Extreme lower probabilities

Erik Quaeghebeur, Gert de Cooman

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


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
Title of host publicationSoft Methods for Integrated Uncertainty Modelling
EditorsJonathan Lawry, Enrique Miranda, Alberto Bugarin, Shoumei Li, Maria Angeles Gil, Przemysaw Grzegorzewski, Olgierd Hyrniewicz
Number of pages11
Publication statusPublished - 2006
Externally publishedYes

Publication series

NameAdvances in Soft Computing
ISSN (Print)1615-3871
ISSN (Electronic)1860-0794


  • Extreme points
  • Imprecise probabilities
  • Lower probabilities

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