<p>Class imbalance poses a significant challenge in domain adaptation, leading to the misclassification of minority classes in the target domain, causing poor overall performance or even negative transfer. Despite the prevalence in many situations, this issue is often overlooked in domain adaptation research. This paper directly addresses the problem of class imbalance in cross-domain and within-domain scenarios within a weakly supervised domain adaptation framework. To this end, we propose Adaptive Weighted One Class Twin Support Vector Machine (AWT-OCSVM) classifier designed for classifying unlabeled target data. Our method utilizes kernelized fuzzy rough set theory during the adaptation phase to adaptively assign weights to labeled and unlabeled samples. Furthermore, we incorporate a loss function to mitigate the sensitivity to class imbalance. The effectiveness of the proposed approach is evaluated through comparisons across various class imbalance protocols, focusing on mean sensitivity. To demonstrate the effectiveness of AWT-OCSVM, we investigate its application to MRI-based brain tumor detection and evaluate it on the ADNI dataset. Additionally, we conduct experiments using the Office-Home, DomainNet, and Digits datasets. The results show that the proposed method slightly outperforms the state-of-the-art methods. Notably, the paper provides theoretical guarantees in the form of generalization bounds for the proposed AWT-OCSVM method.</p>