Comparative study of contradiction measures in the theory of belief functions

Uncertainty measures in the theory of belief functions are important for the uncertainty representation and reasoning. Many measures of uncertainty in the theory of belief functions have been introduced. The degree of discord (or conflict) inside a body of evidence is an important index for measuring uncertainty degree. Recently, distance of evidence is used to define a contradiction measure for quantifying the degree of discord inside a body of evidence. The contradiction measure is actually the weighted summation of the distance values between a given basic belief assignment (bba) and the categorical bba's defined on each focal element of the given bba redefined in this paper. It has normalized value and can well characterize the self-discord incorporated in bodies of evidence. We propose here, some numerical examples with comparisons among different uncertainty measures are provided, together with related analyses, to show the rationality of the proposed contradiction measure.