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Keywords
(6)
choquet integral
Probability Distribution
Random Set
Random Variable
Upper and Lower Probabilities
dempster shafer
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On Random Sets and Belief Functions
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Upper Probabilities Attainable by Distributions of Measurable Selections
Upper Probabilities Attainable by Distributions of Measurable Selections,10.1007/9783642029066_30,Enrique Miranda,Inés Couso,Pedro Gil
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Upper Probabilities Attainable by Distributions of Measurable Selections
(
Citations: 5
)
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Enrique Miranda
,
Inés Couso
,
Pedro Gil
A
random set
can be regarded as the result of the imprecise observation of a random variable. Following this interpretation, we study to which extent the
upper and lower probabilities
induced by the
random set
keep all the information about the values of the
probability distribution
of the random variable. We link this problem to the existence of selectors of a multivalued mapping and with the inner approximations of the upper probability, and prove that under fairly general conditions (although not in all cases), the
upper and lower probabilities
are an adequate tool for modelling the available information. Finally, we study the particular case of consonant random sets and we also derive a relationship between Aumann and Choquet integrals.
Conference:
Symbolic and Quantitative Approaches to Reasoning and Uncertainty  ECSQARU
, pp. 335346, 2009
DOI:
10.1007/9783642029066_30
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Citation Context
(2)
...This is an updated version, with proofs and additional comments, of a paper [
42
] presented at ECSQARU’09, the Tenth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty...
Enrique Miranda
,
et al.
Approximations of upper and lower probabilities by measurable selectio...
...Although working with the upper and lower probabilities leads to a number of mathematical simplications ([20, 21]), the information they provide is in general more imprecise than the one given by the set of distributions of the measurable selections ([16,
18
])...
...It was investigated for the case of X nite in [16], and for some particular innite spaces in [3, 6, 10, 15,
18
]...
...In order to give conditions for the equality, we must see if the maximum and minimum values of P(Γ)(A) coincide with P (A) and P (A), and also if P(Γ)(A) is convex. This problem was studied in [
18
]...
...Theorem 1 [
18
] Consider (Ω; A; P) a probability space, (X; τ) a topological space and Γ : Ω! P(X) a random set...
Enrique Miranda
,
et al.
Study of the Probabilistic Information of a Random Set
References
(21)
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(
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)
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,
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Journal:
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(
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)
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,
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Published in 2001.
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(
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,
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Published in 2002.
A random set description of a possibility measure and its natural extension
(
Citations: 32
)
Gert De Cooman
,
Dirk Aeyels
Journal:
IEEE Transactions on Systems, Man, and Cybernetics  TSMC
, vol. 30, no. 2, pp. 124130, 2000
Upper and Lower Probabilities Induced by a Multivalued Mapping
(
Citations: 1613
)
A. P. Dempster
Journal:
The Annals of Mathematical Statistics
, vol. 38, no. 1967, pp. 325339, 1967
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Citations
(5)
Approximations of upper and lower probabilities by measurable selections
(
Citations: 3
)
Enrique Miranda
,
Inés Couso
,
Pedro Gil
Journal:
Information Sciences  ISCI
, vol. 180, no. 8, pp. 14071417, 2010
Study of the Probabilistic Information of a Random Set
(
Citations: 5
)
Enrique Miranda
,
Inés Couso
,
Pedro Gil
Conference:
International Symposium on Imprecise Probabilities and Their Applications  ISIPTA
, pp. 382394, 2003
Coherence and independence for nonlinear spaces
(
Citations: 8
)
Enrique Miranda
,
Gert de Cooman
Conference:
USENIX Technical Conference  USENIX
Upper probabilities attainable by distributions of measurable selections
(
Citations: 3
)
Enrique Miranda
,
Ines Couso
,
Pedro Gil
Nonlinear Bound Constrained Optimization and Second Order Information
(
Citations: 1
)
Javier M. Moguerza
,
Alberto Olivares
,
Francisco J. Prieto