Disaggregated total uncertainty measure for credal sets

Abstract

We present a new approach to measure uncertainty/information applicable to theories based on convex sets of probability distributions, also called credal sets. A definition of a total disaggregated uncertainty measure on credal sets is proposed in this paper motivated by recent outcomes. This definition is based on the upper and lower values of Shannon's entropy for a credal set. We justify the use of the proposed total uncertainty measure and the parts into which it is divided: the maximum difference of entropies, which can be used as a non-specificity measure (imprecision), and the minimum of entropy, which represents a measure of conflict (contradiction).

Keywords:

• Imprecise probabilities
• Credal sets
• Lower probabilities
• Order-2 capacities
• Theory of evidence
• Uncertainty based information

Acknowledgements

This work has been supported by the Spanish Ministry of Science and Technology under project Algra (TIN2004-06204-C03-02).

Notes

†[email protected]

Additional information

Notes on contributors

G.J. Klir

† †[email protected]