Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Determining OWA Operator Weights by Mean Absolute Deviation Minimization

  • Conference paper
Artificial Intelligence and Soft Computing (ICAISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7267))

Included in the following conference series:

Abstract

The ordered weighted averaging (OWA) operator uses the weights assigned to the ordered values rather than to the specific criteria. This allows one to model various aggregation preferences, preserving simultaneously the impartiality (neutrality) with respect to the individual attributes. The determination of ordered weighted averaging (OWA) operator weights is a crucial issue of applying the OWA operator for decision making. This paper considers determining monotonic weights of the OWA operator by minimization the mean absolute deviation inequality measure. This leads to a linear programming model which can also be solved analytically.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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.

Similar content being viewed by others

References

  1. Amin, G.R., Emrouznejad, A.: An extended minimax disparity to determine the OWA operator weights. Comput. Ind. Eng. 50, 312–316 (2006)

    Article  Google Scholar 

  2. Fuller, R.: On obtaining OWA operator weights: a short survey of recent developments. In: Proc. 5th IEEE Int. Conf. Comput. Cybernetics, Gammarth, Tunisia, pp. 241–244 (2007)

    Google Scholar 

  3. Fuller, R., Majlender, P.: An analytic approach for obtaining maximal entropy OWA operator weights. Fuzzy Sets and Systems 124, 53–57 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fuller, R., Majlender, P.: On obtaining minimal variability OWA operator weights. Fuzzy Sets and Systems 136, 203–215 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gastwirth, J.L.: A general definition of the Lorenz curve. Econometrica 39, 1037–1039 (1971)

    Article  MATH  Google Scholar 

  6. Liu, X.: The solution equivalence of minimax disparity and minimum variance problems for OWA operators. Int. J. Approx. Reasoning 45, 68–81 (2007)

    Article  MATH  Google Scholar 

  7. O’Hagan, M.: Aggregating template or rule antecedents in real-time expert systems with fuzzy set logic. In: Proc. 22nd Annu. IEEE Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, pp. 681–689 (1988)

    Google Scholar 

  8. Ogryczak, W.: Inequality measures and equitable approaches to location problems. Eur. J. Opnl. Res. 122, 374–391 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ogryczak, W., Śliwiński, T.: On solving linear programs with the ordered weighted averaging objective. Eur. J. Opnl. Res. 148, 80–91 (2003)

    Article  MATH  Google Scholar 

  10. Ogryczak, W., Śliwiński, T.: On efficient WOWA optimization for decision support under risk. Int. J. Approx. Reason. 50, 915–928 (2009)

    Article  MATH  Google Scholar 

  11. Sen, A.: On Economic Inequality. Clarendon Press, Oxford (1973)

    Book  Google Scholar 

  12. Torra, V., Narukawa, Y.: Modeling Decisions Information Fusion and Aggregation Operators. Springer, Berlin (2007)

    Google Scholar 

  13. Wang, Y.-M., Luo, Y., Liu, X.: Two new models for determining OWA operator weights. Comput. Ind. Eng. 52, 203–209 (2007)

    Article  Google Scholar 

  14. Wang, Y.-M., Parkan, C.: A minimax disparity approach for obtaining OWA operator weights. Information Sciences 175, 20–29 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu, J., Sun, B.-L., Liang, C.-Y., Yang, S.-L.: A linear programming model for determining ordered weighted averaging operator weights with maximal Yager’s entropy. Comput. Ind. Eng. 57, 742–747 (2009)

    Article  Google Scholar 

  16. Xu, Z.: An overview of methods for determining OWA weights. Int. J. Intell. Syst. 20, 843–865 (2005)

    Article  MATH  Google Scholar 

  17. Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems, Man and Cyber. 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yager, R.R.: Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 11, 49–73 (1996)

    Article  Google Scholar 

  19. Yager, R.R.: Measures of entropy and fuzziness related to aggregation operators. Information Sciences 82, 147–166 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yager, R.R.: On the dispersion measure of OWA operators. Information Sciences 179, 3908–3919 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Yager, R.R., Kacprzyk, J.: The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer AP, Dordrecht (1997)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Control and Computation Engineering, Warsaw University of Technology, Warsaw, Poland

    Michał Majdan & Włodzimierz Ogryczak

  2. National Institute of Telecommunications, Warsaw, Poland

    Michał Majdan

Authors
  1. Michał Majdan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Włodzimierz Ogryczak
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Department of Electrical Engineering and Computer Sciences, Computer Science Division, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Majdan, M., Ogryczak, W. (2012). Determining OWA Operator Weights by Mean Absolute Deviation Minimization. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29347-4_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29347-4_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29346-7

  • Online ISBN: 978-3-642-29347-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation