## 1 Introduction  
Breast cancer, which is the second most widespread cancer among women worldwide, has turned into global public health issue due to its complex intrinsic aetiology [1]. The early diagnosis and monitoring of the cancer significantly reduces the death risks, leads to better prognosis and therapy, and lowers the treatment cost. Mammography wears the crown of being the gold standard among several imaging modalities because it offers the potential of early detection of pathology [2]. However, mammography is a 2D method that reduces the ability to visualize lesions in case of prevalent glandular component in dense breast. Moreover, the mammography representsa 2D projection of a 3D structure for which, geometrically, tissues belonging to different planes are superimposed in the radiographic image. Other imaging techniques including magnetic resonance (MR), computed tomography (CT), and digital breast tomosynthesis (DBT) are strong candidates where in-depth analysis of hazardous cases is required. Among these, the DBT is proven to have higher accuracy with respect to the 2D imaging methods [3]. After acquisition of the multiple thin and high-resolution images, the DBT system produces a quasi-three-dimensional format of the reconstructed breast images aiming to reduce the effect of tissue superimposition. Moreover, the required radiation dose is not high, contrary to the conventional imaging techniques, and the generated images appear to have greater resolution and contrast [4]. The DBT represents a more accurate diagnostic indicator than 2D imaging for evaluating the morphological features, e.g., shape and margin of the different immunophenotypes of the breast cancer, thus being able to play a crucial role in the molecular imaging and prognosis [5; 6; 7; 8; 9]. Over the last decade, deep learning (DL) has emerged as a promising computational approach for the automatic detection, classification, and segmentation of cancerous masses thorough the analysis of diagnostic medical images, thus enabling the computer-aided diagnosis (CAD) and clinical decision support systems [10; 11; 12; 13]. The DL methods along with the traditional image processing techniques have already been established as an effective approach to automatically analyze diagnostic images for breast cancer diagnosis and monitoring [3; 14; 15]. Numerous studies dealt with automatic detection, segmentation, and classification of the breast lesions that achieved considerably moderate to high performances [16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. However, the automatic classification of the breast lesions according to shape, size, and physical appearance remains a challenging task due to the varying shape that refers to different type and stage of the cancer [26] (see Figure 1). The breast cancer is morphologically categorized into several varying shapes based on cancer growth pattern, named as round, oval, lobulated, irregular, and architectural distortion [27; 28]. Numerous existing studies deal with the shape-based breast cancer classification [26; 29; 30]; however, most of these consider the mammogram instead of the DBT that offers several advantages as discussed above. A deep discussion of the state of the art is presented in Section 2. In spite of the enormous success, the complex nature of the DL techniques hides any possible information of the underlying decision mechanism [31; 32], which questions its usage in the healthcare domain where explainability holds paramount significance to build a trust on decisions made by surging artificial intelligence (AI). Explainable artificial intelligence (XAI) brings forward the possibility of explaining the results of DL models and reveals how the models produce these results. Generally, XAI is supposed to fit a model onto four basic attributes [33]:  
* Transparent: open to the degree where humans can understand the decision-making mechanism. * Justifiable: the decision can be supported or justified along each step. * Informative: to provide reasoning and allow reasoning.