Non-atomic fuzzy measures and games
type: Item
instance of: scholarly article
title: Non-atomic fuzzy measures and games
zbMATH Open document ID: 0584.90103
DOI: 10.1016/0165-0114(85)90005-3
published in: Fuzzy Sets and Systems
publication date: 1985-01-01T00:00:00Z
review text: Lyapunov's Theorem for fuzzy measures is proved and it is applied to extend a theorem of \textit{R. J. Aumann} and \textit{L. S. Shapley} [''Values of non-atomic games'' (1974; Zbl 0311.90084)] concerning the existence of the value for non-atomic games. Precisely, it is proved that the range of any non-atomic n-vector fuzzy measure (in the sense of the author [ibid. 10, 135-155 (1983; Zbl 0528.28009)]) is convex and compact and it is shown that this result allows to extend Theorem B from the book cited above (p. 23) from games with unambiguous coalitions to games with fuzzy coalitions (called fuzzy games) defined on \(\sigma\)-algebras of fuzzy sets (which are not necessarily \(\sigma\)-algebras of 'ideal sets').
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 3936971
zbMATH Keywords: Aumann-Shapley value
zbMATH Keywords: Lyapunov's Theorem for fuzzy measures
zbMATH Keywords: existence of the value for non-atomic games
zbMATH Keywords: non-atomic n-vector fuzzy measure
zbMATH Keywords: fuzzy coalitions
zbMATH Keywords: fuzzy games
zbMATH Keywords: \(\sigma \) -algebras of fuzzy sets
author: Dan Butnariu
MaRDI profile type: Publication
full work available at URL: 0165-0114(85)90005-3
OpenAlex ID: W2059426583
cites work: Q4051958
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description: scientific article; zbMATH DE number 3936971