Uncertainty measures for evidential reasoning I: A review

Abstract

This paper is divided into two parts. Part I discusses limitations of the measures of global uncertainty of Lamata and Moral and total uncertainty of Klir and Ramer. We prove several properties of different nonspecificity measures. The computational complexity of different total uncertainty measures is discussed. The need for a new measure of total uncertainty is established in Part I. In Part II, we propose a set of intuitively desirable axioms for a measure of total uncertainty and then derive an expression for the same. Several theorems are proved about the new measure. The proposed measure is additive, and unlike other measures, has a unique maximum. This 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. The computational complexity of the proposed measure is O(N), whereas the previous measures are O(N 2).