Abstract
Given a real-valued random variable defined on a probability space \(\langle {\Omega}, \mathcal{A}, P \rangle\) and given a subset A of the space Ω of all elementary random events, an ω 0 ∈ Ω is called possibly favourable to A with respect to X, if it belongs to the subset A X of Ω with this property: for every \(\omega \in A^X, X(\omega) \leq sup_{\omega_1 \in A} X(\omega_1)\) holds. The mapping Π ascribing to each A⊂Ω the value P(A X), i.e., the probability of the set of all elementary random events possibly favorable to A w.r.to X, defines a possibilistic measure on the power-set of all subsets of Ω. Having at hand two random variables X and Y defined on \(\langle {\Omega}, \mathcal{A}, P \rangle\) and repeating our reasoning with A replaced by A X and with X replaced by Y, we arrive at the idea of second-level possibilistic measures induced by random variables.
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Kramosil, I. (2005). Second-Level Possibilistic Measures Induced by Random Variables. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_74
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DOI: https://doi.org/10.1007/11518655_74
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