The Improved Combination Rule of D Numbers and Its Application in Radiation Source Identification

Abstract

The D numbers theory is a novel theory to express uncertain information. It successfully overcomes some shortcomings of Dempster-Shafer theory, such as the conditions of exclusiveness hypothesis and completeness constraint. However, the combination rule of D numbers does not satisfy the associative property, which leads to limitations in practical application for D numbers. In this paper, the improved D numbers theory is proposed to overcome the weakness based on the analysis of D numbers’ combination rule. A new algorithm is constructed with the strict proof to simplify the combination rule. The similarities and differences among DS theory, D numbers, and the improved D numbers are introduced with the numerical analysis. An illustrative example of the radiation source identification is presented to demonstrate the effectiveness of the improved method.