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\(T\)-conditional possibilities: coherence and inference. (English) Zbl 1178.60006
Summary: We refer to an axiomatic definition of \(T\)-conditional possibility, where \(T\) is any \(t\)-norm. We characterize a full \(T\)-conditional possibility in terms of a suitable set of unconditional possibilities. Starting from this characterization we are able to manage coherent conditional possibility assessments and their enlargements. To compare \(T\)-conditional possibility related to different \(t\)-norm \(T\), we study binary relations locally representable by a \(T\)-conditional possibility.

MSC:
60A86 Fuzzy probability
60A05 Axioms; other general questions in probability
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[1] Amor, N.B.; Mellouli, K.; Benferhat, S.; Dubois, D.; Prade, H., A theoretical framework for possibilistic independence in a weakly ordered setting, Internat. J. uncertainty fuzziness knowledge-based systems, 10, 2, 117-155, (2002) · Zbl 1084.68126
[2] Benferhat, S.; Dubois, D.; Prade, H., Expressing independence in a possibilistic framework and its application to default reasoning, (), 150-154
[3] Bouchon-Meunier, B.; Coletti, G.; Marsala, C., Independence and possibilistic conditioning, Ann. math. artificial intelligence, 35, 107-124, (2002) · Zbl 1004.60001
[4] Coletti, G.; Scozzafava, R., The role of coherence in eliciting and handling ‘imprecise’ probabilities and its application to medical diagnosis, Inform. sci., 130, 41-65, (2000) · Zbl 0984.68155
[5] G. Coletti, R. Scozzafava, Probabilistic logic in a coherent setting, in: Trends in Logic, vol. 15, Kluwer, Dordrecht, Boston, London, 2002. · Zbl 1005.60007
[6] G. Coletti, B. Vantaggi, Comparative conditional possibilities, in: L. Godo (Ed.), Lecture Notes in Computer Science, vol. LNAI 3571, 2005, pp. 872-883. · Zbl 1113.68511
[7] Coletti, G.; Vantaggi, B., Possibility theory: conditional independence, Fuzzy sets and systems, 157, 1491-1513, (2006) · Zbl 1092.68094
[8] Coletti, G.; Vantaggi, B., Comparative models ruled by possibility and necessity: A conditional world, Internat. J. approx. reason., 45, 341-363, (2007) · Zbl 1122.68132
[9] Coletti, G.; Vantaggi, B., A view on conditional measures through local representability of binary relations, Int. J. approx. reason., 47, 268-283, (2008) · Zbl 1184.68500
[10] De Baets, B.; Tsiporkova, E.; Mesiar, R., Conditioning in possibility theory with strict order norms, Fuzzy sets and systems, 106, 221-229, (1999) · Zbl 0985.28015
[11] de Cooman, G., Possibility theory II: conditional possibility, Internat. J. gen. systems, 25, 325-351, (1997) · Zbl 0955.28013
[12] de Finetti, B., Sul significato soggettivo Della probabilità, Fund. math., 17, 293-329, (1931) · JFM 57.0608.07
[13] de Finetti, B., Sull’impostazione assiomatica del calcolo delle probabilitá, Ann. univ. di trieste, 19, 29-81, (1949), (English Trans.: Probability, Induction, Statistics, Wiley, London, 1972, Ch. 5) · Zbl 0036.20703
[14] Dubois, D., Belief structure, possibility theory and decomposable confidence measures on finite sets, Comput. artificial intelligence, 5, 403-416, (1986) · Zbl 0657.60006
[15] D. Dubois, L. Fariñas del Cerro, A. Herzig, H. Prade, An ordinal view of independence with application to plausible reasoning, in: R. Lopez de Mantaras, D. Poole (Eds.), Proc. of the 10th Conf. on Uncertainty in Artificial Intelligence, Seattle, WA, July 29-31, 1994, pp. 195-203.
[16] Dubois, D.; Prade, H., Possibility theory, (1988), Plenum Press New York · Zbl 0645.68108
[17] Dubois, D.; Prade, H., The logical view of conditioning and its application to possibility and evidence theories, Internat. J. approx. reason., 4, 23-46, (1990) · Zbl 0696.03006
[18] Dubois, D.; Prade, H., Bayesian conditioning in possibility theory, Fuzzy sets and systems, 92, 223-240, (1997) · Zbl 1053.62503
[19] Ferracuti, L.; Vantaggi, B., Independence and conditional possibilities for strictly monotone triangular norms, Internat. J. intelligent systems, 21, 299-323, (2006) · Zbl 1088.60003
[20] Goodman, I.R.; Nguyen, H.T., Conditional objects and the modeling of uncertainties, (), 119-138
[21] Hisdal, E., Conditional possibilities independence and noninteraction, Fuzzy sets and systems, 1, 283-297, (1978) · Zbl 0393.94050
[22] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norms, (2000), Kluwer Dordrecht · Zbl 0972.03002
[23] Koopman, B.O., The axioms and algebra of intuitive probability, Ann. math., 41, 269-292, (1940) · Zbl 0024.05001
[24] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
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