Uncertainty of interval probabilities and their identification

Abstract

In this paper, we deal with interval probabilities which are the extension of the conventional probabilities. In case of interval probabilities, the uncertainty of information can be measured by two ways; one is the interval entropy which is the extension of the entropy of the conventional probabilities and the other is the amount of ignorance. The interval probabilities can be identified as the Belief and Plausibility functions by the basic probability assignments in the theory of evidence. However, it is difficult for a decision maker to assign basic probabilities for all the subsets of a set of elements. In order to reduce the judgements given by a decision maker, we use the pairwise comparisons for probabilities of pairs of elements to identify them.