Skip to main content
Springer Nature Link
Log in

Some Properties of the d K -Variance for Interval-Valued Random Sets

  • Conference paper
Soft Methods for Handling Variability and Imprecision

Part of the book series: Advances in Soft Computing ((AINSC,volume 48))

  • 1009 Accesses

Abstract

The suitability of the family of d K -distances for intervals to quantify and estimate the variability of a random interval with respect to its Aumann expectation is discussed. To be precise, we will review some properties of the metrics and the associated variance. Then, we will show that the sample variance is a consistent estimator of the population one, which make it adequate for inferential problems. The use of the d K -variance will be illustrated by means of a real-life example.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Arstein, Z., Vitale, R.A.: A strong law of large numbers for random compact sets. Ann. Probab. 5, 879–882 (1975)

    Article  Google Scholar 

  2. Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Mathware Soft. Comput. 2, 71–84 (1995)

    MATH  MathSciNet  Google Scholar 

  3. Diamond, P., Kloeden, P.: Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific Publishing Co., Inc., River Edge (1994)

    MATH  Google Scholar 

  4. Körner, R.: On the variance of fuzzy random variables. Fuzzy Sets Syst. 92, 83–93 (1997)

    Article  MATH  Google Scholar 

  5. Körner, R., Näther, W.: On the variance of random fuzzy variables. In: Bertoluzza, C., Gil, M., Ralescu, D. (eds.) Statistical Modeling, Analysis and Management of Fuzzy Data, pp. 22–39. Physica-Verlag, Heidelberg (2002)

    Google Scholar 

  6. Lubiano, A.: Generalized measure of the absolute variation of a random set. Definition and statistical applications. In: Proceedings of 11th European Young Statisticians Meeting (EYSM 1999, Marly-le-Roi, Francia), pp. 122–127 (1997)

    Google Scholar 

  7. Lubiano, M.A., Gil, M.A., López-Díaz, M., López, M.T.: The \(\overrightarrow{\lambda}\)-mean squared dispersion associated with a fuzzy random variable. Fuzzy Sets Syst. 111(3), 307–317 (2000)

    Article  MATH  Google Scholar 

  8. Näther, W.: Linear statistical inference for random fuzzy data. Statistics 29, 221–240 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Trutschnig, W., González-Rodríguez, G., Colubi, A., Gil, M.A.: A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread (submitted for publication) (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Oviedo, Spain

    Ángela Blanco, Norberto Corral & M. Asunción Lubiano

  2. European Centre for Soft Computing, Mieres, Spain

    Gil González-Rodríguez

Authors
  1. Ángela Blanco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Norberto Corral
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gil González-Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Asunción Lubiano
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université Paul Sabatier, Toulouse, France

    Didier Dubois  & Henri Prade  & 

  2. Universidad de Oviedo, Spain

    M. Asunción Lubiano  & María Ángeles Gil  & 

  3. Polish Academy of Sciences, Warsaw, Poland

    Przemysław Grzegorzewski

  4. Polish Academy of Sciences,, Warsaw, Poland

    Olgierd Hryniewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Blanco, Á., Corral, N., González-Rodríguez, G., Lubiano, M.A. (2008). Some Properties of the d K -Variance for Interval-Valued Random Sets. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85027-4_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85026-7

  • Online ISBN: 978-3-540-85027-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics