Skip to main content
SpringerLink
Log in

Consensus-reaching methods for hesitant fuzzy multiple criteria group decision making with hesitant fuzzy decision making matrices

  • Published:
Frontiers of Information Technology & Electronic Engineering Aims and scope Submit manuscript

Abstract

Group decision making plays an important role in various fields of management decision and economics. In this paper, we develop two methods for hesitant fuzzy multiple criteria group decision making with group consensus in which all the experts use hesitant fuzzy decision matrices (HFDMs) to express their preferences. The aim of this paper is to present two novel consensus models applied in different group decision making situations, which are composed of consensus checking processes, consensus-reaching processes, and selection processes. All the experts make their own judgments on each alternative over multiple criteria by hesitant fuzzy sets, and then the aggregation of each hesitant fuzzy set under each criterion is calculated by the aggregation operators. Furthermore, we can calculate the distance between any two aggregations of hesitant fuzzy sets, based on which the deviation between any two experts is yielded. After introducing the consensus measure, we develop two kinds of consensus-reaching procedures and then propose two step-by-step algorithms for hesitant fuzzy multiple criteria group decision making. A numerical example concerning the selection of selling ways about ‘Trade-Ins’ for Apple Inc. is provided to illustrate and verify the developed approaches. In this example, the methods which aim to reach a high consensus of all the experts before the selection process can avoid some experts’ preference values being too high or too low. After modifying the previous preference information by using our consensus measures, the result of the selection process is much more reasonable.

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

  • Atanassov, K., Gargov, G., 1989. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst., 31(3): 343–349. https://doi.org/10.1016/0165-0114(89)90205-4

    Article  MathSciNet  Google Scholar 

  • Atanassov, K.T., 2012. On Intuitionistic Fuzzy Sets Theory, Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/978-3-642-29127-2

    Book  Google Scholar 

  • Azarnivand, A., Malekian, A., 2016. Analysis of flood risk management strategies based on a group decision making process via interval-valued intuitionistic fuzzy numbers. Water Resour. Manag., 30(6): 1903–1921. https://doi.org/10.1007/s11269-016-1259-0

    Article  Google Scholar 

  • Ben-Arieh, D., Chen, Z.F., 2006. Fuzzy group decision making. In: Badiru, A.B. (Ed.), Handbook of Industrial and Systems Engineering. CRC Press.

    Google Scholar 

  • Cabrerizo, F.J., Moreno, J.M., Pérez, I.J., et al., 2010. Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft Comput., 14(5): 451–463. https://doi.org/10.1007/s00500-009-0453-x

    Article  Google Scholar 

  • Cabrerizo, F.J., Chiclana, F., Al-Hmouz, R., et al., 2015. Fuzzy decision making and consensus: challenges. J. Intell. Fuzzy Syst., 29(3): 1109–1118. https://doi.org/10.3233/IFS-151719

    Article  MathSciNet  Google Scholar 

  • Chen, N., Xu, Z.S., Xia, M.M., 2013. Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl. Math. Model., 37(4): 2197–2211. https://doi.org/10.1016/j.apm.2012.04.031

    Article  MathSciNet  Google Scholar 

  • Gong, Z.T., Feng, X., 2016. Alpha beta-statistical convergence and strong alpha beta-convergence of order gamma for a sequence of fuzzy numbers. J. Comput. Anal. Appl., 21(2): 228–236.

    MathSciNet  MATH  Google Scholar 

  • Herrera-Viedma, E., Alonso, S., Chiclana, F., et al., 2007. A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans. Fuzzy Syst., 15(5): 863–877. https://doi.org/10.1109/TFUZZ.2006.889952

    Article  Google Scholar 

  • Kong, L.F., 2010. Environmental protection effect of the policy of replacement of household electrical appliances and the electronic waste treatment. Ecol. Econ., 6: 164–167, 174 (in Chinese).

    Google Scholar 

  • Liao, H.C., Xu, Z.S., 2014. Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment. J. Intell. Fuzzy Syst., 26(4): 1601–1617. https://doi.org/10.3233/IFS-130841

    MathSciNet  MATH  Google Scholar 

  • Liao, H.C., Xu, Z.S., 2015. Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making. Soft Comput., 19(9): 2551–2564. https://doi.org/10.1007/s00500-014-1422-6

    Article  Google Scholar 

  • Liao, H.C., Xu, Z.S., Xia, M.M., 2014. Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int. J. Inform. Technol. Decis. Making, 13(1): 47–76. https://doi.org/10.1142/S0219622014500035

    Article  Google Scholar 

  • Liao, H.C., Xu, Z.S., Zeng, X.J., et al., 2015a. Framework of group decision making with intuitionistic fuzzy preference information. IEEE Trans. Fuzzy Syst., 23(4): 1211–1227. https://doi.org/10.1109/TFUZZ.2014.2348013

    Article  Google Scholar 

  • Liao, H.C., Xu, Z.S., Zeng, X.J., 2015b. Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowl.-Based Syst., 82: 115–127. https://doi.org/10.1016/j.knosys.2015.02.020

