Skip to main content
SpringerLink
Log in

A Novel Probabilistic Linguistic Approach for Large-Scale Group Decision Making with Incomplete Weight Information

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

The large-scale group decision-making (GDM) problems with linguistic information have received more and more attentions; however, how to effectively manage the linguistic assessments provided by the large number of experts is still a challenge. In this paper, we employ the probabilistic linguistic term sets (PLTSs), which are the extension form of hesitant fuzzy linguistic term sets, to manage the large number of linguistic assessments. We also present a probabilistic linguistic distance measure for PLTSs. To address the large-scale probabilistic linguistic GDM problems in which the weights of groups are completely unknown or partially known in advance, we develop a probabilistic linguistic GDM method. First, we propose a consistency- and consensus-based model to objectively determine the weights of the groups. Then, to aggregate the opinions of all the groups, we propose a new probabilistic linguistic weighted arithmetic averaging operator and by using it the collective assessment of each alternative is obtained. Finally, the ranking of all alternatives is obtained on the basis of the dominance degrees and the optimal alternative is selected.

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.

Similar content being viewed by others

Notes

  1. In some situations, some participators may fail to provide their assessments or their opinions are loss in the decision-making process, i.e., \(e_{ij}^{k} =\)“–” and “–” denotes “no provided.” For this case, we stipulate that \(r_{ij}^{k\sigma } = 0\) if \(e_{ij}^{k} =\)“–”.

References

  1. Chen, S.M., Hong, J.A.: Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf. Sci. 286, 63–74 (2014)

    Article  Google Scholar 

  2. Chen, Z.S., Chin, K.S., Li, Y.L., et al.: Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making. Inf. Sci. 357, 61–87 (2016)

    Article  MathSciNet  Google Scholar 

  3. Cabrerizo, F.J., Moreno, J.M., Pérez, I.J., et al.: Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft. Comput. 14(5), 451–463 (2010)

    Article  Google Scholar 

  4. Dong, Y.C., 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(4), 780–792 (2015)

    Article  Google Scholar 

  5. Dong, Y.C., Xu, Y., Yu, S.: Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model. IEEE Trans. Fuzzy Syst. 17(6), 1366–1378 (2009)

    Article  Google Scholar 

  6. Gu, X.J., Xu, Z.S.: Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf. Sci. 2(372), 407–427 (2016)

    Article  Google Scholar 

  7. Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8(6), 746–752 (2000)

    Article  Google Scholar 

  8. Herrera-Viedma, E., Cabrerizo, F.J., Kacprzyk, J., et al.: A review of soft consensus models in a fuzzy environment. Inf. Fus. 17, 4–13 (2014)

    Article  Google Scholar 

  9. Lee, L.W., Chen, S.M.: Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators. Inf. Sci. 294, 513–529 (2015)

    Article  MathSciNet  Google Scholar 

  10. Levrat, E., Voisin, A., Bombardier, S., et al.: Subjective evaluation of car seat comfort with fuzzy set techniques. Int. J. Intell. Syst. 12, 891–913 (1997)

    Article  Google Scholar 

  11. Liao, H.C., Xu, Z.S., Zeng, X.J.: Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans. Fuzzy Syst. 23(5), 1343–1355 (2015)

    Article  Google Scholar 

  12. Liao, H., Xu, Z., Zeng, X.J.: Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf. Sci. 271, 125–142 (2014)

    Article  MathSciNet  Google Scholar 

  13. Liu, B., Shen, Y., Chen, X., et al.: A partial binary tree DEA-DA cyclic classification model for decision makers in complex multi-attribute large-group interval-valued intuitionistic fuzzy decision-making problems. Inf. Fus. 18, 119–130 (2014)

    Article  Google Scholar 

  14. Liu, H., Rodríguez, R.M.: A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making. Inf. Sci. 258, 220–238 (2014)

    Article  MathSciNet  Google Scholar 

  15. Liu, Y., Fan, Z.P., Zhang, X.: A method for large group decision-making based on evaluation information provided by participants from multiple groups. Inf. Fus. 29, 132–141 (2016)

    Article  Google Scholar 

  16. Labella, Á., Liu, Y., Rodríguez, R.M., et al.: Analyzing the performance of classical consensus models in large scale group decision making: a comparative study. Appl. Soft Comput. (2017). doi:10.1016/j.asoc.2017.05.045

    Article  Google Scholar 

  17. Mata, F., Martínez, L., Herrera-Viedma, E.: An adaptive consensus support model for group decision-making problems in a multigranular fuzzy linguistic context. IEEE Trans. Fuzzy Syst. 17(2), 279–290 (2009)

    Article  Google Scholar 

  18. Martínez, L., Rodriguez, R.M., Herrera, F.: Dealing with Hesitant Fuzzy Linguistic Information in Decision Making//The 2-tuple Linguistic Model, pp. 113–129. Springer, Berlin (2015)

    Google Scholar 

  19. Martínez, L., Herrera, F.: An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf. Sci. 207, 1–18 (2012)

    Article  MathSciNet  Google Scholar 

  20. Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 369, 128–143 (2016)

