Convex MV-algebras: many-valued logics meet decision theory
type: Item
instance of: scholarly article
title: Convex MV-algebras: many-valued logics meet decision theory
zbMATH Open document ID: 1475.06007
author: S. Lapenta
author: Tommaso Flaminio
author: H. Hosni
published in: Studia Logica
publication date: 2018-10-31T00:00:00Z
review text: In order to have logico-algebraic instruments in the framework of decision theory under uncertainty, the authors introduce the notion of convex combination in MV-algebras. In particular they define algebraic structures obtained by adding to MV-algebras a family of binary operations, indexed by real numbers \(\alpha \in [0,1]\), playing the role of convex combination of two points with parameter \(\alpha\). The obtained class of algebraic structures, called MV-algebras with convexity operators, are shown to be term equivalent to Riesz MV-algebras. Some results for such class are proved, as for example that no countable MV-algebra can be equipped with a family of convexity operators. Finally, MV-algebras with convexity operators are shown to be useful to approach the foundations of decision theory under uncertainty, in particula to give a logico-algebraic representation of the Anscombe-Aumann problem.
reviewed by: Brunella Gerla
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 91B06
zbMATH DE Number: 6969626
zbMATH Keywords: MV-algebras
zbMATH Keywords: convexity
zbMATH Keywords: uncertainty measures
zbMATH Keywords: Anscombe-Aumann problem
MaRDI profile type: Publication
full work available at URL: s11225-016-9705-9
OpenAlex ID: W2589427740
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DOI: 10.1007/S11225-016-9705-9
description: scientific article; zbMATH DE number 6969626