computed using a possibilistic c-means (PCM) algorithm that uses the FCM partition to obtain the final image clusters. The final segmentation is then made to delimit the brain tissue volumes. For the classification stage, a support vector machine (SVM) is used with different kernel functions. Our experimental results show that our system yields higher sensitivity and specificity rates than alternative approaches.