Unifying practical uncertainty representations -- I: Generalized p-boxes

  • Authors:

  • S. Destercke;D. Dubois;E. Chojnacki

  • Affiliations:

  • Institut de Radioprotection et de Sureté Nucléaire (IRSN), 13115 St-Paul Lez Durance, France and Institut de Recherche en Informatique de Toulouse (IRIT), Université Paul Sabatier, ...;Institut de Recherche en Informatique de Toulouse (IRIT), Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France;Institut de Radioprotection et de Sureté Nucléaire (IRSN), 13115 St-Paul Lez Durance, France

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2008

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Abstract

There exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation is equivalent to or can be approximated by other ones. In this paper, we define a generalized form of usual p-boxes. These generalized p-boxes have interesting connections with other previously known representations. In particular, we show that they are equivalent to pairs of possibility distributions, and that they are special kinds of random sets. They are also the missing link between p-boxes and clouds, which are the topic of the second part of this study.