Skip to main content
SpringerLink
Log in

A Novel Approach for Probabilistic Linguistic Multiple Attribute Decision Making Based on Dual Muirhead Mean Operators and VIKOR

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

Abstract

In this study, we concentrate on multiple attribute decision-making (MADM) problems in the probabilistic linguistic preference information surroundings based on novel aggregation operators. Considering interrelationships among the multi-input arguments of probabilistic linguistic term sets (PLTSs), we extend dual Muirhead mean (DMM) operators to the probabilistic linguistic preference environment and develop a decision-making approach to deal with probabilistic linguistic MADM (PLMADM) problems. In specific, we define probabilistic linguistic dual Muirhead mean operators, i.e., probabilistic linguistic dual Muirhead mean (PLDMM) operator and probabilistic linguistic weighted dual Muirhead mean (PLWDMM) operator, and further investigate their corresponding propositions, theorems as well as properties. In the light of VIKOR method, a novel decision-making approach for PLMADM problems has been carefully explored. Finally, an application of hospitals selection can fruitfully demonstrate and signify the practicality and feasibility of the proposed decision-making approach.

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.

Fig. 1

Similar content being viewed by others

Notes

  1. VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) means multi-criteria optimization and compromise solution, in Serbian.

References

  1. Li, Y.L., Du, Y.F., Chin, K.S.: Determining the importance ratings of customer requirements in quality function deployment based on interval linguistic information. Int. J. Prod. Res. 56(14), 4692–4708 (2018)

    Article  Google Scholar 

  2. Liang, D.C., Darko, A.P., Xu, Z.S., Wang, M.W.: Aggregation of dual hesitant fuzzy heterogenous related information with extended Bonferroni mean and its application to MULTIMOORA. Comput. Ind. Eng. 135, 156–176 (2019)

    Article  Google Scholar 

  3. He, Y., Xu, Z.S.: Multi-attribute decision making methods based on reference ideal theory with probabilistic hesitant information. Expert Syst. Appl. 118, 459–469 (2019)

    Article  Google Scholar 

  4. Liang, D.C., Xu, Z.S., Liu, D., Wu, Y.: Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf. Sci. 435, 282–295 (2018)

    Article  MathSciNet  Google Scholar 

  5. Liu, P.D., Teng, F.: Some Muirhead mean operators for probabilistic linguistic term sets and their applications to multiple attribute decision-making. Appl. Soft Comput. 68, 396–431 (2018)

    Article  Google Scholar 

  6. Zhai, Y.L., Xu, Z.S., Liao, H.C.: Measures of probabilistic interval-valued intuitionistic hesitant fuzzy sets and the application in reducing excessive medical examinations. IEEE Trans. Fuzzy Syst. 26(3), 1651–1670 (2017)

    Article  Google Scholar 

  7. Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2011)

    Article  Google Scholar 

  8. 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 

  9. Liao, H.C., Jiang, L.S., Xu, Z.S., Xu, J.P., Herrera, F.: A linear programming method for multiple criteria decision making with probabilistic linguistic information. Inf. Sci. 415, 341–355 (2017)

    Article  Google Scholar 

  10. Lin, M.W., Xu, Z.S., Zhai, Y.L., Yao, Z.Q.: Multi-attribute group decision-making under probabilistic uncertain linguistic environment. J. Oper. Res. Soc. 69(2), 157–170 (2018)

    Article  Google Scholar 

  11. Liao, H.C., Mi, X.M., Xu, Z.S.: A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optim. Decis. Ma. 19(1), 81–134 (2020)

    Article  MathSciNet  Google Scholar 

  12. Gao, J., Xu, Z.S., Ren, P.J., Liao, H.C.: An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations. Int. J. Mach. Learn. Cyb. 10(7), 1613–1629 (2019)

    Article  Google Scholar 

  13. Liao, H.C., Jiang, L.S., Lev, B., Fujita, H.: Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method. Appl. Soft Comput. 80, 450–464 (2019)

    Article  Google Scholar 

  14. Liu, P.D., Teng, F.: Probabilistic linguistic TODIM method for selecting products through online product reviews. Inf. Sci. 485, 441–455 (2019)

    Article  Google Scholar 

  15. Krishankumar, R., Saranya, R., Nethra, R.P., Ravichandran, K.S., Kar, S.: A decision-making framework under probabilistic linguistic term set for multi-criteria group decision-making problem. J. Intell. Fuzzy Syst. 36(6), 1–13 (2019)

    Google Scholar 

  16. Zhang, X.L.: A novel probabilistic linguistic approach for large-scale group decision making with incomplete weight information. Int. J. Fuzzy Syst. 20(7), 2245–2256 (2018)

