Skip to main content

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 12))

Abstract

A notion of a robust aggregation procedure is introduced and studied in connection with invariance properties of aggregation procedures. We prove that a robust aggregation procedure is invariant if measurements are in the ordinal scale. We also show that any robust mean on the set of all fuzzy sets on a finite universe is a pointwise order statistic.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.L. Cauchy: Cours d’analyse de l’École Royale Polytechnique, Ire partie, Analyse algébrique, Paris (1821)

    Google Scholar 

  2. J. Dugundji: Topology, Allyn and Bacon, Boston (1965)

    Google Scholar 

  3. R.D. Luce, D.H. Krantz, P. Suppes, A. Tversky: Foundations of Measurement, Academic Press, New York (1990)

    MATH  Google Scholar 

  4. J.-L. Marichal, M. Roubens: Characterization of some stable aggregation functions. In: Proceedings of the International Conference on Industrial Engineering and Product Management, Mons 1993, 187–196

    Google Scholar 

  5. R.A. McCoy, I. Ntantu: Topological Properties of Spaces of Continuous Functions, Lecture Notes in Mathematics, v. 1315, Springer-Verlag (1988)

    Google Scholar 

  6. A. Orlov: The connection between mean quantities and admissible transformations. Mathematical Notes 30, 774–778 (1981)

    Article  Google Scholar 

  7. S. Ovchinnikov: Means on ordered sets. Mathematical Social Sciences 32, 39–56 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. R.R. Yager: Decision making under Dempster-Shafer uncertainties. International Journal of General Systems 20, 233–245 (1992)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ovchinnikov, S. (1998). On Robust Aggregation Procedures. In: Bouchon-Meunier, B. (eds) Aggregation and Fusion of Imperfect Information. Studies in Fuzziness and Soft Computing, vol 12. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1889-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1889-5_1

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11073-7

  • Online ISBN: 978-3-7908-1889-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics