Advertisement

Group Decision Making Based on Acceptably Consistent Interval Multiplicative Preference Relations

  • Zhen ZhangEmail author
  • Wenyu Yu
  • Chonghui Guo
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 660)

Abstract

In this paper, group decision making problems based on interval multiplicative preference relations are investigated. First, the acceptable consistency property for an interval multiplicative preference relation is discussed, based on which some optimization models are established to derive an acceptably consistent interval multiplicative preference relation based on the initial one. The interval multiplicative preference relation derived by the proposed model has the minimum deviation from the initial one and can preserve the decision information as much as possible. Subsequently, an approach to group decision making with interval multiplicative preference relations is developed based on the proposed models. Eventually, a numerical example is provided to illustrate the proposed approach.

Keywords

Group decision making Interval multiplicative preference relation Consistency Optimization 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 71501023, 71171030), the Funds for Creative Research Groups of China (No. 71421001), the China Postdoctoral Science Foundation (2015M570248) and the Fundamental Research Funds for the Central Universities (DUT15RC(3)003).

References

  1. 1.
    Alonso, S., Cabrerizo, F.J., Chiclana, F., Herrera, F., Herrera-Viedma, E.: Group decision making with incomplete fuzzy linguistic preference relations. Int. J. Intell. Syst. 24, 201–222 (2009). doi: 10.1002/int.20332 CrossRefzbMATHGoogle Scholar
  2. 2.
    Arbel, A.: Approximate articulation of preference and priority derivation. Eur. J. Oper. Res. 43, 317–326 (1989). doi: 10.1016/0377-2217(89)90231-2 MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Conde, E., de la Pérez, M.P.R.: A linear optimization problem to derive relative weights using an interval judgement matrix. Eur. J. Oper. Res. 201, 537–544 (2010). doi: 10.1016/j.ejor.2009.03.029 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dong, Y., Chen, X., Li, C.C., Hong, W.C., Xu, Y.: Consistency issues of interval pairwise comparison matrices. Soft Comput. 19, 2321–2335 (2015). doi: 10.1007/s00500-014-1426-2 CrossRefGoogle Scholar
  5. 5.
    Dong, Y., Herrera-Viedma, E.: Consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relation. IEEE Trans. Cybern. 45, 780–792 (2015). doi: 10.1109/TCYB.2014.2336808 CrossRefGoogle Scholar
  6. 6.
    Liu, F., Zhang, W.G., Wang, Z.X.: A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making. Eur. J. Oper. Res. 218, 747–754 (2012). doi: 10.1016/j.ejor.2015.06.015 MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Set Syst. 1, 155–167 (1978). doi: 10.1016/0165-0114(78)90001-5 MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychol. 15, 234–281 (1977). doi: 10.1016/0022-2496(77)90033-5 MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  10. 10.
    Saaty, T.L., Vargas, L.G.: Uncertainty and rank order in the analytic hierarchy process. Eur. J. Oper. Res. 32, 107–117 (1987). doi: 10.1016/0377-2217(87)90275-X MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Wang, Y.M., Yang, J.B., Xu, D.L.: Interval weight generation approaches based on consistency test and interval comparison matrices. Appl. Math. Comput. 167, 252–273 (2005). doi: 10.1016/j.amc.2004.06.080 MathSciNetzbMATHGoogle Scholar
  12. 12.
    Wang, Z.J.: A note on “a goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”. Eur. J. Oper. Res. 247, 867–871 (2015). doi: 10.1016/j.ejor.2015.06.015 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Xu, Z.: Intuitionistic preference relations and their application in group decision making. Inf. Sci. 177, 2363–2379 (2007). doi: 10.1016/j.ins.2006.12.019 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Xu, Z., Cai, X.: Deriving weights from interval multiplicative preference relations in group decision making. Group Decis. Negot. 23, 695–713 (2014). doi: 10.1007/s10726-012-9315-5 MathSciNetCrossRefGoogle Scholar
  15. 15.
    Xu, Z., Wei, C.: A consistency improving method in the analytic hierarchy process. Eur. J. Oper. Res. 116, 443–449 (1999). doi: 10.1016/S0377-2217(98)00109-X CrossRefzbMATHGoogle Scholar
  16. 16.
    Zhang, Z., Guo, C.: An approach to group decision making with heterogeneous incomplete uncertain preference relations. Comput. Ind. Eng. 71, 27–36 (2014). doi: 10.1016/j.cie.2014.02.004 CrossRefGoogle Scholar
  17. 17.
    Zhang, Z., Guo, C.: Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations. Int. J. Syst. Sci. 47, 2572–2587 (2016). doi: 10.1080/00207721.2014.999732 MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Zhang, Z., Guo, C.: Fusion of heterogeneous incomplete hesitant preference relations in group decision making. Int. J. Comput. Intell. Syst. 9, 245–262 (2016). doi: 10.1080/18756891.2016.1149999 CrossRefGoogle Scholar
  19. 19.
    Zhang, Z., Guo, C.: Minimum adjustment-based consistency and consensus models for group decision making with interval pairwise comparison matrices. In: Proceedings of the 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2016), pp. 1701–1708. IEEE Press (2016)Google Scholar
  20. 20.
    Zhu, B., Xu, Z.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE T. Fuzzy Syst. 22, 35–45 (2014). doi: 10.1109/TFUZZ.2013.2245136 MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  1. 1.Institute of Systems EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Institute of Information Management and Information SystemsDalian University of TechnologyDalianPeople’s Republic of China

Personalised recommendations