Combining Belief Functions Based on Three Mechanisms: Average, Multiplication and Intersection

Applying Dempster´s rule of combination can lead to some counterintuitive results when we combine conflicting evidence. Among most proposed methods that aim to solve this problem, the average method is simple and effective. However, it fails to provide convergence towards certainty. This paper reviews these two methods from a new perspective by investigating three mechanisms used in these methods: average, multiplication and intersection. Then a new combining method integrating these three mechanisms is proposed. The new method contains two parts: the first part is the average of evidences to provide basic estimation, the second part is the multiplication and intersection of evidences to provide convergence, and the result is the integration of both parts with normalization. To balance the two parts, the relative weight of the second part is incorporated to make the degree to converge adjustable. Examples show that the new combining rule can avoid counterintuitive results, achieve convergence and lead to more satisfactory results when compared to some existing approaches.