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On set-valued measures
Volume 4, Issues 1-2 (1993), pp. 21–44
Petr Lachout   Milan Studený   Jan Šindelář  

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https://doi.org/10.3233/INF-1993-41-202
Pub. online: 1 January 1993      Type: Research Article     

Published
1 January 1993

Abstract

As a rule, a measure is a mapping from a σ-field of sets into the set of reals, or more generally, into some Banach space. A concept of set-valued measure (SV-measure) is introduced in the paper being a specific mapping from a σ-field of sets into a power set of a set. Properties of SV-measures are analyzed and illustrated on examples. Close relationship between SV-measures and a new nonstandard approach in artificial intelligence (AI) is explained. Then, the construction of factorization of the measures is mentioned, a special class of σ-quasiatomic SV-measures is defined and corresponding characterization theorem is proved. This class involves SV-measures ranging in a countable set which were used in modelling uncertainty in AI. It enables to answer one question arising in connection with this application.

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Keywords
set-valued measure factorization quasiatom of set-valued measure

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INFORMATICA

  • Online ISSN: 1822-8844
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