A Matrix Method of Basic Belief Assignment's Negation in Dempster–Shafer Theory

Negation is a new perspective to represent knowledge. The negation of probability distribution has been proposed, and it has a lot of interesting properties, which can reach a maximum entropy. Because of the defects of the classical probability theory in the expression of uncertainty, the basic belief assignment (BBA) in the Dempster-Shafer theory (D-S theory) are widely used in decision theory. Thus, negation provides a new perspective for D-S theory to measure fuzziness. In this paper, a new definition of negation of BBA is presented. In the proposed negation, BBAs are represented as vectors, and negation is realized by matrix operators. This method has a good interpretation of the matrix operators and has the merit of simplifying the problem. With several different definitions of entropy to determinate the uncertainty of BBA, the proposed negation of BBA can reach a maximum belief entropy when the entropies satisfy a certain property.