Unbalanced interval-valued OWA operators | Progress in Artificial Intelligence Skip to main content
Springer Nature Link
Log in

Unbalanced interval-valued OWA operators

  • Regular Paper
  • Published:
Progress in Artificial Intelligence Aims and scope Submit manuscript

Abstract

In this work, we introduce a new class of functions defined on the interval-valued setting. These functions extend classical OWA operators but allow for different weighting vectors to handle the lower bounds and the upper bounds of the considered intervals. As a consequence, the resulting functions need not be an interval-valued aggregation function, so we study, in the case of the lexicographical order, when these operators give an interval as output and are monotone. We also discuss an illustrative example on a decision making problem in order to show the usefulness of our developments.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Barrenechea, E., Fernandez, J., Pagola, M., Chiclana, F., Bustince, H.: Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making. Knowl. Based Syst. 58, 33–44 (2014)

    Article  Google Scholar 

  2. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing. Springer, Berlin (2007)

    Google Scholar 

  3. Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Springer, Berlin (2016)

    Book  Google Scholar 

  4. Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.: Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst. 160(13), 1819–1840 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bustince, H., Calvo, T., Baets, B.D., Fodor, J., Mesiar, R., Montero, J., Paternain, D., Pradera, A.: A class of aggregation functions encompassing two-dimensional \(\{\text{ OWA }\}\) operators. Inform. Sci. 180(10), 1977–1989 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. 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 set applications. IEEE Trans Fuzzy Syst. 21(6), 1150–1162 (2013)

    Article  Google Scholar 

  8. Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Xu, Z., Bedregal, B., Montero, J., Hagras, H., Herrera, F., De Baets, B.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. In press (2015)

  9. 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, Studies in Fuzziness and Soft Computing, vol. 97, pp. 3–104. Physica, Heidelberg (2002)

    Google Scholar 

  10. Choquet, G.: Theory of capacities. Annales de l Institut Fourier 5, 131–295 (1954)

  11. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. In: Theory and Decision Library. Kluwer, Boston (1994)

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

    Book  MATH  Google Scholar 

  13. Komorníková, M., Mesiar, R.: Aggregation functions on bounded partially ordered sets and their classification. Fuzzy Sets Syst. 175(1), 48–56 (2011)

  14. Miguel, L.D., Bustince, H., Fernandez, J., Induráin, E., Kolesárová, A., Mesiar, R.: Construction of admissible linear orders for interval-valued atanassov intuitionistic fuzzy sets with an application to decision making. Inform. Fusion 27, 189–197 (2016)

    Article  Google Scholar 

  15. Sambuc, R.: Fonctions and floues: application a l’aide au diagnostic en pathologie thyroidienne. Faculté de Médecine de Marseille (1975)

  16. Sanz, J., Fernandez, A., Bustince, H., Herrera, F.: Ivturs: a linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection. IEEE Trans. Fuzzy Syst. 21(3), 399–411 (2013)

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  18. Xu, Z., Yager, R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35(4), 417–433 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Xu, Z., Yager, R.: Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim. Decis. Mak. 8(2), 123–139 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

Authors were supported by Project TIN2013-40765-P of the Spanish Government.

Author information

Authors and Affiliations

  1. Departamento Automática y Computación, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006, Pamplona, Spain

    Laura De Miguel, Humberto Bustince, Edurne Barrenechea, Miguel Pagola & Javier Fernandez

  2. Institute of Smart Cities, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006, Pamplona, Spain

    Laura De Miguel, Humberto Bustince, Edurne Barrenechea, Miguel Pagola & Javier Fernandez

Authors
  1. Laura De Miguel
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Humberto Bustince
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Edurne Barrenechea
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Miguel Pagola
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Javier Fernandez
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Humberto Bustince.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

De Miguel, L., Bustince, H., Barrenechea, E. et al. Unbalanced interval-valued OWA operators. Prog Artif Intell 5, 207–214 (2016). https://doi.org/10.1007/s13748-016-0086-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13748-016-0086-0

Keywords