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- W2890339901 abstract "In this paper we consider, in the framework of coherence, four different definitions of conjunction among conditional events. In each of these definitions the conjunction is still a conditional event. We first recall the different definitions of conjunction; then, given a coherent probability assessment (x, y) on a family of two conditional events $${A|H,B|K}$$ , for each conjunction $$(A|H) wedge (B|K)$$ we determine the (best) lower and upper bounds for the extension $$z=P[(A|H) wedge (B|K)]$$ . We show that, in general, these lower and upper bounds differ from the classical Fréchet-Hoeffding bounds. Moreover, we recall a notion of conjunction studied in recent papers, such that the result of conjunction of two conditional events A|H and B|K is (not a conditional event, but) a suitable conditional random quantity, with values in the interval [0, 1]. Then, we remark that for this conjunction, among other properties, the Fréchet-Hoeffding bounds are preserved." @default.
- W2890339901 created "2018-09-27" @default.
- W2890339901 creator A5038919038 @default.
- W2890339901 date "2018-01-01" @default.
- W2890339901 modified "2023-09-27" @default.
- W2890339901 title "Lower and Upper Probability Bounds for Some Conjunctions of Two Conditional Events" @default.
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- W2890339901 doi "https://doi.org/10.1007/978-3-030-00461-3_18" @default.
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