Cross-project software defects prediction using fuzzy embedding and deep learning

Context: Cross-project defect prediction (CPDP) aims to predict software defects in a target project using data from related source projects, especially when defect data for the target project is limited or unavailable. A key challenge in CPDP is data heterogeneity and distributional differences across projects, which often lead to poor performance and unreliable predictions. Objectives: This study proposes a new CPDP model that improves prediction accuracy and robustness by introducing fuzzy embedding and deep learning to better capture similarities and differences across projects. The method is designed to mitigate mismatches in data distribution that hinder existing transfer learning and transformation-based approaches. Methods: The fuzzy embedding technique is built on fuzzy clustering and fuzzy set theory, which map each data point into a two-dimensional space of membership degrees across clusters. This representation models complex relationships with partial memberships and preserves contextual information that is often lost in conventional transformations. A deep learning model based on convolutional neural networks (CNN) processes the embedding matrices to learn discriminative defect patterns. The framework is evaluated against state-of-the-art CPDP models across multiple datasets, and sensitivity analysis is conducted on the number of clusters used in fuzzy embeddings. Results: Empirical evaluation shows that the proposed model consistently outperforms advanced CPDP approaches that rely on standard transformation or weighting methods. Improvements are observed in AUC and other key metrics across diverse datasets, demonstrating that fuzzy embeddings enhance the ability of deep learning to generalize knowledge across projects with varying characteristics. Conclusion: This work contributes a practical and effective solution for addressing heterogeneity in CPDP. By combining fuzzy embeddings with deep learning, the model not only achieves higher predictive accuracy but also improves reliability in real-world scenarios where project data distributions differ significantly. These findings highlight the potential of fuzzy embedding to support more resilient software quality assurance practices and provide actionable insights for practitioners dealing with limited or imbalanced defect data.