Skip to main content

OWA Operators and Choquet Integrals in the Interval-Valued Setting

  • Chapter
  • First Online:
Granular, Soft and Fuzzy Approaches for Intelligent Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 344))

Abstract

In this chapter, we make use of the notion of admissible order between intervals to extend the definition of OWA operators and Choquet integrals to the interval-valued setting. We also present an algorithm for decision making based on these developments.

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 EPUB and 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

References

  1. Aumann, R.J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12, 1–12 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barrenechea, E., Bustince, H., De Baets, B., Lopez-Molina, C.: Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images. IEEE Trans. Fuzzy Syst. 19(5), 819–830 (2011)

    Article  Google Scholar 

  3. Beliakov, G., Bustince, H., Paternain, D.: Image reduction using means on discrete product lattices. IEEE Trans. Image Process. 21(3), 1070–1083 (2012)

    Google Scholar 

  4. Beliakov, G., Bustince, H., Goswami, D.P., Mukherjee, U.K., Pal, N.R.: On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inf. Sci. 181, 1116–1124 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bustince, H.: Interval-valued fuzzy sets in soft computing. Int. J. Comput. Intell. Syst. 3(2), 215–222 (2010)

    Article  Google Scholar 

  6. Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.: Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst. 160, 1819–1840 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bustince, H., Calvo, T., De Baets, B., Fodor, J., Mesiar, R., Montero, J., Paternain, D., Pradera, A.: A class of aggregation functions encompassing two-dimensional OWA operators. Inf. Sci. 180, 1977–1989 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bustince, H., Fernandez, J., Kolesárová, A., Mesiar, R.: Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst. 220, 69–77 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bustince, H., Galar, M., Bedregal, B., Kolesárová, A., Mesiar, R.: A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy sets applications. IEEE Trans. Fuzzy Syst. 21, 1150–1162 (2013)

    Article  Google Scholar 

  10. Choquet, G.: Theory of capacities. Annales de l’Institute Fourier 5, 131–292 (1953–54)

    Google Scholar 

  11. Galar, M., Fernandez, J., Beliakov, G., Bustince, H.: Interval-valued fuzzy sets applied to stereo matching of color images. IEEE Trans. Image Process. 20, 1949–1961 (2011)

    Article  MathSciNet  Google Scholar 

  12. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  13. Jang, L.C.: Interval-valued Choquet integrals and their applications. J. Appl. Math. Comput. 16, 429–443 (2004)

    Google Scholar 

  14. Klement, E.P., Mesiar, R., Pap, E.: A universal integral as common frame for Choquet and Sugeno integral. IEEE Trans. Fuzzy Syst. 18(1), 178–187 (2010)

    Article  Google Scholar 

  15. Komorníková, M., Mesiar, R.: Aggregation functions on bounded partially ordered sets and their classification. Fuzzy Sets Syst. 175, 48–56 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lizasoain, I., Moreno, C.: OWA operators defined on complete lattices. Fuzzy Sets Syst. 224, 36–52 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mitchel, H.B.: An intuitionistic OWA operator. Int. J. Uncertainty, Fuzziness Knowl. Based Syst. 12, 843–860 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Shapley, L.S.: A Value for n-Person Game. Princeton University Press, Princenton (1953)

    MATH  Google Scholar 

  19. Sugeno, M.: Theory of Fuzzy Integrals and Its Applications. Ph.D. thesis, Tokyo Institute of Technology (1974)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  21. Xu, Z.S., Yager, R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35, 417–433 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  23. Yager, R.: OWA aggregation of intuitionistic fuzzy sets. Int. J. Gen. Syst. 38, 617–641 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yager, R.: On prioritized multiple-criteria aggregation. IEEE Trans. Syst. Man Cybern. B Cybern. 42(5), 1297–1305 (2012)

    Article  Google Scholar 

  25. Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning. Inf. Sci. 8, Part I, 199–251 (1975), Part II, 301–357, 9, Part III, 43–80

    Google Scholar 

  26. Zhang, D., Wang, Z.: On set-valued fuzzy integrals. Fuzzy Sets Syst. 56, 237–247 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The first two authors were supported by the project TIN2013-40765-P of the Spanish Ministry of Science. A. Kolesárová and R. Mesiar were supported by grant APVV-14-0013.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. Bustince .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Bustince, H., Fernandez, J., De Miguel, L., Barrenechea, E., Pagola, M., Mesiar, R. (2017). OWA Operators and Choquet Integrals in the Interval-Valued Setting. In: Kacprzyk, J., Filev, D., Beliakov, G. (eds) Granular, Soft and Fuzzy Approaches for Intelligent Systems. Studies in Fuzziness and Soft Computing, vol 344. Springer, Cham. https://doi.org/10.1007/978-3-319-40314-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40314-4_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40312-0

  • Online ISBN: 978-3-319-40314-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics