Skip to main content
SpringerLink
Log in

Improving the consistency of incomplete hesitant multiplicative preference relation

  • Application Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

As it know, most decision processes are depends on preference relations as in the forms by comparing different alternatives over criteria. In the process of decision making, a decision maker may give his/her judgement by means of hesitant multiplicative preference relation (HMPR) using the scale of \(1/9-9\) for hesitancy and uncertainty. Shortage of of time, experience and lack of the experts’ professional knowledge lead to form an incomplete hesitant multiplicative preference relation. In this paper we have defined a multiplicative transitive property of HMPR that preserves the hesitancy property. Another aim of this paper is to characterise two different approaches to calculate the missing element of incomplete HMPR from the incomplete one. The first approach involves two step, estimating step calculate the initial values of the missing element and the adjusting step minimizing the error. A linear programming model is developed in the second approach to calculate the missing values of incomplete hesitant multiplicative preference relation. The satisfaction degree and the acceptable consistency of complete HMPR is also checked. The whole procedure is explained with a suitable example.

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

  1. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  Google Scholar 

  2. Dong, Y., Xu, Y., Li, H.: On consistency measures of linguistic preference relations. Eur. J. Oper. Res. 189(2), 430–444 (2008)

    Article  Google Scholar 

  3. Herrera-Viedma, E., Alonso, S., Chiclana, F., Herrera, F.: A Consensus Model for group decision making with incomplete fuzzy preference relations. IEEE T Fuzzy Syst. 15, 863–877 (2007)

    Article  Google Scholar 

  4. Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy sets syst. 1(3), 155–167 (1978)

    Article  Google Scholar 

  5. Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychol. 15, 234–281 (1977)

    Article  Google Scholar 

  6. Saaty, T.L.: The Analytical Hierarchy Process. MC Graw-Hill, New York (1980)

    Google Scholar 

  7. Tanino, T.: Fuzzy preference ordering in group decision making. Fuzzy Sets Syst. 12(2), 117–131 (1984)

    Article  Google Scholar 

  8. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529539 (2010)

    Google Scholar 

  9. Xia, M.M., Xu, Z.S., Chen, J.: Algorithms for improving consistency or consensus of reciprocal [0,1]-valued preference relations. Fuzzy Sets Syst. 216, 108–133 (2013)

    Article  Google Scholar 

  10. Xia, M.M., Xu, Z.S., Liao, H.C.: Preference relations based on intuitionistic multiplicative information. IEEE Trans. Fuzzy Syst. 21(1), 113–133 (2013)

    Article  Google Scholar 

  11. Xia, M.M., Xu, Z.S.: Managing hesitant information in GDM problems under fuzzy and multiplicative preference relations. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 21, 865–897 (2013)

    Article  Google Scholar 

  12. Xu, Y., Chen, L., Rodrguez, R.M., Herrera, F., Wang, H.: Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowl.-Based Syst. 99, 71–78 (2016)

    Article  Google Scholar 

  13. Xu, Z.S.: A method for priorities of triangular fuzzy number complementaryjudgment matrices. Fuzzy Syst. Math. 16, 47–50 (2002)

    Google Scholar 

  14. Xu, Z.S., Cai, X.Q.: Incomplete interval valued intuitionistic fuzzy preference relations. Int. J. Gen. Syst. 38, 871–886 (2009)

    Article  Google Scholar 

  15. Xu, Z.S.: Goal programming models for obtaining the priority vector of incom-plete fuzzy preference relation. Int. J. Approx. Reason. 36(3), 261270 (2004)

    Article  Google Scholar 

  16. Xu, Z.S.: Intuitionistic Fuzzy Preference Modeling and Interactive Decision Making. Springer, Berlin (2013)

    Google Scholar 

  17. Xu, Z.S.: Intuitionistic preference relations and their application in group decision making. Inf. Sci. 177(11), 2363–2379 (2007)

    Article  Google Scholar 

  18. Xu, Z.S.: On consistency of the weighted geometric mean complex judgmentmatrix in AHP. Eur. J. Oper. Res. 126(3), 683–687 (2000)

    Article  Google Scholar 

  19. Xu, Z.S., Wei, C.P.: A consistency improving method in the analytic hierarchy process. Eur. J. Oper. Res. 116(2), 443–449 (1999)

    Article  Google Scholar 

  20. Xu, Z.S., Xia, M.M.: Distance and similarity measures for hesitant fuzzy sets. Inf. Sci. 181(11), 2128–2138 (2011)

    Article  Google Scholar 

  21. Xu, Z.S., Yager, R.R.: Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim. Decis. Mak. 8, 123–139 (2009)

    Article  Google Scholar 

  22. Yu, D.J., Merig, J.M., Zhou, L.G.: Interval valued multiplicative intuitionistic fuzzy preference relations. Int. J. Fuzzy Syst. 15(4), 412–422 (2013)

    Google Scholar 

  23. Zhang, Z., Guo, C.: Fusion of heterogeneous incomplete hesitant preference relations in group decision making. Int. J. Comput. Intell. Syst. 9(2), 245–262 (2016)

    Article  Google Scholar 

  24. Zhang, Z., Kou, X., Dong, Q.: Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Syst. Appl. 98, 118–128 (2018)

    Article  Google Scholar 

  25. Zhang, Z., Kou, X., Yu, W., Guo, C.: On priority weights and consistency for incomplete hesitant fuzzy preference relations. Knowl.-Based Syst. 000, 1–12 (2017)

    Google Scholar 

  26. Zhang, Z., Wu, C.: Deriving the priority weights from hesitant multiplicative preference relations in group decision making. Appl. Soft Comput. 25, 107–117 (2014)

    Article  Google Scholar 

  27. Zhu, B., Xu, Z.: Analytic hierarchy process hesitant group decision making. Eur. J. Oper. Res. 239(3), 794–801 (2014)

    Article  Google Scholar 

  28. Zhu, B., Xu, Z.: Regression methods for hesitant fuzzy preference relations. Technol. Econ. Dev. Econ. 19(Suppl. 1), S214–S227 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, New Delhi, Delhi, 110042, India

    Mamata Sahu & Anjana Gupta

Authors
  1. Mamata Sahu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anjana Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anjana Gupta.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sahu, M., Gupta, A. Improving the consistency of incomplete hesitant multiplicative preference relation. OPSEARCH 56, 324–343 (2019). https://doi.org/10.1007/s12597-018-00350-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-018-00350-3

Keywords

Search

Navigation