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.
Access this article
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
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
Atanassov, K.T., 2012. On Intuitionistic Fuzzy Sets Theory, Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/978-3-642-29127-2
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
Ben-Arieh, D., Chen, Z.F., 2006. Fuzzy group decision making. In: Badiru, A.B. (Ed.), Handbook of Industrial and Systems Engineering. CRC Press.
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
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
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
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.
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
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).
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
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
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
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
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
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
Torra, V., 2010. Hesitant fuzzy sets. Int. J. Intell. Syst., 25(6): 529–539. https://doi.org/10.1002/int.20418
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
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
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).
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
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
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
Xu, Z.S., 2014. Hesitant Fuzzy Sets Theory. Springer, Cham, Berlin. https://doi.org/10.1007/978-3-319-04711-9
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
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
Zadeh, L.A., 1965. Fuzzy sets. Inform. Contr., 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
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.
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
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
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
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
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
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 61273209, 71501135, 71571123, and 71532007)
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1601546
Keywords
- Multiple criteria group decision making
- Group consensus
- Consensus-reaching process
- Hesitant fuzzy decision making matrices
- Aggregation operators