Skip to main content
SpringerLink
Log in

A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy bonferroni means

  • Published:
Journal of Systems Science and Systems Engineering Aims and scope Submit manuscript

Abstract

Inspired by the idea of Bonferroni mean, in this paper we develop an aggregation technique called the interval-valued intuitionistic fuzzy Bonferroni mean for aggregating interval-valued intuitionistic fuzzy information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define a weighted interval-valued intuitionistic fuzzy Bonferroni mean, based on which we give a procedure for multi-criteria decision making under interval-valued intuitionistic fuzzy environments.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Atanassov, K.& Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31: 343–349

    Article  MATH  MathSciNet  Google Scholar 

  2. Beliakov, G., James, S., Mordelová, J., Rückschlossová, T.& Yager, R.R. (2010). Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets and Systems, 161: 2227–2242

    Article  MATH  MathSciNet  Google Scholar 

  3. Beliakov, G., Pradera, A. & Calvo, T. (2007). Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg

    Google Scholar 

  4. Bonferroni, C. (1950). Sulle medie multiple di potenze. Bolletino Matematica Italiana, 5: 267–270

    MATH  MathSciNet  Google Scholar 

  5. Bullen, P.S. (2003). Handbook of Mean and Their Inequalties. Kluwer, Dordrecht

    Google Scholar 

  6. Chen, Q., Xu, Z.S., Liu, S.S.& Yu, X.H. (2010). A method based on interval-valued intuitionistic fuzzy entropy for multiple attribute decision making. Information: An International Interdisciplinary Journal, 13: 67–77

    Google Scholar 

  7. Choquet, G. (1953). Theory of capacities. Annales de l’Institut Fourier, 5: 131–296

    MathSciNet  Google Scholar 

  8. Dempster, A.P. (1967). Upper and lower probabilities induced by a multi-valued mapping. Annals of Mathematical Statistics, 38: 325–339

    Article  MATH  MathSciNet  Google Scholar 

  9. Dujmovic, J.J. (2007). Continuous preference logic for system evaluation. IEEE Transactions on Fuzzy Systems, 15: 1082–1099

    Article  Google Scholar 

  10. Marichal, J.L. (2007). k-Intolerant capacities and Choquet integrals. European Journal of Operational Research, 177: 1453–1468

    Article  MATH  MathSciNet  Google Scholar 

  11. Shafer, G. (1976). Mathematical Theory of Evidence. Princeton University Press, Princeton, NJ

    MATH  Google Scholar 

  12. Sugeno, M. (1974). Theory of fuzzy integrals and its applications. Ph.D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan

    Google Scholar 

  13. Wang, Z.J., Li, K.W.& Wang, W.Z. (2009). An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Information Sciences, 179: 3026–3040

    Article  MATH  MathSciNet  Google Scholar 

  14. Xu, Z.S. (2005). An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 20: 843–865

    Article  MATH  Google Scholar 

  15. Xu, Z.S. (2010a). A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Information Sciences, 180: 181–190

    Article  MATH  Google Scholar 

  16. Xu, Z.S. (2010b). Uncertain Bonferroni mean operators. International Journal of Computational Intelligence Systems, 3: 761–769

    Article  Google Scholar 

  17. Xu, Z.S. (2010c). A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decision and Negotiation, 19: 57–76

    Article  Google Scholar 

  18. Xu, Z.S. (2010d). Choquet integrals of weighted intuitionistic fuzzy information. Information Sciences, 180: 726–736

    Article  MATH  MathSciNet  Google Scholar 

  19. Xu, Z.S.& Cai, X.Q. (2009). Incomplete interval-valued intuitionistic preference relations. International Journal of General Systems, 38: 871–886

    Article  MATH  MathSciNet  Google Scholar 

  20. Xu, Z.S. & Cai, X.Q. (2010). Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. International Journal of Intelligent Systems, 25: 489–513

    MATH  MathSciNet  Google Scholar 

  21. Xu, Z.S., Chen, J.& Wu, J.J. (2008). Clustering algorithm for intuitionistic fuzzy sets. Information Sciences, 178: 3775–3790

    Article  MATH  MathSciNet  Google Scholar 

  22. Xu, Z.S.& Yager, R.R. (2008). Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning, 48: 246–262

    Article  MATH  MathSciNet  Google Scholar 

  23. Xu, Z.S.& Yager, R.R. (2009). Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optimization and Decision Making, 8: 123–139

    Article  MATH  MathSciNet  Google Scholar 

  24. Xu, Z.S.& Yager, R.R. (2011). Intuitionistic fuzzy Bonferroni means. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 41: 568–578

    Article  Google Scholar 

  25. Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18: 183–190

    Article  MATH  MathSciNet  Google Scholar 

  26. Yager, R.R. (2009). On generalized Bonferroni mean operators for multi-criteria aggregation. International Journal of Approximate Reasoning, 50: 1279–1286

    Article  MATH  MathSciNet  Google Scholar 

  27. Yager, R., Beliakov, G.& James, S. (2009). On generalized Bonferroni means. In: Proceedings of the Eurofuse Workshop Preference Modelling and Decision Analysis, 1–6, Pamplona, Spain, September 16–18, 2009

    Google Scholar 

  28. Yoon, K. (1989). The propagation of errors in multiple-attribute decision analysis: a practical approach. Journal of Operational Research Society, 40: 681–686

    MathSciNet  Google Scholar 

  29. Zhao, H, Xu, Z.S., Ni, M.F. & Liu, S.S. (2010). Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 25: 1–30

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Economics and Management, Southeast University, Nanjing, Jiangsu, 211189, China

    Zeshui Xu

  2. Institute of Communications Engineering, PLA University of Science and Technology, Nanjing Jiangsu, 210007, China

    Zeshui Xu & Qi Chen

  3. Institute of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu, 210007, China

    Qi Chen

Authors
  1. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zeshui Xu.

Additional information

The work was supported in part by the National Natural Science Foundation of China (No.71071161), and the National Science Fund for Distinguished Young Scholars of China (No.70625005).

Zeshui Xu received the Ph.D. degree in management science and engineering from Southeast University, Nanjing, China, in 2003. From April 2003 to May 2005, he was a Postdoctoral Researcher with the School of Economics and Management, Southeast University. From October 2005 to December 2007, he was a Postdoctoral Researcher with the School of Economics and Management, Tsinghua University, Beijing, China. He is an Adjunct Professor with the School of Economics and Management, Southeast University. He is a Chair Professor with PLA University of Science and Technology, Nanjing. He is a member of the Editorial Boards of Information: An International Journal, the International Journal of Applied Management Science, the International Journal of Data Analysis Techniques and Strategies, and the System Engineering-Theory and Practice and Fuzzy Systems and Mathematics. He has authored three books and contributed more than 280 journal articles to professional journals. His current research interests include information fusion, group decision making, computing with words, and aggregation operators.

Qi Chen received the master’s degree in applied mathematics from Institute of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu, China, in 2003. She is currently working toward the Ph.D. degree at Institute of Communications Engineering, PLA University of Science and Technology. Her research interests include fuzzy mathematics and multicriteria decision making.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, Z., Chen, Q. A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy bonferroni means. J. Syst. Sci. Syst. Eng. 20, 217–228 (2011). https://doi.org/10.1007/s11518-011-5163-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11518-011-5163-0

Keywords

Search

Navigation