Consonant Belief Function Induced by a Confidence Set of Pignistic Probabilities

  • Astride Aregui
  • Thierry Denoeux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4724)


A new method is proposed for building a predictive belief function from statistical data in the Transferable Belief Model framework. The starting point of this method is the assumption that, if the probability distribution ℙ X of a random variable X is known, then the belief function quantifying our belief regarding a future realization of X should have its pignistic probability distribution equal to ℙ X . When PX is unknown but a random sample of X is available, it is possible to build a set \(\mathcal{P}\) of probability distributions containing ℙ X with some confidence level. Following the Least Commitment Principle, we then look for a belief function less committed than all belief functions with pignistic probability distribution in \(\mathcal{P}\). Our method selects the most committed consonant belief function verifying this property. This general principle is applied to the case of the normal distribution.


Dempster-Shafer theory Evidence theory Transferable BeliefModel possibility distribution statistical data 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Astride Aregui
    • 1
    • 2
  • Thierry Denoeux
    • 1
  1. 1.HEUDIASYC, UTC, CNRS Centre de Recherche de RoyallieuCompiègneFrance
  2. 2.CIRSEE, Suez EnvironnementLe PecqFrance

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