Extreme lower probabilities

Erik Quaeghebeur; Gert de Cooman

doi:10.1007/3-540-34777-1_26

Extreme lower probabilities

Erik Quaeghebeur
, Gert de Cooman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

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 language	English
Title of host publication	Soft Methods for Integrated Uncertainty Modelling
Editors	Jonathan Lawry, Enrique Miranda, Alberto Bugarin, Shoumei Li, Maria Angeles Gil, Przemysaw Grzegorzewski, Olgierd Hyrniewicz
Pages	211-221
Number of pages	11
DOIs	https://doi.org/10.1007/3-540-34777-1_26
Publication status	Published - 2006
Externally published	Yes

Publication series

Name	Advances in Soft Computing
Volume	37
ISSN (Print)	1615-3871
ISSN (Electronic)	1860-0794

Funding

This paper presents research results of the Belgian Program on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its authors. ∗Corresponding author. E-mail addresses: [email protected] (E. Quaeghebeur), [email protected] (G. de Cooman) 1Research financed by a Ph.D. grant from the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen).

Keywords

Extreme points
Imprecise probabilities
Lower probabilities

Access to Document

10.1007/3-540-34777-1_26

http://hdl.handle.net/1854/LU-406341

Cite this

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title = "Extreme lower probabilities",

abstract = "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.",

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Extreme lower probabilities. / Quaeghebeur, Erik; de Cooman, Gert.
Soft Methods for Integrated Uncertainty Modelling. ed. / Jonathan Lawry; Enrique Miranda; Alberto Bugarin; Shoumei Li; Maria Angeles Gil; Przemysaw Grzegorzewski; Olgierd Hyrniewicz. 2006. p. 211-221 (Advances in Soft Computing; Vol. 37).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - 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.

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Extreme lower probabilities

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Keywords

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