Non additive ordinal relations representable by lower or upper probabilities

Andrea Capotorti; Giulianella Coletti; Barbara Vantaggi

Kybernetika (1998)

  • Volume: 34, Issue: 1, page [79]-90
  • ISSN: 0023-5954

Abstract

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We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means of “dual” conditions given on the contrary events, like in the numerical case.

How to cite

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Capotorti, Andrea, Coletti, Giulianella, and Vantaggi, Barbara. "Non additive ordinal relations representable by lower or upper probabilities." Kybernetika 34.1 (1998): [79]-90. <http://eudml.org/doc/33336>.

@article{Capotorti1998,
abstract = {We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means of “dual” conditions given on the contrary events, like in the numerical case.},
author = {Capotorti, Andrea, Coletti, Giulianella, Vantaggi, Barbara},
journal = {Kybernetika},
keywords = {coherent lower probability},
language = {eng},
number = {1},
pages = {[79]-90},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Non additive ordinal relations representable by lower or upper probabilities},
url = {http://eudml.org/doc/33336},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Capotorti, Andrea
AU - Coletti, Giulianella
AU - Vantaggi, Barbara
TI - Non additive ordinal relations representable by lower or upper probabilities
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 1
SP - [79]
EP - 90
AB - We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means of “dual” conditions given on the contrary events, like in the numerical case.
LA - eng
KW - coherent lower probability
UR - http://eudml.org/doc/33336
ER -

References

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  7. Regoli G., Rational Comparison and Numerical Representation, Decision Theory and Decision Analysis: Trends and challenges. Academic Publishers, Dordrecht 1994 
  8. Scott D., 10.1016/0022-2496(64)90002-1, J. Math. Psych. 1 (1964), 233–247 (1964) Zbl0129.12102DOI10.1016/0022-2496(64)90002-1
  9. Walley P., Statistical Reasoning with Imprecise Probabilities, Chapman & Hall, London 1990 Zbl0732.62004MR1145491
  10. Wong S. K. M., Yao Y. Y., Bollmann P., Bürger H. C., 10.1109/21.108290, IEEE Trans. Systems Man Cybernet. 21 (1991), 726–734 (1991) Zbl0737.60006MR1143669DOI10.1109/21.108290

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