Skip to main content
SpringerLink
Log in

Choquet Stieltjes Integral, Losonczi’s Means and OWA Operators

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5285))

Abstract

Neat OWA operators have been defined as a generalization of the OWA operators. In this paper we study these operators establishing some relationships with some other operators. In particular, we link them with the Losonczi’s mean.

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

Access this chapter

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bajraktarević, M.: Sur une equation fonctionnelle aux valeurs moyennes. Glanik Mat.-Fiz. i Astr., Zagreb 13, 243–248 (1958)

    MATH  Google Scholar 

  2. Bajraktarević, M.: Sur une genéralisation des moyennes quasilineaire. Publ. Inst. Math. Beograd. 3(17), 69–76 (1963)

    MathSciNet  MATH  Google Scholar 

  3. Bullen, P.S., Mitrinović, D.S., Vasić, P.M.: Means and their Inequalities. D. Reidel Publishing Company (1988)

    Google Scholar 

  4. Calvo, T., Mayor, G., Mesiar, R. (eds.): Aggregation Operators. Physica-Verlag (2002)

    Google Scholar 

  5. Choquet, G.: Theory of capacities. Ann. Inst. Fourier, Grenoble 5, 131–295 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dellacherie, C.: Quelques commentaires sur les prolongements de capacités. In: Séminaire de Probabilités 1969/1970, Strasbourg. Lecture Notes in Mathematics, vol. 191, pp. 77–81 (1971)

    Google Scholar 

  7. Fodor, J., Marichal, J.-L., Roubens, M.: Characterization of the ordered weighted averaging operators. IEEE Trans. on Fuzzy Systems 3(2), 236–240 (1995)

    Article  Google Scholar 

  8. Grabisch, M., Murofushi, T., Sugeno, M. (eds.): Fuzzy Measures and Integrals: Theory and Applications. Physica-Verlag (2000)

    Google Scholar 

  9. Losonczi, L.: Über eine neue Klasse von Mittelwerte. Acta Sci. Math (Acta Univ. Szeged) 32, 71–78 (1971)

    MATH  Google Scholar 

  10. Miranda, P., Grabisch, M.: p-symmetric fuzzy measures. In: Proc. of the IPMU 2002 Conference, Annecy, France, pp. 545–552 (2002)

    Google Scholar 

  11. Murofushi, T., Sugeno, M.: An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy Sets and Systems 29, 201–227 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Narukawa, Y., Murofushi, T.: Choquet Stieltjes integral as a tool for decision modeling. Int. J. of Intel. Syst. 23, 115–127 (2008)

    Article  MATH  Google Scholar 

  13. Narukawa, T.: Distances defined by Choquet integral. In: IEEE International Conference on Fuzzy Systems, London, CD-ROM [#1159] (2007)

    Google Scholar 

  14. Riesz, F., Nagy, B.: Functional analysis. Frederick Unger Publishing (1955)

    Google Scholar 

  15. Schmeidler, D.: Integral representation without additivity. Proceedings of the American Mathematical Society 97, 253–261 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sugeno, M., Narukawa, Y., Murofushi, T.: Choquet integral and fuzzy measures on locally compact space. Fuzzy Sets and Systems 99, 205–211 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Sugeno, M.: Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology (1974)

    Google Scholar 

  18. Torra, V.: The weighted OWA operator. Int. J. of Intel. Syst. 12, 153–166 (1997)

    Article  MATH  Google Scholar 

  19. Torra, V., Narukawa, Y.: Modeling decisions: information fusion and aggregation operators. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  20. Torra, V., Narukawa, Y.: Modelització de decisions: fusió d’informació i operadors d’agregació. UAB Press (2007)

    Google Scholar 

  21. van der Waerden, B.L.: Mathematical statistics. Springer, Berlin (1969)

    Book  MATH  Google Scholar 

  22. Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. on Systems, Man and Cybernetics 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yager, R.R., Filev, D.P.: Parameterized and-like and or-like OWA operators. Int. J. of General Systems 22, 297–316 (1994)

    Article  Google Scholar 

  24. Yager, R.R.: Families of OWA operators. Fuzzy Sets and Systems 59, 125–148 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IIIA-CSIC, Institut d’Investigació en Intel·ligència Artificial, Campus UAB, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10 Naka, Kunitachi, Tokyo, 186-0004, Japan

    Yasuo Narukawa

Authors
  1. Vicenç Torra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yasuo Narukawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IIIA, Artificial Intelligence Research Institute CSIC, Spanish National Research Council,, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen,, 3-1-10 Naka, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Torra, V., Narukawa, Y. (2008). Choquet Stieltjes Integral, Losonczi’s Means and OWA Operators. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2008. Lecture Notes in Computer Science(), vol 5285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88269-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88269-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88268-8

  • Online ISBN: 978-3-540-88269-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation