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Random Sets pp 107-127 | Cite as

On the Maximum of Conditional Entropy for Upper/Lower Probabilities Generated by Random Sets

  • Jean-Yves Jaffray
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 97)

Abstract

Imprecision on probabilities is expressed through upper/lower probability intervals. The lower probability is always assumed to be a convex capacity and sometimes to be an m—monotone capacity. A justification of this latter assumption based on the existence of underlying random sets is given. Standard uncertainty measures of information theory, such as the Shannon entropy and other indices consistent with the Lorenz ordering, are extended to imprecise probability situations by taking their worst-case evaluation, which is shown to be achieved for a common probability. In the same spirit, the information brought by a question is evaluated by the maximum value of the associated conditional entropy. Computational aspects, which involve the resolution of decomposable convex programs, are discussed.

Key words

Ambiguity Capacities Conditioning Entropy Random Sets Uncertainty Upper/Lower Probabilities 

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Jean-Yves Jaffray
    • 1
  1. 1.LIP6, Université Paris VIParis Cedex 05France

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