# A Novel Ensemble Belief Rule-Based Model for Online Payment Fraud Detection
###### Abstract
Some attributes may lead to overfitting, and randomly selecting attributes can reduce the risk of overfitting and improve the generalization ability of the model. Additionally, multi-attribute datasets may contain missing values, outliers and other issues. This method can help mitigate the impact of such noise, improving the robustness of the ensemble model. Assigning different attributes to different classifiers for training can also enhance training speed and efficiency. Apart from the class imbalance issue, another problem that needs to be solved is the low interpretability problem in methods used in fraud detection Currently, there are numerous methods available for fraud detection, such as ANN (Artificial Neural Network) [16], SVM (support vector machine) [17], KNN (K-Nearest Neighbors) [18], etc. However, these algorithms primarily focus on maximizing the predictive accuracy of the models, without addressing the issue of model interpretability. Nowadays, with a growing concern for model interpretability, the BRB model, functioning as an expert system, has gained wide acceptance for classification problems. The BRB model (belief rule base), proposed by [PERSON] in 2006 [19], serves as a rule-based expert system. Compared to traditional machine learning approaches, BRB offers advantages such as the ability to integrate expert knowledge, handling both qualitative and quantitative data, and offering a traceable inference process and strong interpretability. Due to these advantages, BRB has rapidly gained prominence since its inception. In recent years, it has been widely applied to classification tasks such as fault diagnosis [20], intrusion detection [21], medical diagnosis [22] and the classification and prediction of complex systems [23], among others. Therefore, this paper integrates the BRB model as the base model with the bagging ensemble learning framework to address the fraud detection problem. The BRB model can tackle interpretability issues, while the ensemble learning framework effectively addresses the problem of sample imbalance in fraud detection and improves model performance. In summary, there are two main challenges in fraud detection tasks. The first one is to increase the interpretability of the models used in fraud detection. Another one is solving the negative effect caused by an imbalanced dataset. In response to these two challenges and aforementioned issues, this article outlines three main contributions as follows:  
* Improving the interpretability of model used in fraud detection task by adopting BRB model as the main method;
* Improving the model's performance, especially in the minority class, by combining the BRB model with the bagging framework. Unlike the traditional methods used for solving the class imbalance, ensemble learning approaches are less prone to overfitting and less likely to lose important information, which could lead to a decline in model performance;
* Optimizing the traditional ensemble learning process to reduce the modeling complexity of the ensemble BRB model while enhancing the stability of its final performance. The remainder of this paper is organized as follows. Section 2 introduces the related work of solving class imbalance in fraud detection. Section 3 introduces the technical principles utilized in this paper, including the BRB classification principle, XGBoost (eX-treme Gradient Boosting) feature selection method and bagging ensemble learning method. Section 4 proposes a novel ensemble BRB model for solving fraud detection. Section 5 provides an experimental study to validate the effectiveness of the proposed model. Finally, Section 6 draws a conclusion from this work.