Extreme Lower Probabilities

  • Erik Quaeghebeur
  • Gert de Cooman
Part of the Advances in Soft Computing book series (AINSC, volume 37)


We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets – the extreme lower probabilities – can be calculated and we give an illustration of our results.


Lower Probability Extreme Point Redundant Constraint Vertex Enumeration Imprecise Probability 
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Copyright information

© Springer 2006

Authors and Affiliations

  • Erik Quaeghebeur
    • 1
  • Gert de Cooman
    1. 1.EESA Department, SYSTeMS Research Group Technologiepark-Zwijnaarde 914Ghent UniversityZwijnaardeBelgium

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