Accurate segmentation of the myocardial scar may supply relevant advancements in predicting and controlling deadly ventricular arrhythmias in subjects with cardiovascular disease. In this paper, we propose the architecture of inclusion and classification of prior information U-Net (ICPIU-Net) to efficiently segment the left ventricle (LV) myocardium, myocardial infarction (MI), and microvascular-obstructed (MVO) tissues from late gadolinium enhancement magnetic resonance (LGE-MR) images. Our approach was developed using two subnets cascaded to first segment the LV cavity and myocardium. Then, we used inclusion and classification constraint networks to improve the resulting segmentation of the diseased regions within the pre-segmented LV myocardium. This network incorporates the inclusion and classification information of the LGE-MRI to maintain topological constraints of pathological areas. In the testing stage, the outputs of each segmentation network obtained with specific estimated parameters from training were fused using the majority voting technique for the final label prediction of each voxel in the LGE-MR image. The proposed method was validated by comparing its results to manual drawings by experts from 50 LGE-MR images. Importantly, compared to various deep learning-based methods participating in the EMIDEC challenge, the results of our approach have a more significant agreement with manual contouring in segmenting myocardial diseases.