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Non additive ordinal relations representable by lower or upper probabilities

Andrea Capotorti;  Giulianella Coletti;  Barbara Vantaggi — 1998

Kybernetika

We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means...

Standard and nonstandard representability of positive uncertainty orderings

Andrea Capotorti;  Giulianella Coletti;  Barbara Vantaggi — 2014

Kybernetika

Axioms are given for positive comparative probabilities and plausibilities defined either on Boolean algebras or on arbitrary sets of events. These axioms allow to characterize binary relations representable by either standard or nonstandard measures (i. e. taking values either on the real field or on a hyperreal field). We also study relations between conditional events induced by preferences on conditional acts.

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