    Article  Google Scholar 

  • Liao, H.C., Xu, Z.S., Zeng, X.J., et al., 2016. An enhanced consensus-reaching process in group decision making with intuitionistic fuzzy preference relations. Inform. Sci., 329: 274–286. https://doi.org/10.1016/j.ins.2015.09.024

    Article  Google Scholar 

  • Torra, V., 2010. Hesitant fuzzy sets. Int. J. Intell. Syst., 25(6): 529–539. https://doi.org/10.1002/int.20418

    MATH  Google Scholar 

  • Torra, V., Narukawa, Y., 2009. On hesitant fuzzy sets and decision. Proc. IEEE Int. Conf. on Fuzzy Systems, p.1378–1382. https://doi.org/10.1109/FUZZY.2009.5276884

    Google Scholar 

  • Wei, G.W., 2012. Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl.- Based Syst., 31: 176–182. https://doi.org/10.1016/j.knosys.2012.03.011

    Article  Google Scholar 

  • Wu, P., Liu, J., Wang, M.C., 2014. Considering about the pricing strategy optimization model of Trade-Ins. Jilin Univ. J. Soc. Sci. Ed., 54(6): 82–90 (in Chinese).

    Google Scholar 

  • Xia, M.M., Xu, Z.S., 2011. Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason., 52(3): 395–407. https://doi.org/10.1016/j.ijar.2010.09.002

    Article  MathSciNet  Google Scholar 

  • Xia, M.M., Xu, Z.S., Chen, N., 2013. Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negot., 22(2): 259–279. https://doi.org/10.1007/s10726-011-9261-7

    Article  Google Scholar 

  • Xu, G.L., Wan, S.P., Wang, F., et al., 2016. Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations. Knowl.-Based Syst., 98: 30–43. https://doi.org/10.1016/j.knosys.2015.12.007

    Article  Google Scholar 

  • Xu, Z.S., 2014. Hesitant Fuzzy Sets Theory. Springer, Cham, Berlin. https://doi.org/10.1007/978-3-319-04711-9

    Book  Google Scholar 

  • Xu, Z.S., Xia, M.M., 2011a. Distance and similarity measures for hesitant fuzzy sets. Inform. Sci., 181(11): 2128–2138. https://doi.org/10.1016/j.ins.2011.01.028

    Article  MathSciNet  Google Scholar 

  • Xu, Z.S., Xia, M.M., 2011b. On distance and correlation measures of hesitant fuzzy information. Int. J. Intell. Syst., 26(5): 410–425. https://doi.org/10.1002/int.20474

    Article  Google Scholar 

  • Zadeh, L.A., 1965. Fuzzy sets. Inform. Contr., 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X

    Article  Google Scholar 

  • Zeng, S.Z., Baležentis, A., Su, W.H., 2013. The multi-criteria hesitant fuzzy group decision making with MULTI-MOORA method. Econ. Comput. Econ. Cybern. Stud. Res., 47(3): 171–184.

    Google Scholar 

  • Zhang, J.L., Qi, X.W., Huang, H.B., 2013. A hesitant fuzzy multiple attribute group decision making approach based on TOPSIS for parts supplier selection. Appl. Mech. Mater., 357–360: 2730–2737. https://doi.org/10.4028/www.scientific.net/AMM.357-360.2730

    Article  Google Scholar 

  • Zhang, L.Y., Li, T., Xu, X.H., 2014. Consensus model for multiple criteria group decision making under intuitionistic fuzzy environment. Knowl.-Based Syst. 57: 127–135. https://doi.org/10.1016/j.knosys.2013.12.013

    Article  Google Scholar 

  • Zhang, Z.M., Wang, C., Tian, X.D., 2015a. A consensus model for group decision making with hesitant fuzzy information. Int. J. Uncert. Fuzz. Knowl.-Based Syst., 23(3): 459–480. https://doi.org/10.1142/S0218488515500208

    Article  MathSciNet  Google Scholar 

  • Zhang, Z.M., Wang, C., Tian, X.D., 2015b. A decision support model for group decision making with hesitant fuzzy preference relations. Knowl.-Based Syst., 86: 77–101. https://doi.org/10.1016/j.knosys.2015.05.023

    Article  Google Scholar 

  • Zhou, L., 2016. On Atanassov’s intuitionistic fuzzy sets in the complex plane and the field of intuitionistic fuzzy numbers. IEEE Trans. Fuzzy Syst., 24(2): 253–259. https://doi.org/10.1109/TFUZZ.2015.2452957

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610065, China

    Jie Ding, Ze-shui Xu & Hu-chang Liao

Authors
  1. Jie Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ze-shui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hu-chang Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ze-shui Xu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 61273209, 71501135, 71571123, and 71532007)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, J., Xu, Zs. & Liao, Hc. Consensus-reaching methods for hesitant fuzzy multiple criteria group decision making with hesitant fuzzy decision making matrices. Frontiers Inf Technol Electronic Eng 18, 1679–1692 (2017). https://doi.org/10.1631/FITEE.1601546

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/FITEE.1601546

Keywords

CLC number

Search

Navigation