6533b828fe1ef96bd128834e
RESEARCH PRODUCT
Lower and Upper Probability Bounds for Some Conjunctions of Two Conditional Events
Giuseppe Sanfilipposubject
CombinatoricsSettore MAT/06 - Probabilita' E Statistica MatematicaProbability assessmentCoherence Conditional event Conditional random quantity Kleene-Lukasiewicz-Heyting conjunction Lukasiewicz conjunction Bochvar internal conjunction Sobocinski conjunction Lower and upper bounds Fréchet-Hoeffding bounds010102 general mathematics0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing02 engineering and technology0101 mathematics01 natural sciencesMathematicsdescription
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 Frechet-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 Frechet-Hoeffding bounds are preserved.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 |