Ensemble extended belief rule-based systems with different similarity measures for classification problems

The extended belief rule-based (EBRB) system is shown to have the potential to handle both quantitative and qualitative information under uncertainty, and it has been used as an effective tool for decision support and classification problems. However, despite these advances, several drawbacks have emerged recently, and the most significant one is caused by its similarity measure using Euclidean distance, which could lead to counterintuitive individual matching degrees, while other widely used similarity measures have not been studied for their application in the EBRB system. To this end, seventeen similarity measures are investigated and applied in the EBRB system in this paper, and based on the analysis, an ensemble method for EBRB system with different similarity measures is proposed. Firstly, the problem of the similarity measure of the conventional EBRB system is investigated. Then, a variety of similarity measures are analyzed and their application in the EBRB system is studied. Next, the ensemble method for EBRB systems with different similarity measures is proposed, which consists of two parts, the adaptive weight learning method for determining the weight of each EBRB system with different similarity measures, and the evidential reasoning (ER)-based combination method for combining the inferential results of different methods. Finally, 25 classification datasets are studied to test the performance of EBRB systems with different similarity measures as well as the proposed method, and the results are compared with existing works. The comparison results show that the proposed method could not only achieve better results than any other EBRB systems with different similarity measures, but also outperform other conventional classifiers on some classification datasets, especially small-scale datasets.