A notion of comparative probabilistic entropy based on the possibilistic specificity ordering

  • Authors:

  • Didier Dubois;Eyke Hüllermeier

  • Affiliations:

  • Institut de Recherche en Informatique de Toulouse, France;Faculty of Computer Science, University of Magdeburg, Germany

  • Venue:
  • ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
  • Year:
  • 2005

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Abstract

In this paper, we reconsider the problem of deciding whether one probability distribution is more informative (in the sense of representing a less indeterminate situation) than another one. Instead of using well-established information measures such as the Shannon entropy, however, we take up the idea of comparing probability distributions in a qualitative way. More specifically, we focus on a natural partial ordering induced by what is called the “peakedness” of a distribution. Moreover, there is a close connection between this ordering between probability distributions and the standard specificity ordering on possibility distributions that can be constructed from them. The main result of the paper is a proof showing that possibilistic specificity is consistent with probabilistic entropy in the sense that the (total) ordering defined by the latter refines the (partial) ordering defined by the former.