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Mammography remains the most prevalent imaging tool for early breast cancer screening. The language used to describe abnormalities in mammographic reports is based on the breast Imaging Reporting and Data System (BI-RADS). Assigning a correct BI-RADS category to each examined mammogram is a strenuous and challenging task for even experts. This paper proposes a new and effective computer-aided diagnosis (CAD) system to classify mammographic masses into four assessment categories in BI-RADS. The mass regions are first enhanced by means of histogram equalization and then semiautomatically segmented based on the region growing technique. A total of 130 handcrafted BI-RADS features are then extrcated from the shape, margin, and density of each mass, together with the mass size and the patient's age, as mentioned in BI-RADS mammography. Then, a modified feature selection method based on the genetic algorithm (GA) is proposed to select the most clinically significant BI-RADS features. Finally, a back-propagation neural network (BPN) is employed for classification, and its accuracy is used as the fitness in GA. A set of 500 mammogram images from the digital database of screening mammography (DDSM) is used for evaluation. Our system achieves classification accuracy, positive predictive value, negative predictive value, and Matthews correlation coefficient of 84.5%, 84.4%, 94.8%, and 79.3%, respectively. To our best knowledge, this is the best current result for BI-RADS classification of breast masses in mammography, which makes the proposed system promising to support radiologists for deciding proper patient management based on the automatically assigned BI-RADS categories.