A correlation coefficient for belief functions

How to manage conflict is still an open issue in Dempster–Shafer (D-S) evidence theory. The conflict coefficient k in D-S evidence theory cannot represent conflict reasonably, especially sometimes two Basic Probability Assignments (BPAs) are identical but k is not zero. Jousselme distance can well measure the similarity or conflict between two BPAs but it becomes invalid in some cases. Some scholars introduced the concept of correlation coefficient to measure the similarity of two BPAs. However, existing correlation coefficients of BPAs are unstable or insensitive to quantify the conflict and sometimes deduce wrong results. In this paper, a novel correlation coefficient is proposed which takes into consideration both the non-intersection and the difference among the focal elements. It satisfies all the requirements for a metric. Some numerical examples and comparisons of this paper demonstrate the effectiveness of the correlation coefficient.