Alternative definitions of conditional possibilistic measures

Ivan Kramosil

Kybernetika (1998)

  • Volume: 34, Issue: 2, page [137]-147
  • ISSN: 0023-5954

Abstract

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The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning the decision problem under uncertainty in question. The properties and qualities of various approaches to conditionalizing can be estimated from various points of view. Here we apply the idea according to which the properties of independence relations defined by particular conditional possibilistic measures are confronted with those satisfied by the relation of statistical (or stochastical) independence descending from the notion of conditional probability measure. For the reader’s convenience the notions of conditional probability and statistical independence are recalled in the introductory chapter.

How to cite

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Kramosil, Ivan. "Alternative definitions of conditional possibilistic measures." Kybernetika 34.2 (1998): [137]-147. <http://eudml.org/doc/33341>.

@article{Kramosil1998,
abstract = {The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning the decision problem under uncertainty in question. The properties and qualities of various approaches to conditionalizing can be estimated from various points of view. Here we apply the idea according to which the properties of independence relations defined by particular conditional possibilistic measures are confronted with those satisfied by the relation of statistical (or stochastical) independence descending from the notion of conditional probability measure. For the reader’s convenience the notions of conditional probability and statistical independence are recalled in the introductory chapter.},
author = {Kramosil, Ivan},
journal = {Kybernetika},
keywords = {possibilistic measure; conditional probability; statistical independence; possibilistic measure; conditional probability; statistical independence},
language = {eng},
number = {2},
pages = {[137]-147},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Alternative definitions of conditional possibilistic measures},
url = {http://eudml.org/doc/33341},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Kramosil, Ivan
TI - Alternative definitions of conditional possibilistic measures
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 2
SP - [137]
EP - 147
AB - The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning the decision problem under uncertainty in question. The properties and qualities of various approaches to conditionalizing can be estimated from various points of view. Here we apply the idea according to which the properties of independence relations defined by particular conditional possibilistic measures are confronted with those satisfied by the relation of statistical (or stochastical) independence descending from the notion of conditional probability measure. For the reader’s convenience the notions of conditional probability and statistical independence are recalled in the introductory chapter.
LA - eng
KW - possibilistic measure; conditional probability; statistical independence; possibilistic measure; conditional probability; statistical independence
UR - http://eudml.org/doc/33341
ER -

References

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  2. Dubois D., Prade H., Théorie des Possibilités – Applications à la Représentation de Connaissances en Informatique, Mason, Paris 1985 
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  5. Kramosil I., An axiomatic approach to extensional probability measures, In: Proceedings of the European Conference Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Fribourg (Lecture Notes in Artificial Intelligence 946.) Springer–Verlag, Berlin 1995, pp. 267–276 (1995) MR1464978
  6. Lewis D., 10.2307/2184045, Philos. Review 85 (1976), 297–315 (1976) DOI10.2307/2184045
  7. Loève M., Probability Theory, D. van Nostrand, New York 1955 Zbl0385.60001MR0203748
  8. Pearl J., Probabilistic Reasoning in Intelligent Systems – Networks of Plausible Inference, Morgan and Kaufmann, San Matteo, California 1988 Zbl0746.68089MR0965765
  9. Shafer G., A Mathematical Theory of Evidence, Princeton Univ. Press, Princeton, New Jersey 1976 Zbl0359.62002MR0464340
  10. Smets, Ph., About updating, In: Uncertainty in Artificial Intelligence 91 (D’Ambrosio, Ph. Smets and P. P. Bonissone, eds.), Morgan Kaufman, Sao Matteo, California 1991, pp. 378–385 (1991) 
  11. Zadeh L. A., 10.1016/0165-0114(78)90029-5, Fuzzy Sets and Systems 1 (1978), 3–28 (1978) MR0480045DOI10.1016/0165-0114(78)90029-5

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