Skip to main content
SpringerLink
Log in
Book cover

Combining Soft Computing and Statistical Methods in Data Analysis pp 209–216Cite as

Coherent Upper Conditional Previsions and Their Integral Representation with Respect to Hausdorff Outer Measures

  • Conference paper

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

Abstract

In a metric space, a necessary and sufficient condition is given for a coherent upper conditional prevision to be uniquely represented by the Choquet integral with respect to the upper conditional probability defined by its Hausdorff outer measure.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. de Cooman, G., Troffaes, M., Miranda, E.: n-Monotone exact functional. J. Math. Anal. Appl. 347(1), 133–146 (2008)

    Google Scholar 

  2. Denneberg, D.: Non-additive measure and integral. Kluwer Academic Publishers, Dordrecht (1984)

    Google Scholar 

  3. Doria, S.: Probabilistic independence with respect to upper and lower conditional probabilities assigned by Hausdorff outer and inner measures. Internat. J. Approx. Reason. 46, 617–635 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Falconer, K.J.: The geometry of fractals sets. Cambridge University Press, Cambridge (1986)

    Google Scholar 

  5. Greco, G.: Sur la mesurabilité d’une fonction numérique par rapport à une famille d’ensembles. Rend. Sem. Mat. Univ. Padova 65, 21–42 (1981)

    MathSciNet  Google Scholar 

  6. Rogers, C.A.: Hausdorff measures. Cambridge University Press, Cambridge (1970)

    MATH  Google Scholar 

  7. Walley, P.: Coherent lower (and upper) probabilities. Statistics Research Report, University of Warwick (1981)

    Google Scholar 

  8. Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Sciences, University G. d’Annunzio, Chieti-Pescara, Italy

    Serena Doria

Authors
  1. Serena Doria
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing Edificio Científico-Tecnológico. 3a Planta, C/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt , Gil González-Rodríguez  & Wolfgang Trutschnig ,  & 

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Asunción Lubiano

  3. Departamento de Estadística e I.O. yD.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Ángeles Gil

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

    Przemysław Grzegorzewski

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

    Olgierd Hryniewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Doria, S. (2010). Coherent Upper Conditional Previsions and Their Integral Representation with Respect to Hausdorff Outer Measures. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14746-3_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation