Basic Probability Assignment Generation for Dempster-Shafer Evidence Theory via Gaussian Overlap Modeling and KL Divergence Weighting

The creation of Basic Probability Assignment (BPA) still represents a basic problem in the Dempster-Shafer (D-S) theory of evidence especially when it comes to representing continuous uncertainty and class ambiguity. In order to overcome this problem, this paper suggests a BPA construction model depending on Gaussian overlap. The main principle behind the approach is the creation of focal elements based on the overlaps between conditional probability distributions of classes, allowing characterisation of uncertainty in a data driven manner. Namely, attribute level evidence is represented by Gaussian distributions, and singleton and composite focal elements are composite focal elements are generated through Gaussian product responses and normalized to obtain BPAs. Composite focal elements are further projected into singleton-level decision scores through proportional belief and plausibility transformations for decision-making and attribute-weight calculation. Moreover, to dynamically modify the role played by different attributes, a Kullback-Leibler (KL) divergence-based weighting scheme is used. These parts combine to form a full pipeline of continuous evidence modeling to BPA generation as proposed by the given method. The experimental results show that the proposed method achieves 98.00 ± 2.67% accuracy on the Iris dataset, 97.21 ± 1.76% accuracy on the Wine dataset, and 90.86 ± 1.20% accuracy on the Breast Cancer Wisconsin dataset. Compared with existing BPA generation methods, the proposed method obtains the best performance on the Iris and Wine datasets. Compared with classical machine learning models, the method also achieves the highest accuracy on the Iris dataset and remains competitive on the Wine and Breast Cancer Wisconsin datasets.