NON ADDITIVE ORDINAL RELATIONS REPRESENTABLE BY LOWER OR UPPER PROBABILITIES

We characterize (in terms of necessary and sufficient conditions) bina ry 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 b elief function). Moreover we characterize relations representable by u pper probabilities and those representable by plausibility. In fact th e conditions characterizing these relations are not immediately deduci ble by means of ''dual'' conditions given on the contrary events, like in the numerical case.