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Non additive ordinal relations representable by lower or upper probabilities. (English) Zbl 1274.68518
Summary: 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.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
03B48 Probability and inductive logic
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