Fuzzy Optimization and Decision Making

, Volume 5, Issue 1, pp 5–20 | Cite as

On the Parameterized OWA Operators for Fuzzy MCDM Based on Vague Set Theory

  • Jue Wang
  • San-Yang Liu
  • Jie Zhang
  • Shou-Yang Wang


The family of Ordered Weighted Averaging (OWA) operators, as introduced by Yager, appears to be very useful in multi-criteria decision-making (MCDM). In this paper, we extend a family of parameterized OWA operators to fuzzy MCDM based on vague set theory, where the characteristics of the alternatives are presented by vague sets. These families are specified by a few parameters to aggregate vague values instead of the intersection and union operators proposed by Chen. The proposed method provides a “soft” and expansive way to help the decision maker to make his decisions. Examples are shown to illustrate the procedure of the proposed method at the end of this paper.


fuzzy set fuzzy MCDM OWA operator S-OWA operator vague set 


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  1. Chen, S. M., Tan, J. M. 1994“Handling Multicriteria Fuzzy Decision-making Problems Based on Vague set Theory”Fuzzy Sets and Systems67163172CrossRefMathSciNetGoogle Scholar
  2. Filev, D. P. and R. R. Yager. (1994). “Learning OWA Operator Weights from Data.” In Proceedings of the 3rd IEEE International Conference Fuzzy Systems, Orlando, FL, pp. 468–473.Google Scholar
  3. Filev, D. P., Yager, R. R. 1998“On the Issue of Obtaining OWA Operator Weights”Fuzzy Sets Systems94157169CrossRefMathSciNetGoogle Scholar
  4. Larsen, H. L. (1999). “Importance Weighted OWA Aggregation of Multicriteria Queries,” In Proceeding of the North American Fuzzy Information Processing Society conference (NAFIPS’99), New York, 10–12 June 1999, pp. 740–744.Google Scholar
  5. Gau, W.-L., Buehrer, D. J. 1993“Vague Sets”IEEE Transactions on Systems, Man and Cybernetics23610614CrossRefGoogle Scholar
  6. Hong, D. J., Choi, C. H. 2000“Multicriteria Fuzzy Decision-making Problems Based on Vague set Theory”Fuzzy Sets and Systems114103113CrossRefGoogle Scholar
  7. Hwang, C. L., Yoon, K. 1981Multiple Attributes Decision Making Methods and ApplicationsSpringerBerlin, HeidelbergGoogle Scholar
  8. Kickert, W. J. M. 1978Fuzzy Theories on Decision Making: A Critical ReviewKluwerBostonGoogle Scholar
  9. Laarhoven, P. J. M., Pedrycz, W. 1983“A Fuzzy Extension of Saaty’s Priority Theory”Fuzzy Sets and System11229241MathSciNetGoogle Scholar
  10. Mitchell, H. B., Estrakh, D. D. 1997“A Modified OWA Operator and its use in Lossless DPCM Image Compression”International Journal of Uncertainty, Fuzziness, Knowledge Based Systems5429436Google Scholar
  11. O’Hagan, M. (1988) “Aggregating Template or rule antecedents in Real-time expert Systems with Fuzzy set Logic,” In Proceedings of the 22nd Annual IEEE Asilomar Conference Signals, Systems, Computers, Pacific Grove, CA, pp. 81–689.Google Scholar
  12. Yager, R. R. 1978“Fuzzy Decision Making Including Unequal Objectives”Fuzzy Sets and Systems18795MATHGoogle Scholar
  13. Yager, R. R. 1988“On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making”IEEE Trans. Systems Man Cybernetics18183190MATHMathSciNetGoogle Scholar
  14. Yager, R. R. 1993“Families of OWA Operator”Fuzzy Sets and System59125148MATHMathSciNetGoogle Scholar
  15. Yager, R. R. 1997“On the Inclusion of Importances in OWA Aggregations”Yager, R. R.Kacprzyk, J. eds. The Ordered Weighted Averaging Operators: Theory and ApplicationsKluwerNorwell, MA4159Google Scholar
  16. Yager, R. R., Filev, D. 1999“Induced Ordered Weighted Averaging Operators”IEEE Trans. on Systems, Man and Cybernetics. Part B: Cybernetics29141150Google Scholar
  17. Yager, R. R., Kacprzyk, J. 1997The Ordered Weighted Averaging Operators: Theory and ApplicationsKluwerNorwell, MAGoogle Scholar
  18. Zadeh, L. A. 1965Fuzzy SetsInformation and Control8338356CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Jue Wang
    • 1
    • 2
  • San-Yang Liu
    • 1
  • Jie Zhang
    • 1
  • Shou-Yang Wang
    • 2
  1. 1.School of ScienceXidian UniversityXi’anP. R. China
  2. 2.Institute of Systems Science, Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingP. R. China

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