A complete characterization of all weakly additive measures and of all valuations on the canonical extension of any finite MV-chain
type: Item
instance of: scholarly article
title: A complete characterization of all weakly additive measures and of all valuations on the canonical extension of any finite MV-chain
zbMATH Open document ID: 1195.06008
author: S. Weber
published in: Fuzzy Sets and Systems
publication date: 2010-05-07T00:00:00Z
review text: A Girard algebra is a commutative lattice-ordered semigroup satisfying some properties; every MV-algebra is a Girard algebra. Let \(m\) is a mapping from a Girard algebra \(L\) to the unit interval, \(m\) be isotone, \(m(a')= 1- m(a)\), \(m(0)= 0\), \(m(1)= 1\). The mapping \(m\) is called weakly additive if it fulfills the additivity condition on all MV-subalgebras of \(L\). The author proves the existence of weakly additive extensions from MV chains in \(L\). This is interesting because of the non-existence of strongly additive measure extensions [\textit{S. Weber}, Fuzzy Sets Syst. 160, No. 3, 371--383 (2009; Zbl 1180.28012)].
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 5705405
zbMATH Keywords: MV-algebra
zbMATH Keywords: finite MV-chain
zbMATH Keywords: Girard algebra
zbMATH Keywords: canonical extension
zbMATH Keywords: uncertainty measure
zbMATH Keywords: additive measure
zbMATH Keywords: state
zbMATH Keywords: valuation
zbMATH Keywords: weakly additive measure
MaRDI profile type: Publication
full work available at URL: j.fss.2009.06.004
OpenAlex ID: W2012618254
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DOI: 10.1016/J.FSS.2009.06.004
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description: scientific article; zbMATH DE number 5705405