Geodesic
Non additive ordinal relations representable by lower or upper probabilities
Kybernetika, Tome 34 (1998) no. 1, pp. 79-90 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 of “dual” conditions given on the contrary events, like in the numerical case.
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 of “dual” conditions given on the contrary events, like in the numerical case.
Classification : 03B48, 68T30, 68T37
Keywords: coherent lower probability 
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Capotorti, Andrea; Coletti, Giulianella; Vantaggi, Barbara. Non additive ordinal relations representable by lower or upper probabilities. Kybernetika, Tome 34 (1998) no. 1, pp. 79-90. http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a7/

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