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The Goodman-Nguyen Relation in Uncertainty Measurement

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Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 190))

Abstract

The Goodman-Nguyen relation generalises the implication (inclusion) relation to conditional events. As such, it induces inequality constraints relevant in extension problems with precise probabilities. We extend this framework to imprecise probability judgements, highlighting the role of this relation in determining the natural extension of lower/upper probabilities defined on certain sets of conditional events. Further, a generalisation of the Goodman–Nguyen relation to conditional random numbers is proposed.

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Authors and Affiliations

  1. Università di Trieste, 34127, Trieste, Italy

    Renato Pelessoni & Paolo Vicig

Authors
  1. Renato Pelessoni
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  2. Paolo Vicig
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Corresponding author

Correspondence to Renato Pelessoni .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Otto-von-Guericke University of Magdebur, Geb. 29, Raum 008, Universitätsplatz 2, Magdeburg, 39106, Germany

    Rudolf Kruse

  2. , FB Informatik & Informationswissenschaft, University of Konstanz, Konstanz, 78457, Germany

    Michael R. Berthold

  3. of Magdeburg, Faculty of Computer Science, Otto-von-Guericke University, Geb. 29, Universitätsplatz 2 008, Magdeburg, 39106, Germany

    Christian Moewes

  4. , Department of Statistics and OR, University of Oviedo, C/ Calvo Sotelo, s/n, Oviedo, 33007, Spain

    María Ángeles Gil

  5. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Przemysław Grzegorzewski

  6. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Olgierd Hryniewicz

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Pelessoni, R., Vicig, P. (2013). The Goodman-Nguyen Relation in Uncertainty Measurement. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-33042-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33041-4

  • Online ISBN: 978-3-642-33042-1

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