Abstract
By means of a logical condition between two partitions \(\mathcal{L}\) and \({\mathcal{L}}\) (“weak logical independence”), we find connections between probabilities and possibilities. We show that the upper envelope of the extensions of a probability on \({\mathcal{L}}\) is a possibility on the algebra generated by \({\mathcal{L}^\prime}\). Moreover we characterize the set of possibilities obtained as extensions of a coherent probability on an arbitrary set: in particular, we find the two “extreme” (i.e., dominated and dominating) possibilities.
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References
Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting. Trends in Logic, vol. 15. Kluwer Academic Publishers, Dordrecht (2002)
Coletti, G., Scozzafava, R.: Toward a general theory of conditional beliefs. Internat. J. Intelligent. Syst. 21, 229–259 (2006)
Coletti, G., Scozzafava, R., Vantaggi, B.: Possibility measures through a probabilistic inferential process. In: Barone, J., Tastle, B., Yager, R. (eds.) Proceedings of North America Fuzzy Information Processing Society 2008 (NAFIPS 2008, New York, USA), IEEE CN: CFP08750-CDR Omnipress (2008)
Coletti, G., Vantaggi, B.: T-conditional possibilities: coherence and inference. Fuzzy Sets Syst. (in press, 2008) doi:10.1016/j.fss.2008.04.006
De Cooman, G., Troffaes, M., Miranda, E.: n-Monotone lower previsions and lower integrals. In: Cozman, F.G., Nau, R., Seidenfeld, T. (eds.) Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications (ISIPTA 2005, Pittsburgh, Pennsylvania, USA), pp. 145–154 (2005)
De Finetti, B.: Teoria della probabilitá. Einaudi, Torino. In: Theory of Probability: A Critical Introductory Treatment, John Wiley & Sons, Chichester (1970) (Engl. Transl. 1974)
Delgado, M., Moral, S.: On the concept of possibility-probability consistency. Fuzzy Sets Syst. 21(3), 311–318 (1987)
Dubois, D., Nguyen, H.T., Prade, H.: Possibility theory, probability and fuzzy sets: misunderstandings, bridges and gaps. In: Dubois, D., Prade, H. (eds.) Fundamentals of Fuzzy Sets. The Handbooks of Fuzzy Sets, vol. 7, pp. 343–438. Kluwer Academic, Dordrecht (2000)
Dubois, D., Prade, H.: When upper probabilities are possibility measures. Fuzzy Sets Syst. 49, 65–74 (1992)
Dubois, D., Prade, H.: Qualitative possibility theory and its probabilistic connections. In: Grzegorzewski, P., Hryniewicz, O., Gil, M.A. (eds.) Soft Methods in Probability, Statistics and Data Analysis, pp. 3–26. Physica Verlag, Heidelberg-Germany (2002)
Dubois, D., Prade, H., Smets, P.: A definition of subjective possibility. Operacyjne I Decyzje (Pologne) 4, 7–22 (2003)
Shapley, L.S.: Cores of convex games. Internat. J. Game Theory 1, 11–26 (1971)
Sudkamp, T.: On probability-possibility transformations. Fuzzy Sets Syst. 51(1), 311–318 (1992)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
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Coletti, G., Scozzafava, R., Vantaggi, B. (2008). Possibility Measures in Probabilistic Inference. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_7
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DOI: https://doi.org/10.1007/978-3-540-85027-4_7
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