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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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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