With the rapid expansion of scale and complexity, defects inevitably exist within software systems. In recent years, defect prediction techniques based on deep learning have become a prominent research topic in the field of software engineering. These techniques can identify potential defects without executing the code, garnering significant attention from both industry and academia. Nevertheless, existing approaches mostly concentrate on determining the presence of defects at the method-level code, lacking the ability to precisely classify specific defect categories. Consequently, this undermines the efficiency of developers in locating and rectifying defects. Furthermore, in practical software development, new projects often lack sufficient defect data to train high-accuracy deep learning models. Models trained on historical data from existing projects frequently struggle to achieve satisfactory generalization performance on new projects. Hence, this study initially reformulates the traditional binary defect prediction task into a multi-label classification problem, employing defect categories described in the common weakness enumeration (CWE) as fine-grained predictive labels. To enhance the model performance in cross-project scenarios, this study proposes a multi-source domain adaptation framework that integrates adversarial training and attention mechanisms. Specifically, the proposed framework employs adversarial training to mitigate domain (i.e., software projects) discrepancies, and further utilizes domain-invariant features to capture feature correlations between each source domain and the target domain. Simultaneously, the proposed framework employs a weighted maximum mean discrepancy as an attention mechanism to minimize the representation distance between source and target domain features, facilitating model in learning more domain-independent features. The experiments on the dataset consisting of 8 real-world open-source projects constructed in this study show that the proposed approach achieves significant performance improvements compared with state-of-the-art baselines.