Skip to main content

Group decision-making based on heterogeneous preference relations with self-confidence

Abstract

Preference relations are very useful to express decision makers’ preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing preference relations. In this study, we define the preference relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the preference relation with self-confidence. Furthermore, we present a two-stage linear programming model for estimating the collective preference vector for the group decision-making based on heterogeneous preference relations with self-confidence. Finally, numerical examples are used to illustrate the two-stage linear programming model, and a comparative analysis is carried out to show how self-confidence levels influence on the group decision-making results.

This is a preview of subscription content, access via your institution.

References

  1. Alonso, S., Chiclana, F., Herrera, F., Herrera-Viedma, E., Alcalá-Fdez, J., & Porcel, C. (2008). A consistency-based procedure to estimate missing pairwise preference values. International Journal of Intelligent Systems, 23, 155–175.

    Article  MATH  Google Scholar 

  2. Cabrerizo, F. J., Chiclana, F., Al-Hmouz, R., Morfeq, A., Balamash, A. S., & Herrera-Viedma, E. (2015). Fuzzy decision making and consensus: Challenges. Journal of Intelligent & Fuzzy Systems, 29(3), 1109–1118.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cabrerizo, F. J., Pérez, I. J., & Herrera-Viedma, E. (2010). Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information. Knowledge-Based Systems, 23, 169–181.

    Article  Google Scholar 

  4. Chen, X., Zhang, H. J., & Dong, Y. C. (2015). The fusion process with heterogeneous preference structures in group decision making: A survey. Information Fusion, 24, 72–83.

    Article  Google Scholar 

  5. Chiclana, F., Garcia, J. M. Tapia, Moral, M. J. Del, & Herrera-Viedma, E. (2013). A statistical comparative study of different similarity measures of consensus in group decision making. Information Sciences, 221, 110–123.

    Article  MathSciNet  Google Scholar 

  6. Chiclana, F., Herrera, F., & Herrera-Viedma, E. (1998). Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems, 97, 33–48.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chiclana, F., Herrera-Viedma, E., Alonso, S., & Herrera, F. (2009). Cardinal consistency of reciprocal preference relations: A characterization of multiplicative transitivity. IEEE Transactions on Fuzzy Systems, 17(1), 14–23.

    Article  Google Scholar 

  8. Dong, Y. C., & Herrera-Viedma, E. (2015). Consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relations. IEEE Transactions on Cybernetics, 45, 780–792.

    Article  Google Scholar 

  9. Dong, Y. C., Li, C. C., & Herrera, F. (2016). Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its uses to deal with hesitant unbalanced linguistic information. Information Sciences, 367–368, 259–278.

    Article  Google Scholar 

  10. Dong, Y. C., Li, C. C., Xu, Y. F., & Gu, X. (2015). Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations. Group Decision and Negotiation, 24, 217–242.

    Article  Google Scholar 

  11. Dong, Y. C., & Zhang, H. J. (2014). Multiperson decision making with different preference representation structures: A direct consensus framework and its properties. Knowledge-Based Systems, 58, 45–57.

    Article  Google Scholar 

  12. Dong, Y. C., Zhang, H. J., & Herrera-Viedma, E. (2016). Integrating experts’ weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors. Decision Support Systems, 84, 1–15.

    Article  Google Scholar 

  13. Fodor, J., & Roubens, (1994). Fuzzy preference modelling and multicriteria decision support. Dordrecht: Kluwer.

    Book  MATH  Google Scholar 

  14. Herrera, F., & Martínez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8, 746–752.

    Article  Google Scholar 

  15. Herrera-Viedma, E., Chiclana, F., Herrera, F., & Alonso, S. (2007). Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Transactions on Systems, Man, and Cybernetics—Part B, 37(1), 176–189.

    Article  MATH  Google Scholar 

  16. Herrera-Viedma, E., Herrera, F., Chiclana, F., & Luque, M. (2004). Some issues on consistency of fuzzy preference relations. European Journal of Operational Research, 154, 98–109.

    Article  MATH  MathSciNet  Google Scholar 

  17. Li, C. C., Dong, Y. C., Herrera, F., Herrera-Viedma, E., & Martínez, L. (2017). Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching. Information Fusion, 33, 29–40.

    Article  Google Scholar 

  18. Orlovsky, S. A. (1978). Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems, 1(3), 155–167.

    Article  MATH  MathSciNet  Google Scholar 

  19. Pérez, I. J., Cabrerizo, F. J., & Herrera-Viedma, E. (2010). A mobile decision support system for dynamic group decision making problems. IEEE Transactions on Systems, Man and Cybernetics—Part A: Systems and Humans, 40(6), 1244–1256.

    Article  Google Scholar 

  20. Saaty, T. L. (1980). The analytical hierarchy process. New York: McGraw-Hill.

    MATH  Google Scholar 

  21. Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems, 12(2), 117–131.

    Article  MATH  MathSciNet  Google Scholar 

  22. Ureña, R., Chiclana, F., Fujita, H., & Herrera-Viedma, E. (2015a). Confidence-consistency driven group decision making approach with incomplete reciprocal intuitionistic preference relations. Knowledge-Based Systems, 89, 86–96.

    Article  Google Scholar 

  23. Ureña, R., Chiclana, F., Morente, J. A., & Herrera-Viedma, E. (2015b). Managing incomplete preference relations in decision making: A review and future trends. Information Sciences, 302, 14–32.

    Article  MATH  MathSciNet  Google Scholar 

  24. Wen, X., Yan, M., Xian, J., Yue, R., & Peng, A. (2016). Supplier selection in supplier chain management using Choquet integral-based linguistic operators under fuzzy heterogeneous environment. Fuzzy Optimization and Decision Making, 15, 307–330.

    Article  MathSciNet  Google Scholar 

  25. Zadeh, L. A. (2011). A note on Z-numbers. Information Sciences, 181, 2923–2932.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported in part by NSF of China under Grants Nos. 71171160 and 71571124, the Grant (No. skqy201606) from Sichuan University, FEDER funds under Grants TIN2013-40658-P and TIN2016-75850-R, and the Andalusian Excellence Project Grant TIC-5991.

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Yucheng Dong or Enrique Herrera-Viedma.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, W., Dong, Y., Chiclana, F. et al. Group decision-making based on heterogeneous preference relations with self-confidence. Fuzzy Optim Decis Making 16, 429–447 (2017). https://doi.org/10.1007/s10700-016-9254-8

Download citation

Keywords

  • Preference relations
  • Self-confidence levels
  • Collective preference vector
  • Linear programming model