Reliable Computing

, Volume 10, Issue 4, pp 273–297

Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities

  • Didier Dubois
  • Laurent Foulloy
  • Gilles Mauris
  • Henri Prade
Article

DOI: 10.1023/B:REOM.0000032115.22510.b5

Cite this article as:
Dubois, D., Foulloy, L., Mauris, G. et al. Reliable Computing (2004) 10: 273. doi:10.1023/B:REOM.0000032115.22510.b5

Abstract

A possibility measure can encode a family of probability measures. This fact is the basis for a transformation of a probability distribution into a possibility distribution that generalises the notion of best interval substitute to a probability distribution with prescribed confidence. This paper describes new properties of this transformation, by relating it with the well-known probability inequalities of Bienaymé-Chebychev and Camp-Meidel. The paper also provides a justification of symmetric triangular fuzzy numbers in the spirit of such inequalities. It shows that the cuts of such a triangular fuzzy number contains the “confidence intervals” of any symmetric probability distribution with the same mode and support. This result is also the basis of a fuzzy approach to the representation of uncertainty in measurement. It consists in representing measurements by a family of nested intervals with various confidence levels. From the operational point of view, the proposed representation is compatible with the recommendations of the ISO Guide for the expression of uncertainty in physical measurement.

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Didier Dubois
    • 1
  • Laurent Foulloy
    • 2
  • Gilles Mauris
    • 2
  • Henri Prade
    • 1
  1. 1.Institut de Recherche en Informatique de Toulouse IRITUniversite Paul SabatierToulouseFrance
  2. 2.Laboratoire d'Informatique, Systemes, Traitement de l'Information et de la Connaissance, LISTICUniversite de SavoieAnnecyFrance