In this chapter, the authors consider the problem of classification of breast tumors on medical images. As a solution, the authors have developed a new hybrid convolutional network in which convolutional neural network (CNN) is used as a feature extractor while fuzzy neural network (FNN) NEFClass is used as a classifier. The authors implemented and investigated training algorithms of FNN. They carried out experimental investigations of the suggested hybrid network on the standard data set and compared them with known results. This chapter considers the problem of data dimensionality reduction and investigates the application of principal components method.