Several Results on Set-Valued Possibilistic Distributions

0444153 - ÚI 2016 RIV CZ eng J - Journal Article
Kramosil, Ivan - Daniel, Milan
Several Results on Set-Valued Possibilistic Distributions.
Kybernetika. Roč. 51, č. 3 (2015), s. 391-407. ISSN 0023-5954
R&D Projects: GA ČR GAP202/10/1826
Institutional support: RVO:67985807
Keywords : probability measures * possibility measures * non-numerical uncertainty degrees * set-valued uncertainty degrees * possibilistic uncertainty functions * set-valued entropy functions
Subject RIV: BA - General Mathematics
Impact factor: 0.628, year: 2015
http://dml.cz/handle/10338.dmlcz/144376

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.
Permanent Link: http://hdl.handle.net/11104/0246735