Measuring mutual aggregate uncertainty in evidence theory

Mutual information as a tool for measuring the amount of dependency is used in many applications in probability theory. But no similar measures have been introduced to calculate the mutual uncertainty between two variables in Dempster-Shafer theory. In this paper three mutual measures based on three uncertainty measures are proposed. These uncertainty measures are: 1) Aggregate Uncertainty (AU) proposed by Klir et al.; 2) Ambiguity Measure (AM) proposed by Jousselme et al.; and 3) Modified Ambiguity Measure (MAM) that is proposed in this paper. MAM is the modification of AM that resolves the non-subadditivity problem of AM. A threat assessment problem constructed by Dempster-Shafer network is used for testing these mutual measures. We use the proposed mutual measures to identify which input variables of the network are more influential on the threat value. Finally it is concluded that mutual uncertainty based on MAM is a justifiable measure to compute the relevancy in decision making applications.