Extreme lower probabilities

Erik Quaeghebeur, Gert de Cooman

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2163-2175
Number of pages13
JournalFuzzy Sets and Systems
Issue number16
Publication statusPublished - 16 Aug 2008
Externally publishedYes


  • Combinatorial problems
  • Extreme points
  • Imprecise probabilities
  • Lower probabilities
  • Non-additive measures


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