Capotorti, Andrea; Coletti, Giulianella; Vantaggi, Barbara Non additive ordinal relations representable by lower or upper probabilities. (English) Zbl 1274.68518 Kybernetika 34, No. 1, 79-90 (1998). 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. Cited in 5 Documents MSC: 68T37 Reasoning under uncertainty in the context of artificial intelligence 03B48 Probability and inductive logic Keywords:coherent lower probability PDF BibTeX XML Cite \textit{A. Capotorti} et al., Kybernetika 34, No. 1, 79--90 (1998; Zbl 1274.68518) Full Text: Link References: [1] Coletti G.: Coherent qualitative probability. J. Math. Psych. 34 (1990), 297-310 · Zbl 0713.60003 · doi:10.1016/0022-2496(90)90034-7 [2] Coletti G.: Non additive ordinal relations representable by conditional probabilities and their use in expert systems. Proceedings 6th International Conference IPMU’96, 1 (1996), pp. 43-48 [3] Dubois D.: Belief structure, possibility theory and decomposable confidence measures on finite sets. Comput. Artificial Intelligence 5 (1986), 5, 403-416 · Zbl 0657.60006 [4] Finetti B. de: Sul Significato Soggettivo della Probabilità. Fundamenta Matematicae 17 (1931), 293-329 · Zbl 0003.16303 · eudml:212523 [5] Koopman B. O.: The axioms and algebra of intuitive probability. Ann. Math. 41 (1940), 269-292 · Zbl 0024.05001 · doi:10.2307/1969003 [6] Kraft C. H., Pratt J. W., Seidenberg A.: Intuitive probabilities on finite sets. Ann. Math. Statist. 30 (1959), 408-419 · Zbl 0173.19606 · doi:10.1214/aoms/1177706260 [7] Regoli G.: Rational Comparison and Numerical Representation. Decision Theory and Decision Analysis: Trends and challenges. Academic Publishers, Dordrecht 1994 [8] Scott D.: Measurement structures and linear inequalities. J. Math. Psych. 1 (1964), 233-247 · Zbl 0129.12102 · doi:10.1016/0022-2496(64)90002-1 [9] Walley P.: Statistical Reasoning with Imprecise Probabilities. Chapman & Hall, London 1990 · Zbl 0732.62004 [10] Wong S. K. M., Yao Y. Y., Bollmann P., Bürger H. C.: Axiomatization of qualitative belief structure. IEEE Trans. Systems Man Cybernet. 21 (1991), 726-734 · Zbl 0737.60006 · doi:10.1109/21.108290 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.