Skip to main content
SpringerLink
Log in

A Defuzzification Method of Fuzzy Numbers Induced from Weighted Aggregation Operations

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

Part of the book series: Lecture Notes in Computer Science ((LNAI,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 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. Aczél, J.: On weighted mean values. Bulletin of the American Math. Society 54, 392–400 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  2. Campos, L., Munoz, A.: A subjective approach for ranking fuzzy numbers. Fuzzy Sets and Systems 29, 145–153 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  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. Calvo, T., Pradera, A.: Double weighted aggregation operators. Fuzzy Sets and Systems 142, 15–33 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315–326 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fishburn, P.C.: Utility Theory for Decision Making. John Wiley and Sons, New York (1970)

    MATH  Google Scholar 

  7. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multi-Criteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)

    Book  MATH  Google Scholar 

  8. Fortemps, P., Roubens, M.: Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems 82, 319–330 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Goetshel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets and Systems 18, 31–43 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  10. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, London (1995)

    MATH  Google Scholar 

  11. Kolmogoroff, A.N.: Sur la notion de la moyenne. Acad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12, 388–391 (1930)

    MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  13. Nagumo, K.: Über eine Klasse der Mittelwerte. Japanese Journal of Mathematics 6, 71–79 (1930)

    MATH  Google Scholar 

  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. Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems 118, 375–385 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Inform. Sciences 24, 143–161 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  20. Yoshida, Y.: Mean values on intervals induced from weighted aggregation operation (preprint)

    Google Scholar 

  21. Zadeh, L.A.: Fuzzy sets. Inform. and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Economics and Business Administration, University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu, 802-8577, Japan

    Yuji Yoshida

Authors
  1. Yuji Yoshida
    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

Yoshida, Y. (2006). A Defuzzification Method of Fuzzy Numbers Induced from Weighted Aggregation Operations. 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_17

Download citation

  • DOI: https://doi.org/10.1007/11681960_17

  • 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