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Title: Several results on set-valued possibilistic distributions (English)
Author: Kramosil, Ivan
Author: Daniel, Milan
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 51
Issue: 3
Year: 2015
Pages: 391-407
Summary lang: English
Category: math
Summary: When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like $\sigma$-additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical uncertainty degrees, at least the following two criteria may be considered. The first criterion should be systems with rather complicated, but sophisticated and nontrivially formally analyzable uncertainty degrees, e. g., uncertainties supported by some algebras or partially ordered structures. Contrarily, we may consider easier relations, which are non-numerical but interpretable on the intuitive level. Well-known examples of such structures are set-valued possibilistic measures. Some specific interesting results in this direction are introduced and analyzed in this contribution. (English)
Keyword: probability measures
Keyword: possibility measures
Keyword: non-numerical uncertainty degrees
Keyword: set-valued uncertainty degrees
Keyword: possibilistic uncertainty functions
Keyword: set-valued entropy functions
MSC: 03E72
MSC: 28E99
MSC: 60A86
MSC: 68T37
MSC: 94A17
idZBL: Zbl 06487086
idMR: MR3391675
DOI: 10.14736/kyb-2015-3-0391
Date available: 2015-09-01T09:07:23Z
Last updated: 2016-01-03
Stable URL:
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