Title: | Alternative definitions of conditional possibilistic measures (English) |

Author: | Kramosil, Ivan |

Language: | English |

Journal: | Kybernetika |

ISSN: | 0023-5954 |

Volume: | 34 |

Issue: | 2 |

Year: | 1998 |

Pages: | [137]-147 |

Summary lang: | English |

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Category: | math |

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Summary: | 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. (English) |

Keyword: | possibilistic measure |

Keyword: | conditional probability |

Keyword: | statistical independence |

MSC: | 28E05 |

MSC: | 60A99 |

MSC: | 68T30 |

MSC: | 68T37 |

idZBL: | Zbl 1274.28031 |

idMR: | MR1621506 |

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Date available: | 2009-09-24T19:14:32Z |

Last updated: | 2015-03-28 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/135193 |

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Reference: | [1] Campos L. M. de, Heuter J. F., Moral S.: Possibilistic independence.In: Proceedings of EUFIT 95 (Third European Congress on Intelligent Techniques and Soft Computing), Verlag Mainz and Wissenschaftsverlag, Aachen 1995, vol. 1, pp. 69–73 |

Reference: | [2] Dubois D., Prade H.: Théorie des Possibilités – Applications à la Représentation de Connaissances en Informatique.Mason, Paris 1985 |

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Reference: | [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 MR 1464978 |

Reference: | [6] Lewis D.: Probabilities of conditionals and conditional probabilities.Philos. Review 85 (1976), 297–315 10.2307/2184045 |

Reference: | [7] Loève M.: Probability Theory.D. van Nostrand, New York 1955 Zbl 0385.60001, MR 0203748 |

Reference: | [8] Pearl J.: Probabilistic Reasoning in Intelligent Systems – Networks of Plausible Inference.Morgan and Kaufmann, San Matteo, California 1988 Zbl 0746.68089, MR 0965765 |

Reference: | [9] Shafer G.: A Mathematical Theory of Evidence.Princeton Univ. Press, Princeton, New Jersey 1976 Zbl 0359.62002, MR 0464340 |

Reference: | [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 |

Reference: | [11] Zadeh L. A.: Fuzzy sets as a basis for a theory of possibility.Fuzzy Sets and Systems 1 (1978), 3–28 MR 0480045, 10.1016/0165-0114(78)90029-5 |

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