Critique of Recent Uncertainty Measures Developed Under the Evidence Theory and Belief Intervals

Abstract

The theory of evidence (TE) has been largely used for many applications. This theory is a generalization of probability distribution and offers a mathematical representation for two types of uncertainty-based information: 1) discord and 2) nonspecificity. Several measures have already been developed to quantify these two types of uncertainty. They have been called total uncertainty (TU) measures since they quantify both types of uncertainty. The generalized Hartley measure and the maximum entropy have been the only measures so far that satisfy a list of properties very desirable for practical applications. Recently, two new measures of nonspecificity and TU based on belief intervals have been proposed. These two measures do not satisfy the properties of additivity, superadditivity, and subadditivity in the TE. The present critique is about these shortcomings and provides a more complete analysis of those uncertainty measures with respect to a list of desired properties. A potential consequence of an ill-characterized measure may yield selecting an inappropriate rule for decision-making in the processing chain from data to information to decisions.