Possibility Theory and its Applications: a Retrospective and Prospective view

  • Didier Dubois
  • Henri Prade
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 482)


This paper provides an overview of possibility theory, emphasising its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. It has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.


Belief Function Possibility Distribution Fuzzy Random Variable Possibility Theory Possibility Measure 


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© CISM, Udine 2006

Authors and Affiliations

  • Didier Dubois
    • 1
  • Henri Prade
    • 1
  1. 1.IRIT-CNRSUniversite Paul SabatierToulouseFrance

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