Uncertainty measures for evidential reasoning II: A new measure of total uncertainty

Abstract

In Part I we discussed limitations of two measures of global (non-fuzzy) uncertainty of Lamata and Moral, and a measure of total (non-fuzzy) uncertainty due to Klir and Ramer and established the need for a new measure. In this paper we propose a set of intuitively desirable axioms for a measure of total uncertainty (TU) associated with a basic assignment m(A), and then derive an expression for a (unique) function that satisfies these requirements. Several theorems are proved about the new measure. Our measure is additive, and unlike other TU measures, has a unique maximum. The new measure reduces to Shannon's probabilistic entropy when the basic probability assignment focuses only on singletons. On the other hand, complete ignorance—basic assignment focusing only on the entire set, as a whole—reduces it to Hartley's measure of information. We show that the computational complexity of the new measure is O(N), whereas previous measures of TU are O(N 2). Finally, we compare the new measure to its predecessors by extending the numerical example of Part I so that it includes values of the new measure.