Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Possibility Theory

  • Didier Dubois
  • Henri Prade
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_413

Definition of the Subject

Possibility theory is the simplest uncertainty theory devoted to the modeling of incomplete information. It is characterized by the use of two basic dual set functions that respectively grade the possibility and the necessity of events. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory is closely related to fuzzy sets if one considers that a possibility distribution is a particular fuzzy set (of mutually exclusive) possible values. However fuzzy sets and fuzzy logic are primarily motivated by the representation of gradual properties while possibility theory handles the uncertainty of classical (or fuzzy) propositions. 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...

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Didier Dubois
    • 1
  • Henri Prade
    • 1
  1. 1.IRIT-CNRSUniversite Paul SabatierToulouse CedexFrance