    Article  Google Scholar 

  21. Palomares, I., Martinez, L., Herrera, F.: A consensus model to detect and manage noncooperative behaviors in large-scale group decision making. IEEE Trans. Fuzzy Syst. 22(3), 516–530 (2014)

    Article  Google Scholar 

  22. Palomares, I., Martínez, L., Herrera, F.: MENTOR: a graphical monitoring tool of preferences evolution in large-scale group decision making. Knowl. Based Syst. 58, 66–74 (2014)

    Article  Google Scholar 

  23. Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2012)

    Article  Google Scholar 

  24. Xu, Z., Wang, H.: On the syntax and semantics of virtual linguistic terms for information fusion in decision making. Inf. Fus. 34, 43–48 (2017)

    Article  Google Scholar 

  25. Wang, H.: Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making. Int. J. Comput. Intell. Syst. 8(1), 14–33 (2015)

    Article  Google Scholar 

  26. Wang, H., Xu, Z.: Some consistency measures of extended hesitant fuzzy linguistic preference relations. Inf. Sci. 297, 316–331 (2015)

    Article  MathSciNet  Google Scholar 

  27. Wang, J., Wang, J., Zhang, H., et al.: Multi-criteria decision-making based on hesitant fuzzy linguistic term sets: an outranking approach. Knowl. Based Syst. 86, 224–236 (2015)

    Article  Google Scholar 

  28. Wu, Z., Xu, J.: Possibility distribution-based approach for MAGDM with hesitant fuzzy linguistic information. IEEE Trans. Cybern. 46(3), 694–705 (2016)

    Article  Google Scholar 

  29. Wu, Z., Xu, J.: A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis. Support Syst. 52(3), 757–767 (2012)

    Article  Google Scholar 

  30. Wu, Z., Xu, J.: Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65, 28–40 (2016)

    Article  Google Scholar 

  31. Xu, Z.: Deviation measures of linguistic preference relations in group decision making. Omega 33(3), 249–254 (2005)

    Article  MathSciNet  Google Scholar 

  32. Xu, Z.: A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci. 166(1), 19–30 (2004)

    Article  MathSciNet  Google Scholar 

  33. Xu, Z.: Linguistic Decision Making: Theory and Methods. Springer, Berlin (2013)

    Google Scholar 

  34. Xu, X., Du, Z., Chen, X.: Consensus model for multi-criteria large-group emergency decision making considering non-cooperative behaviors and minority opinions. Decis. Support Syst. 79, 150–160 (2015)

    Article  Google Scholar 

  35. Yager, R.: An approach to ordinal decision making. Int. J. Approx. Reason. 12(3), 237–261 (1995)

    Article  MathSciNet  Google Scholar 

  36. Zhang, Y., Xu, Z., Wang, H., et al.: Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft Comput. 49, 817–833 (2016)

    Article  Google Scholar 

  37. Zhang, G., Dong, Y., Xu, Y.: Consistency and consensus measures for linguistic preference relations based on distribution assessments. Inf. Fus. 17, 46–55 (2014)

    Article  Google Scholar 

  38. Zhang, X.: Non-homogeneous linguistic multi-criteria group decision making with aspiration. Technique Report, pp. 1–15 (2017)

  39. Zhang, X., Xu, Z.: Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making. Appl. Soft Comput. 26, 42–56 (2015)

    Article  Google Scholar 

  40. Zhang, Z., Guo, C., Martínez, L.: Managing multi-granular linguistic distribution assessments in large-scale multiattribute group decision making. IEEE Trans. Syst. Man Cybern. Syst. (2016). doi:10.1109/TSMC.2016.2560521

    Article  Google Scholar 

  41. Zhai, Y., Xu, Z., Liao, H.: Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information. Appl. Soft Comput. 49, 801–816 (2016)

    Article  Google Scholar 

  42. Zahir, S.: Clusters in a group: decision making in the vector space formulation of the analytic hierarchy process. Eur. J. Oper. Res. 112(3), 620–634 (1999)

    Article  Google Scholar 

  43. Zhu, B., Xu, Z.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22(1), 35–45 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

The author is very grateful to the anonymous reviewers and the editor for their insightful and constructive comments and suggestions that have led to an improved version of this paper. The work was supported by the National Natural Science Foundation of China (No. 71661010), the Natural Science Foundation of Jiangxi Province of China (No. 20161BAB211020) and the Technology Project of Education Department of Jiangxi Province of China (No. GJJ160455).

Author information

Authors and Affiliations

  1. The Collaborative Innovation Center, Jiangxi University of Finance and Economics, Nanchang, 330013, China

    Xiaolu Zhang

Authors
  1. Xiaolu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaolu Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X. A Novel Probabilistic Linguistic Approach for Large-Scale Group Decision Making with Incomplete Weight Information. Int. J. Fuzzy Syst. 20, 2245–2256 (2018). https://doi.org/10.1007/s40815-017-0375-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0375-1

Keywords

Search

Navigation