Skip to main content
SpringerLink
Log in

A projection method for multiple attribute group decision making with probabilistic linguistic term sets

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

In multiple attribute group decision making (MAGDM) processes, decision makers often use hesitant fuzzy linguistic term sets (HFLTSs) to express their opinions. However, it is incapable of representing the importance degrees or weights of different linguistic terms. The probabilistic linguistic term set (PLTS) gives each linguistic term a probability to denote their importance degree, and thus is more suitable for group decision making problems where the distribution information is available. In this paper, the PLTSs are utilized to express the experts’ assessments on each alternative with respect to each attribute in the MAGDM problem. Additionally, we establish two optimization models to derive the attribute weights. Then we propose a projection model to calculate the alternatives’ projections on both the positive and negative ideal solutions. A practical decision making problem about crossover development is given to validate the effectiveness of the projection method with PLTS information. Finally, we make some comparisons between the projection method and other existing methods, meanwhile, the advantages and limitations of the projection model are summarized.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Xu ZS (2004) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168:171–184

    Article  MATH  Google Scholar 

  2. Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119

    Article  Google Scholar 

  3. Liao HC, Xu ZS, Zeng XJ (2015) and J.M. Merigó. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst 76:127–138

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Wang H, Xu ZS (2018) and X. J. Zeng. Modeling complex linguistic expressions in qualitative decision making: an overview. Knowl-Based Syst 144:174–187

    Article  Google Scholar 

  6. Zhang YX, Xu ZS, Wang H (2016) and H. C. Liao. Consistency-based risk assessment with probabilistic linguistic preference relation. Appl Soft Comput 49:817–833

    Article  Google Scholar 

  7. Bai CZ, Zhang R, Qian LX, Wu YN (2017) Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowl-Based Syst 119:284–291

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Gou XJ, Xu ZS (2016) Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf Sci 372:407–427

    Article  Google Scholar 

  10. Lai VS, Bo KW, Cheung W (2002) Group decision making in a multiple criteria environment: a case using the AHP in software selection. Eur J Oper Res 137(1):134–144

    Article  MATH  Google Scholar 

  11. Roostaee SR, Izadikhah M, Lotfi FH, Rostamy-Malkhalifeh M (2012) A multi-criteria intuitionistic fuzzy group decision making method for supplier selection with VIKOR method. Int J Fuzzy Syst Appl 2(1):1–17

    Article  Google Scholar 

  12. Gul M, Celik E, Aydin N, Gumus AT, Guneri AF (2016) A state of the art literature review of vikor and its fuzzy extensions on applications. Appl Soft Comput 46:60–89

    Article  Google Scholar 

  13. Chen CT (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114(1):1–9

    Article  MATH  Google Scholar 

  14. Shih HS, Shyur HJ, Lee ES (2007) An extension of TOPSIS for group decision making. Math Comput Model 45(7–8):801–813

    Article  MATH  Google Scholar 

  15. Zheng GZ, Jing YY, Huang HX, Gao YF (2010) Application of improved grey relational projection method to evaluate sustainable building envelope performance. Appl Energy 87(2):710–720

    Article  Google Scholar 

  16. Xu ZS, Hu H (2011) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(2):267–280

    Article  MATH  Google Scholar 

  17. Yue ZL (2012) Approach to group decision making based on determining the weights of experts by using projection method. Appl Math Model 36(7):2900–2910

    Article  MathSciNet  MATH  Google Scholar 

  18. Xu GL, Liu F (2013) An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection. Appl Math Model 37(6):3929–3943

    Article  MathSciNet  MATH  Google Scholar 

  19. Herrera F, Herrera-Viedma E, Verdegay JL (1995) A sequential selection process in group decision making with a linguistic assessment approach. Inf Sci 85(4):223–239

    Article  MATH  Google Scholar 

  20. Xu ZS (2004) Uncertain multiple attribute decision making: methods and applications. Springer-Verlag, Berlin

    Google Scholar 

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

    Article  Google Scholar 

  22. Wang YM 1998) Using the method of maximizing deviations to make decision for multi-indices, Syst Eng Electron 7(3):24–26

    Google Scholar 

  23. Shannon CE, Weaver W (1949) The mathematical theory of communication (Urbana, IL). Philos Rev 60(3):31–32

    Google Scholar 

  24. Liu PD, Zhang X (2011) Research on the supplier selection of a supply chain based on entropy weight and improved ELECTRE-III method. Int J Prod Res 49:637–646

    Article  Google Scholar 

  25. Kildiene S, Kaklauskas A, Zavadskas EK (2011) COPRAS Based comparative analysis of the European country management capabilities within the construction sector in the time of crisis. J Bus Econ Manag 12:417–434

    Article  Google Scholar 

  26. Saparauskas J, Zavadskas EK, Turskis Z (2011) Selection of Facade’s alternatives of commercial and public buildings based on multiple criteria. Inte J Strateg Prop Manag 15:189–203

    Article  Google Scholar 

  27. Simanaviciene R, Liaudanskiene R, Ustinovichius L (2012) A new synthesis method of structural, technological and safety decisions (SyMAD-3). J Civ Eng Manag 18:265–276

    Article  Google Scholar 

  28. Yang JP, Qiu WH (2005) A measure of risk and a decision-making model based on expected utility and entropy. Eur J Oper Res 164:792–799

    Article  MathSciNet  MATH  Google Scholar 

  29. Wang YM, Chin KS (2006) An eigenvector method for generating normalized interval and fuzzy weights. Appl Math Comput 181:1257–1275

    MathSciNet  MATH  Google Scholar 

  30. Xu R (2000) Fuzzy least-square priority method in the analytic hierarchy process. Fuzzy Sets Syst 112:395–404

    Article  MathSciNet  MATH  Google Scholar 

  31. Dalkey N (1969) The Delphi method: an experimental study of group opinion. Futures 1(5):408–426

    Article  Google Scholar 

  32. Kim SH (1999) and B. S. Ahn. Interactive group decision making procedure under incomplete information. Eur J Oper Res 116(3):498–507

    Article  MATH  Google Scholar 

  33. Kim SH, Sang HC, Kim JK (1999) An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach. Eur J Oper Res 118(1):139–152

    Article  MATH  Google Scholar 

  34. Lai YJ, Liu TY, Hwang CL (1994) TOPSIS for MODM. Eur J Oper Res 76(3):486–500

    Article  MATH  Google Scholar 

  35. Doukas H, Karakosta C, Psarras J (2010) Computing with words to assess the sustainability of renewable energy options. Expert Syst Appl 37(7):5491–5497

    Article  Google Scholar 

  36. Kuo T (2016) A modified TOPSIS with a different ranking Index, Eur J Oper Res 260:152–160

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This study was funded by the National Natural Science Foundation of China (Nos. 71571123, 71771155).

Author information

Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610064, China

    Xiaofang Zhang, Xunjie Gou, Zeshui Xu & Huchang Liao

  2. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, China

    Zeshui Xu

Authors
  1. Xiaofang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xunjie Gou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Huchang Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zeshui Xu.

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

Zhang, X., Gou, X., Xu, Z. et al. A projection method for multiple attribute group decision making with probabilistic linguistic term sets. Int. J. Mach. Learn. & Cyber. 10, 2515–2528 (2019). https://doi.org/10.1007/s13042-018-0886-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-018-0886-6

Keywords

Search

Navigation