Some recommendation systems (RSs) achieve high accuracy but lack explainability regarding their recommendation mechanisms. Conversely, other RSs offer explanations for their recommendations but at the cost of lower accuracy. To address this trade-off, this study proposes a hybrid Explainable Biased Multi-Relational Matrix Factorization (EBMRMF) model. The proposed model operates in two main phases. Initially, it learns from a training set that includes information fields such as user-item ratings and user-item attributes. Subsequently, the model extracts latent factors (LFs) for users and items by analyzing relationships between users, items, and other relevant entities. It also leverages user neighbor preferences to update LFs and calculate the explanation score for user-item pairs. After training, the model utilizes these latent factors to predict ratings and generate item recommendations for users. Experimental results demonstrate an accuracy improvement of this model on three actual datasets: two from MovieLens and one from subset of the Amazon Review 2023 dataset. Furthermore, this approach proves suitable for diverse data domains.