Study on the Basic Probability Assignment Based on Grey Relational Analysis and Gaussian Membership

Abstract

Dempster-Shafer(D-S) evidence theory is one of the most widely used methods in the field of data fusion. The key step in applying D-S evidence theory is to determine the basic probability assignment(BPA), but how to determine it appropriately is still a problem to be solved. In this paper, a novel method to determine the BPA is proposed. Firstly, a method to obtain the initial BPA by combining weighted grey correlation degrees and Gaussian membership degrees is proposed. The initial BPA is obtained by constructing the integration form between the weighted grey correlation degrees and the Gaussian membership degrees, and applying the Bayesian optimization algorithm to obtain the better adjusting parameter. Secondly, a BPA reconstruction process is introduced. The BPA is reconstructed by using the matching degrees between the initial BPA and the BPA benchmarks. Finally, the reconstructed BPA is combined by applying Dempster’s combination rule. The conflicts between the BPA of different attributes can be mitigated during the process of restructuring the initial BPA, which can prevent from getting a counterintuitive result. By applying this method to the classification experiments on UCI datasets, the results confirmed that this method can effectively improve the classification performance.