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.

Keywords:

• Imprecise probabilities
• Credal sets
• Order-2 capacities
• Theory of evidence
• Uncertainty
• Entropy

Notes

^‡[email protected]

^†This work has been supported by the Spanish Ministry of Science and Technology under project Elvira II (TIC2001-2973-C05-01).

^†This work has been supported by the Spanish Ministry of Science and Technology under project Elvira II (TIC2001-2973-C05-01).

^† In Abellan and Moral (2000) we claimed that IG was subadditive for general credal sets, but there is an error in the proof and the counterexample is also applicable to show that IG is not subadditive for general credal sets.

^‡ Considering that we can not consider subadditivity a reasonable property for non-specificity measures in the case of general credal sets.

Joaquín Abellán received his Ph. D. degree in January of 2003 from the University of Granada. He is an assistant professor of Computer Science and Artificial Intelligence at the University of Granada. His current research interests are representation of the uncertainty through convex sets of probability distributions and its applications to classification.

Serafín Moral received his Ph. D. degree in 1984 from the University of Granada. He is a professor of Computer Science and Artificial Intelligence and member of the research group on Uncertainty Treatment on Artificial Intelligence (UTAI) at the University of Granada. His current research interests are imprecise probabilities, propagation algorithms in dependence graphs and uncertainty and defeasible reasoning in general.

Additional information

Notes on contributors

Serafín Moral ‡

‡[email protected] †This work has been supported by the Spanish Ministry of Science and Technology under project Elvira II (TIC2001-2973-C05-01).