Skip to main content
SpringerLink
Log in
Book cover

Soft Methods for Handling Variability and Imprecision pp 289–296Cite as

On Convergence in Necessity and Its Laws of Large Numbers

  • Conference paper

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

Abstract

We aim at clarifying the relationship between laws of large numbers for fuzzy sets or possibility distributions and laws of large numbers for fuzzy or possibilistic variables. We contend that these two frameworks are different and present the relationships between them that explain why this fact was unrecognized so far.

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   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
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. Badard, R.: The law of large numbers for fuzzy processes and the estimation problem. Inform. Sci. 28, 161–178 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baddeley, A.: Hausdorff Metric for Capacities. Technical Report, CWI Report BS-R9127 (1991)

    Google Scholar 

  3. Fullér, R.: A law of large numbers for fuzzy numbers. Fuzzy Sets Syst. 45, 293–303 (1992)

    Google Scholar 

  4. Hong, D.H., Ahn, C.H.: Equivalent conditions for laws of large numbers for ⊤-related L-R fuzzy numbers. Fuzzy Sets Syst. 136, 387–395 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Norberg, T.: Random capacities and their distributions. Probab. Theory Related Fields 73, 281–297 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Rao, M.B., Rashed, A.: Some comments on fuzzy variables. Fuzzy Sets Syst. 6, 285–292 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  7. Terán, P.: Paradoxes in the law of large numbers without probability. Seminar talk at the Department of Mathematics, Universidad de Extremadura, Spain (paper in preparation) (February 2007)

    Google Scholar 

  8. Terán, P.: Probabilistic foundations for measurement modelling using fuzzy random variables. Fuzzy Sets Syst 158, 973–986 (2007)

    Article  MATH  Google Scholar 

  9. Terán, P.: A strong law of large numbers for t-normed arithmetics. Fuzzy Sets Syst. 159, 343–360 (2008)

    Article  Google Scholar 

  10. Terán, P., Molchanov, I.: The law of large numbers in a metric space with a convex combination operation. J. Theoret. Probab. 19, 875–898 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Williamson, R.C.: The law of large numbers for fuzzy variables under a general triangular norm extension principle. Fuzzy Sets Syst. 41, 55–81 (1991)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Grupo Decisión Multicriterio Zaragoza, Facultad de Ciencias Económicas y Empresariales, Universidad de Zaragoza, Zaragoza, Spain

    Pedro Terán

Authors
  1. Pedro Terán
    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

Terán, P. (2008). On Convergence in Necessity and Its Laws of Large Numbers. 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_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85027-4_35

  • 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

Search

Navigation