Kybernetika 51 no. 3, 391-407, 2015

Several results on set-valued possibilistic distributions

Ivan Kramosil and Milan DanielDOI: 10.14736/kyb-2015-3-0391


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.


probability measures, possibility measures, non-numerical uncertainty degrees, set-valued uncertainty degrees, possibilistic uncertainty functions, set-valued entropy functions


03E72, 28E99, 68T37, 94A17


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