Abstract
Recently, generalized credal sets have been introduced for modeling contradiction (incoherence) in the information. In previous papers, we did not discuss how such information could be updated if some events occur. In this paper, we show that it can be done by the conjunctive rule based on generalized credal sets. We show that the application of generalized credal sets results in several types of conditioning for imprecise probabilities.
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Notes
- 1.
The value \(n.ext({\varPhi ^{(1)}})(f)\) for \(f \in K\) is computed by \(n.ext({\varPhi ^{(1)}})(f) = {\overline{E} _{{\mathbf {P}}({\varPhi ^{(1)}})}}(f)\), where \({\mathbf {P}}({\varPhi ^{(1)}})\) is the usual credal set that corresponds to \({\varPhi ^{(1)}}\).
- 2.
A monotone measure \(\mu \) is called 2-alternating if \(\mu (A) + \mu (B) \geqslant \mu (A \cap B) + \mu (A \cup B)\) for all \(A,B \in {2^X}\).
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Acknowledgment
This work was partially supported by the grant 18-01-00877 of RFBR (Russian Foundation for Basic Research).
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Bronevich, A.G., Rozenberg, I.N. (2019). Conditioning of Imprecise Probabilities Based on Generalized Credal Sets. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_31
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