A new distance measure between two basic probability assignments based on penalty coefficient

Abstract

Uncertainty information processing is a challenging topic in information science. Dempster-Shafer evidence theory shows excellent performance when dealing with uncertainty in information representation, fusion, and processing. The measurement of the distance between the basic probability assignments (BPA) in Dempster-Shafer evidence theory is a powerful tool that deals with uncertainty in evidential information processing. Most of the existing methods are based on the difference in the assessment of evidential degree for different hypotheses, with a notable example Belief-Jensen-Shannon (BJS) divergence. However, these methods ignore the information that is carried by different units in the power sets that represent the hypotheses, i.e., the difference on the hypotheses themselves that include in the evidential degree assessment of different BPA should be considered in the distance measurement. Therefore, in this paper, a novel method grounded in BJS divergence and incorporating a penalty coefficient to rectify the distance between basic probability assignments is proposed. This methodology showcases commendable properties, including symmetry, boundedness, and adherence to the triangle inequality. To demonstrate the efficiency of the proposed distance measurement method between BPAs, we apply it to two common-used machine learning data sets: Iris data set and Dry Beans data set. Compared to the represented existing evidence distance measurement approaches, the proposed method yields superior performance in both data sets with respect to classification accuracy.