    Article  Google Scholar 

  17. Liang, D.C., Kobina, A., Quan, W.: Grey relational analysis method for probabilistic linguistic multi-criteria group decision-making based on geometric Bonferroni mean. Int. J. Fuzzy Syst. 20(7), 2234–2244 (2018)

    Article  Google Scholar 

  18. Xiao, F., Wang, J.Q.: Multistage decision support framework for sites selection of solar power plants with probabilistic linguistic information. J. Clean. Prod. 230, 1396–1409 (2019)

    Article  Google Scholar 

  19. Liu, P.D., Li, Y.: Multi-attribute decision making method based on generalized maclaurin symmetric mean aggregation operators for probabilistic linguistic information. Comput. Ind. Eng. 131, 282–294 (2019)

    Article  Google Scholar 

  20. Hong, Z.Y., Rong, Y., Qin, Y., Liu, Y.: Hesitant fuzzy dual Muirhead mean operators and its application to multiple attribute decision making. J. Intell. Fuzzy Syst. 35(2), 2161–2172 (2018)

    Article  Google Scholar 

  21. Xu, Y., Shang, X.P., Wang, J.: Pythagorean fuzzy interaction Muirhead means with their application to multi-attribute group decision-making. Inf. 9(7), 157 (2018)

    Google Scholar 

  22. Krishankumar, R., Ravichandran, K.S., Ahmed, M.I., Kar, S., Peng, X.D.: Interval-valued probabilistic hesitant fuzzy set based muirhead mean for multi-attribute group decision-making. Mathematics 7(4), 342 (2019)

    Article  Google Scholar 

  23. Wang, J., Zhang, R.T., Zhu, X.M., Zhou, Z., Shang, X.P., Li, W.Z.: Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making. J. Intell. Fuzzy Syst. 36(2), 1599–1614 (2019)

    Article  Google Scholar 

  24. Liu, P.D., Khan, Q., Mahmood, T., Hassan, N.: T-spherical fuzzy power Muirhead mean operator based on novel operational laws and their application in multi-attribute group decision making. IEEE Access 7, 22613–22632 (2019)

    Article  Google Scholar 

  25. Opricovic, S.: Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade 2(1), 5–21 (1998)

    MathSciNet  Google Scholar 

  26. Rani, P., Mishra, A.R., Pardasani, K.R., Mardani, A., Liao, H.C., Streimikiene, D.: A novel VIKOR approach based on entropy and divergence measures of Pythagorean fuzzy sets to evaluate renewable energy technologies in India. J. Clean. Prod. 238, 117936 (2019)

    Article  Google Scholar 

  27. Opricovic, S., Tzeng, G.H.: Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 156(2), 445–455 (2004)

    Article  Google Scholar 

  28. Opricovic, S., Tzeng, G.H.: Extended VIKOR method in comparison with outranking methods. Eur. J. Oper. Res. 178(2), 514–529 (2007)

    Article  Google Scholar 

  29. Ding, X.F., Liu, H.C.: An extended prospect theory-VIKOR approach for emergency decision making with 2-dimension uncertain linguistic information. Soft Comput. 23(22), 12139–12150 (2019)

    Article  Google Scholar 

  30. Bai, C.G., Sarkis, J.: Integrating and extending data and decision tools for Sustainable third-party reverse logistics provider selection. Comput. Oper. Res. 110, 188–207 (2019)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  32. Bai, C.Z., Zhang, R., Qian, L.X., Wu, Y.N.: Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowl.-based Syst 119, 284–291 (2017)

    Article  Google Scholar 

  33. Muirhead, R.F.: Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society 21, 144–162 (1902)

    Article  Google Scholar 

  34. Qin, J.D., Liu, X.W.: 2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection. Kybernetes 45(1), 2–29 (2016)

    Article  MathSciNet  Google Scholar 

  35. Liu, P.D., Li, D.F.: Some Muirhead mean operators for intuitionistic fuzzy numbers and their applications to group decision making. PloS one 12(1), e0168767 (2017)

    Article  Google Scholar 

  36. Jing, S.W., Niu, Z.W., Chang, P.C.: The application of VIKOR for the tool selection in lean management. J. Intell. Manuf. 30(8), 2901–2912 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61876157, 71571148), and the Yanghua Scholar Plan (Part A) of SWJTU.

Author information

Authors and Affiliations

  1. School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, China

    Yinfeng Du & Dun Liu

Authors
  1. Yinfeng Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dun Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, Y., Liu, D. A Novel Approach for Probabilistic Linguistic Multiple Attribute Decision Making Based on Dual Muirhead Mean Operators and VIKOR. Int. J. Fuzzy Syst. 23, 243–261 (2021). https://doi.org/10.1007/s40815-020-00897-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00897-8

Keywords

Search

Navigation