This paper describes a new hybrid approach, based on modular artificial neural networks with fuzzy logic integration, for the diagnosis of pulmonary diseases such as pneumonia and lung nodules. In particular, the proposed approach analyzes medical images, which are digitized chest X-rays, focusing on a classification method based on descriptors, such as grayscale histogram features, gray-level co-occurrence matrix (GLCM) texture-based features, and local binary pattern texture features. Then, to perform feature reduction, a multi-objective genetic algorithm is used to obtain an optimized neuro-fuzzy classifier, which is able to classify the pathology found in the analyzed chest X-ray. The main contribution of this paper is the proposed modular neural network approach, which divides features to achieve specialized analysis in the modules for digital image analysis and classification. The proposed approach achieves high classification accuracy after evaluating the neuro-fuzzy model with three large datasets of chest X-rays.