Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion
type: Item
instance of: scholarly article
title: Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion
zbMATH Open document ID: 0669.90003
DOI: 10.1016/0165-4896(89)90056-5
author: Alain Chateauneuf
author: Jean-Yves Jaffray
published in: Mathematical Social Sciences
publication date: 1989-01-01T00:00:00Z
review text: Monotone capacities (on finite sets) of finite or infinite order (lower probabilities) are characterized by properties of their Möbius inverses. A necessary property of probabilities dominating a given capacity is demonstrated through the use of Gale's theorem for the transshipment problem. This property is shown to be also sufficient if and only if the capacity is monotone of infinite order. A characterization of dominating probabilities specific to capacities of order 2 is also proved.
Mathematics Subject Classification ID: 91B06
zbMATH DE Number: 4097064
zbMATH Keywords: belief functions
zbMATH Keywords: representation of uncertainty
zbMATH Keywords: Monotone capacities
zbMATH Keywords: lower probabilities
zbMATH Keywords: Möbius inverses
zbMATH Keywords: transshipment problem
zbMATH Keywords: dominating probabilities
MaRDI profile type: Publication
full work available at URL: 0165-4896(89)90056-5
OpenAlex ID: W3122552476
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description: scientific article; zbMATH DE number 4097064