Search results for "Frank t-norm."

showing 3 items of 3 documents

Compound conditionals, Fr\'echet-Hoeffding bounds, and Frank t-norms

2021

Abstract In this paper we consider compound conditionals, Frechet-Hoeffding bounds and the probabilistic interpretation of Frank t-norms. By studying the solvability of suitable linear systems, we show under logical independence the sharpness of the Frechet-Hoeffding bounds for the prevision of conjunctions and disjunctions of n conditional events. In addition, we illustrate some details in the case of three conditional events. We study the set of all coherent prevision assessments on a family containing n conditional events and their conjunction, by verifying that it is convex. We discuss the case where the prevision of conjunctions is assessed by Lukasiewicz t-norms and we give explicit s…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaLogical independenceFrank t-normsApplied MathematicsLinear systemProbabilistic logicRegular polygon02 engineering and technologyConjunction and disjunctionConditional previsionTheoretical Computer ScienceConvexityFréchet-Hoeffding boundArtificial Intelligence020204 information systems0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingPairwise comparisonCoherenceSoftwareMathematics - ProbabilityCounterexampleMathematicsCorresponding conditional
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Conjunction of Conditional Events and t-Norms

2019

We study the relationship between a notion of conjunction among conditional events, introduced in recent papers, and the notion of Frank t-norm. By examining different cases, in the setting of coherence, we show each time that the conjunction coincides with a suitable Frank t-norm. In particular, the conjunction may coincide with the Product t-norm, the Minimum t-norm, and Lukasiewicz t-norm. We show by a counterexample, that the prevision assessments obtained by Lukasiewicz t-norm may be not coherent. Then, we give some conditions of coherence when using Lukasiewicz t-norm

Frank t-norm.Settore MAT/06 - Probabilita' E Statistica MatematicaConjunction02 engineering and technologyCoherence (statistics)01 natural sciencesConjunction (grammar)Mathematics::Logic010104 statistics & probabilitySettore SECS-S/06 -Metodi Mat. dell'Economia e d. Scienze Attuariali e Finanz.Product (mathematics)0202 electrical engineering electronic engineering information engineeringCalculus020201 artificial intelligence & image processing0101 mathematicsCoherenceConditional EventCounterexampleMathematics
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Triangular norms and conjunction of conditional events

2019

We study the relationship between a notion of conjunction among conditional events, introduced in recent papers, and the notion of Frank t-norm. By examining different cases, in the setting of coherence, we show each time that the conjunction coincides with a suitable Frank t-norm. In particular, the conjunction may coincide with the Product t-norm, the Minimum t- norm, and Lukasiewicz t-norm. We show by a counterexample, that the prevision assessments obtained by Lukasiewicz t-norm may be not coherent. Then, we give some conditions of coherence when using Lukasiewicz t-norm.

Frank t-norm.Settore MAT/06 - Probabilita' E Statistica MatematicaConjunctionConditional random quantityCoherenceConditional Event
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