On possibilistic marginal problem

Jiřina Vejnarová

Kybernetika (2007)

  • Volume: 43, Issue: 5, page 657-674
  • ISSN: 0023-5954

Abstract

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A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a T -product extension. Finally, a necessary and sufficient condition for the existence of a solution will be presented.

How to cite

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Vejnarová, Jiřina. "On possibilistic marginal problem." Kybernetika 43.5 (2007): 657-674. <http://eudml.org/doc/33887>.

@article{Vejnarová2007,
abstract = {A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a $T$-product extension. Finally, a necessary and sufficient condition for the existence of a solution will be presented.},
author = {Vejnarová, Jiřina},
journal = {Kybernetika},
keywords = {marginal problem; possibility distributions; triangular norm; conditioning; conditional independence; extension; conditioning; conditional independence; marginal problem; possibility distribution; triangular norm},
language = {eng},
number = {5},
pages = {657-674},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On possibilistic marginal problem},
url = {http://eudml.org/doc/33887},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Vejnarová, Jiřina
TI - On possibilistic marginal problem
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 5
SP - 657
EP - 674
AB - A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a $T$-product extension. Finally, a necessary and sufficient condition for the existence of a solution will be presented.
LA - eng
KW - marginal problem; possibility distributions; triangular norm; conditioning; conditional independence; extension; conditioning; conditional independence; marginal problem; possibility distribution; triangular norm
UR - http://eudml.org/doc/33887
ER -

References

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  10. Vejnarová J., Composition of possibility measures on finite spaces: Preliminary results, In: Proc. 7th Internat. Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU’98, Paris 1998, pp. 25–30 (1998) 
  11. Vejnarová J., Possibilistic independence and operators of composition of possibility measures, In: Prague Stochastics’98 (M. Hušková, J. Á. Víšek, and P. Lachout, eds.), Union of the Czech Mathematicians and Physicists, Prague 1998, pp. 575–580 (1998) 
  12. Vejnarová J., Conditional independence relations in possibility theory, Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 8 (2000), 253–269 Zbl1113.68536MR1770487
  13. Vejnarová J., Markov properties and factorization of possibility distributions, Ann. Math. Artif. Intell. 35 (2002), 357–377 Zbl1014.68155MR1899959
  14. Walley P., Cooman G. de, Coherence rules for defining conditional possibility, Internat. J. Approx. Reason. 21 (1999), 63–104 (1999) MR1693207

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