Decomposition of Possibilistic Belief Functions into Simple Support Functions

  • Matthieu Chemin
  • Agnès Rico
  • Henri Prade
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 107)


In Shafer evidence theory some belief functions, called separable belief functions, can be decomposed in terms of simple support functions. Moreover this decomposition is unique. Recently, a qualitative counterpart to Shafer evidence theory has been proposed. The mass functions in Shafer (addition-based) evidence theory are replaced by basic possibilistic assignments. The sum of weights is no longer 1, but their maximum is equal to 1. In such a context, a maxitive counterpart to belief functions, called possibilistic belief functions can be defined, replacing the addition by the maximum. The possibilistic evidence framework provides a general setting for describing imprecise possibility and necessity measures. This paper investigates a qualitative counterpart of the result about the decomposition of belief functions. Considering the qualitative Möbius transform, conditions for the existence of a decomposition of possibilistic belief functions into simple support functions are presented. Moreover the paper studies the unicity of such a decomposition.


Mass Function Combination Rule Belief Function Fuzzy Measure Evidence Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Matthieu Chemin
    • 1
  • Agnès Rico
    • 2
  • Henri Prade
    • 3
  1. 1.Université Claude Bernard Lyon 1VilleurbanneFrance
  2. 2.ERICBronFrance
  3. 3.IRITToulouse cedex 09France

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