Mutual Information and Kullback-Leibler Divergence in the Dempster-Shafer Theory

In probability theory, the mutual information between two discrete random variables, X and Y, measures the average reduction in uncertainty about Y when we learn the value of X. It is defined using the Shannon entropy of probability distributions. This paper defines a corresponding concept of mutual information between two variables in the Dempster-Shafer (D-S) belief function theory using the decomposable entropy defined by Jirousek and Shenoy. We also define the Kullback-Liebler (KL) divergence for the D-S theory as similar to the KL divergence for probability theory.