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Conditional problem for objective probability

Otakar Kříž (1998)

Kybernetika

Marginal problem (see [Kel]) consists in finding a joint distribution whose marginals are equal to the given less-dimensional distributions. Let’s generalize the problem so that there are given not only less-dimensional distributions but also conditional probabilities. It is necessary to distinguish between objective (Kolmogorov) probability and subjective (de Finetti) approach ([Col,Sco]). In the latter, the coherence problem incorporates both probabilities and conditional probabilities in a unified...

El valor difuso esperado con integrales semiconormadas.

Fermín Suárez, Pedro Gil (1986)

Trabajos de Estadística

In this paper we first use the semiconormed fuzzy integrals in order to extend the definition of the fuzzy expected value (F.E.V.) (Kandel, 1979). We generalize some of the properties due to Kandel with a criticism about his purpose of constraining the F.E.V. to be linear. Finally, a necessary and sufficient condition is given in order to guarantee some linearity properties for any semiconormed fuzzy integral.

Esperanza condicionada para probabilidades finitamente aditivas.

Luis A. Sarabia (1982)

Trabajos de Estadística e Investigación Operativa

Let (Ω, θ, J) be a finitely additive probabilistic space formed by any set Ω, an algebra of subsets θ and a finitely additive probability J. In these conditions, if F belongs to V1(Ω, θ, J) there exists f, element of the completion of L1(Ω, θ, J), such that F(E) = ∫E f dJ for all E of θ and conversely.The integral representation gives sense to the following result, which is the objective of this paper, in terms of the point function: if β is a subalgebra of θ, for every F of V1(Ω, θ, J) there exists...

Extensión de medidas difusas usando la esperanza monótona.

Manuel Jorge Bolaños Carmona, María Teresa Lamata Jiménez, Serafín Moral Callejón (1987)

Stochastica

The monotone expectation is defined as a functional over fuzzy measures on finite sets. The functional is based on Choquet functional over capacities and its more relevant properties are proved, including the generalization of classical mathematical expectation and Dempster's upper and lower expectations of an evidence. In second place, the monotone expectation is used to define measures of fuzzy sets. Such measures are compared with the ones based on Sugeno integral. Finally, we prove a generalization...

Null events and stochastical independence

Giulianella Colleti, Romano Scozzafava (1998)

Kybernetika

In this paper we point out the lack of the classical definitions of stochastical independence (particularly with respect to events of 0 and 1 probability) and then we propose a definition that agrees with all the classical ones when the probabilities of the relevant events are both different from 0 and 1, but that is able to focus the actual stochastical independence also in these extreme cases. Therefore this definition avoids inconsistencies such as the possibility that an event A can be at the...

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