A Defuzzification Method of Fuzzy Numbers Induced from Weighted Aggregation Operations

  • Yuji Yoshida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3885)

Abstract

An evaluation method of fuzzy numbers is presented from the viewpoint of aggregation operators in decision making modeling. The method is given by the quasi-arithmetic means induced from weighted aggregation operators with a decision maker’s subjective utility. The properties of the weighted quasi-arithmetic mean and its translation invariance are investigated. For the mean induced from the dual aggregation operators, a formula for the calculation is also given. The movement of the weighted quasi-arithmetic means is studied in comparison between two decision maker’s utilities, which are essentially related to their attitude in decision making. Several examples are examined to discuss the properties of this defuzzification method.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aczél, J.: On weighted mean values. Bulletin of the American Math. Society 54, 392–400 (1948)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Campos, L., Munoz, A.: A subjective approach for ranking fuzzy numbers. Fuzzy Sets and Systems 29, 145–153 (1989)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: Basic concepts, issues and properties. In: Calvo, T., Gmayor, Mesiar, R. (eds.) Aggregation Operators: New Trends and Applications, pp. 3–104. Phisica-Verlag/Springer (2002)Google Scholar
  4. 4.
    Calvo, T., Pradera, A.: Double weighted aggregation operators. Fuzzy Sets and Systems 142, 15–33 (2004)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315–326 (2001)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Fishburn, P.C.: Utility Theory for Decision Making. John Wiley and Sons, New York (1970)MATHGoogle Scholar
  7. 7.
    Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multi-Criteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)CrossRefMATHGoogle Scholar
  8. 8.
    Fortemps, P., Roubens, M.: Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems 82, 319–330 (1996)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Goetshel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets and Systems 18, 31–43 (1986)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, London (1995)MATHGoogle Scholar
  11. 11.
    Kolmogoroff, A.N.: Sur la notion de la moyenne. Acad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12, 388–391 (1930)MATHGoogle Scholar
  12. 12.
    López-Díaz, M., Gil, M.A.: The λ-average value and the fuzzy expectation of a fuzzy random variable. Fuzzy Sets and Systems 99, 347–352 (1998)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Nagumo, K.: Über eine Klasse der Mittelwerte. Japanese Journal of Mathematics 6, 71–79 (1930)MATHGoogle Scholar
  14. 14.
    Torra, V., Godo, L.: Continuous WOWA operators with applications to defuzzification. In: Calvo, T., Gmayor, Mesiar, R. (eds.) Aggregation Operators: New Trends and Applications, pp. 159–176. Phisica-Verlag/Springer (2002)Google Scholar
  15. 15.
    Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems 118, 375–385 (2001)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Inform. Sciences 24, 143–161 (1981)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Yager, R.R.: OWA aggragation over a continuous interval argument with application to decision making. IEEE Trans. on Systems, Man, and Cybern. - Part B: Cybernetics 34, 1952–1963 (2004)CrossRefGoogle Scholar
  18. 18.
    Yoshida, Y., Kerre, E.E.: A fuzzy ordering on multi-dimensional fuzzy sets induced from convex cones. Fuzzy Sets and Systems 130, 343–355 (2002)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Yoshida, Y.: A mean estimation of fuzzy numbers by evaluation measures. In: Negoita, M.G., Howlett, R.J., Jain, L.C. (eds.) KES 2004. LNCS (LNAI), vol. 3214, pp. 1222–1229. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Yoshida, Y.: Mean values on intervals induced from weighted aggregation operation (preprint)Google Scholar
  21. 21.
    Zadeh, L.A.: Fuzzy sets. Inform. and Control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yuji Yoshida
    • 1
  1. 1.Faculty of Economics and Business AdministrationUniversity of KitakyushuKokuraminami, KitakyushuJapan

Personalised recommendations