Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Generated Universal Fuzzy Measures

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3885))

Abstract

The concepts of generated universal fuzzy measures and of basic generated universal fuzzy measures are introduced. Special classes and properties of generated universal fuzzy measures are discussed, especially the additive, the symmetric and the maxitive case. Additive (symmetric) basic universal fuzzy measures are shown to correspond to the Yager quantifier-based approach to additive (symmetric) fuzzy measures. The corresponding Choquet integral-based aggregation operators are then generated weighted means (generated OWA operators).

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. Beljakov, G., Mesiar, R., Valášková, L.: Fitting generated aggregation operators to empirical data. Int. J. Uncertainty, Fuzziness and Knowledge-Based System 12, 219–236 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation Operators: Properties, Classes and Construction Methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators, pp. 3–107. Physica- Verlag, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Denneberg, D.: Non-additive Measure and Integral. Kluwer Acad. Publ., Dordrecht (1994)

    Book  MATH  Google Scholar 

  4. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  5. Grabisch, M., Murofushi, T., Sugeno, M.: Fuzzy Measures and Integrals. Physica-Verlag, Heidelberg (2000)

    MATH  Google Scholar 

  6. Klir, G.J., Folger, T.A.: Fuzzy Sets. Uncertainty, and Information. Prentice-Hall, Englewoods Cliffs (1988)

    MATH  Google Scholar 

  7. Kolesárová, A., Komorníková, M.: Triangular norm-based iterative compensatory operators. Fuzzy Sets and Systems 104, 109–120 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Komorníková, M.: Generated aggregation operators. In: Proc. EUSFLAT 1999. Palma de Mallorca, pp. 355–358 (1999)

    Google Scholar 

  9. Komorníková, M.: Aggregation operators and additive generators. Int. J. Uncertainty, Fuzziness and Knowledge-Based System 9, 205–215 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mesiar, R., Mesiarová, A.: Fuzzy integrals. In: Torra, V., Narukawa, Y. (eds.) MDAI 2004. LNCS (LNAI), vol. 3131, pp. 7–14. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Mesiar, R., Valášková, L.: Universal fuzzy measures. In: Proc. 10th IFSA World Congress, Istanbul, Turkey, pp. 139–142 (2003)

    Google Scholar 

  12. Mišík, L.: Sets of positive integers with prescribed values of densities. Math. Slovaca 52, 289–296 (2002)

    MathSciNet  MATH  Google Scholar 

  13. Pap, E.: Null-additive Set Functions. Kluwer Acad. Publ., Dordrecht (1995)

    MATH  Google Scholar 

  14. Struk, P.: Extremal fuzzy integrals. Soft Computing 9 (in press, 2005)

    Google Scholar 

  15. Sugeno, M.: Theory of Fuzzy Integrals and Applications. PhD Thesis, Tokyo Institute of Technology (1974)

    Google Scholar 

  16. Štrauch, O.: Tóth, J.: Asymptotic density and density of ratio set R(A). Acte Arithmetica LXXXVII, 67–78 (1998)

    Google Scholar 

  17. Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst., Man, Cybern. 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yager, R.R., Filev, D.P.: Essentials of Fuzzy Modelling and Control. J. Wiley & Sons, NewYork (1994)

    Google Scholar 

  19. Yager, R.R., Kacprzyk, J.: The Ordered Weighted Averaging Operators, Theory and Applications. Kluwer Academic Publishers, Boston (1997)

    Book  MATH  Google Scholar 

  20. Valášková, L’.: Non-additive Measures and Integrals. PhD Thesis, Slovak University of Technology (2005)

    Google Scholar 

  21. Wang, Z., Klir, G.J.: Fuzzy Measure Theory. Plenum Press, New York (1992)

    Book  MATH  Google Scholar 

  22. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Slovak University of Technology, Radlinského 11, 81368, Bratislava, Slovakia

    Radko Mesiar & L’ubica Valášková

  2. Mathematical Institute of SAS, Štefánikova 49, 81473, Bratislava, Slovakia

    Andrea Mesiarová

  3. Institute for Research and Application of Fuzzy Modelling, University of Ostrava, Czech Republic

    Radko Mesiar

Authors
  1. Radko Mesiar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Mesiarová
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L’ubica Valášková
    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, Catalonia, 08193, Bellaterra, Spain

    Vicenç Torra

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

    Yasuo Narukawa

  3. Department of Computer Science and Mathematics Intelligent Technologies for Advanced Knowledge Acquisition Research Group,, University Rovira i Virgili, Av. Països Catalans, 26., 43007, Tarragona, Catalonia, Spain

    Aïda Valls

  4. Department of Computer Engineering and Mathematics, Universitat Rovira i Virgili, UNESCO Chair in Data Privacy, Av. Països Catalans 26, E-43007, Tarragona, Catalonia, Spain

    Josep Domingo-Ferrer

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mesiar, R., Mesiarová, A., Valášková, L. (2006). Generated Universal Fuzzy Measures. In: Torra, V., Narukawa, Y., Valls, A., Domingo-Ferrer, J. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2006. Lecture Notes in Computer Science(), vol 3885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11681960_20

Download citation

  • DOI: https://doi.org/10.1007/11681960_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32780-6

  • Online ISBN: 978-3-540-32781-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation