Difference of entropies as a non-specificity function on credal sets†

Abstract

This paper proposes the use of the maximum difference of entropies as a non-specificity measure for credal sets and studies its properties. The main advantage of the new measure is that it does not only take into account the absolute imprecision of the credal set, but also the position of the credal set with respect to the uniform distribution. The paper provides an algorithm to compute the most difficult part of the difference of entropies, the minimum of entropy. The algorithm computes the exact minimum of entropy for order-2 capacities and it is based on the branch and bound technique with some additional procedures to prune the search.