A new method to determine basic probability assignment from training data

Abstract

The Dempster–Shafer evidence theory (D–S theory) is one of the primary tools for knowledge representation and uncertain reasoning, and has been widely used in many information fusion systems. However, how to determine the basic probability assignment (BPA), which is the main and first step in D–S theory, is still an open issue. In this paper, based on the normal distribution, a method to obtain BPA is proposed. The training data are used to build a normal distribution-based model for each attribute of the data. Then, a nested structure BPA function can be constructed, using the relationship between the test data and the normal distribution model. A normality test and normality transformation are integrated into the proposed method to handle non-normal data. The missing attribute values in datasets are addressed as ignorance in the framework of the evidence theory. Several benchmark pattern classification problems are used to demonstrate the proposed method and to compare against existing methods. Experiments provide encouraging results in terms of classification accuracy, and the proposed method is seen to perform well without a large amount of training data.