Skip to main content

The DEMATEL–COPRAS hybrid method under probabilistic linguistic environment and its application in Third Party Logistics provider selection


With the emergence of outsourcing logistics and the rapid development of the e-commerce business, Third Party Logistics (TPL) plays an indispensable role in modern business. In the TPL provider selection process, uncertain information brings more challenges to decision makers. This paper uses probabilistic linguistic term sets (PLTSs) to describe uncertain decision making information. Firstly, we propose an improved Decision Making Trial and Evaluation Laboratory method, which allows a certain relationship between decision criteria and calculates criteria weights in multi-criteria decision making (MCDM) problems. Then, in order to make full use of uncertain TPL provider information and maximize the values of data, the probabilistic linguistic complex proportional assessment method is proposed and applied to solve the MCDM problems under probabilistic linguistic environment, which needs much less computation than other MCDM methods. Finally, an application example of TPL provider selection is presented to demonstrate the proposed method. A comparative analysis is further conducted to validate the effectiveness of the proposed method.

This is a preview of subscription content, access via your institution.

Fig. 1


  • Dadashpour, I., & Bozorgi-Amiri, A. (2020). Evaluation and ranking of sustainable third-party logistics providers using the D-analytic hierarchy process. International Journal of Engineering, 33(11), 2233–2244.

    Google Scholar 

  • Das, M. C., Sarkar, B., & Ray, S. (2012). A framework to measure relative performance of Indian technical institutions using integrated fuzzy AHP and COPRAS methodology. Socio-Economic Planning Sciences, 46(3), 230–241.

    Article  Google Scholar 

  • Gabus, A., & Fontela, E. (1972). World problems, an invitation to further thought within the framework of DEMATEL. (pp. 1–8). Battelle Geneva Research Center.

    Google Scholar 

  • Gorabe, D., Pawar, D., & Pawar, N. (2014). Selection of industrial robots using complex proportional assessment method. American International Journal of Research in Science, Technology, Engineering and Mathematics, 5(2), 140–143.

    Google Scholar 

  • He, S. S., Wang, Y. T., Peng, J. J., & Wang, J. Q. (2021). Risk ranking of wind turbine systems through an improved FMEA based on probabilistic linguistic information and the TODIM method. Journal of the Operational Research Society.

    Article  Google Scholar 

  • Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1995). A sequential selection process in group decision making with a linguistic assessment approach. Information Sciences, 85(4), 223–239.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lin, M. W., & Xu, Z. S. (2018). Probabilistic linguistic distance measures and their applications in multi-criteria group decision making. Soft Computing Applications for Group Decision-Making and Consensus Modeling. (pp. 411–440). Springer.

    Chapter  Google Scholar 

  • Organ, A., & Yalçın, E. (2016). Performance evaluation of research assistants by COPRAS method. European Scientific Journal, 12(10), 102–109.

    Google Scholar 

  • Pang, Q., Wang, H., & Xu, Z. S. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369, 128–143.

    Article  Google Scholar 

  • Rodriguez, R. M., Martinez, L., & Herrera, F. (2011). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109–119.

    Article  Google Scholar 

  • Shyur, H. J., & Shih, H. S. (2006). A hybrid MCDM model for strategic vendor selection. Mathematical and Computer Modelling, 44(7–8), 749–761.

    Article  Google Scholar 

  • Tavana, M., Momeni, E., Rezaeiniya, N., Mirhedayatian, S. M., & Rezaeiniya, H. (2013). A novel hybrid social media platform selection model using fuzzy ANP and COPRAS-G. Expert Systems with Applications, 40(14), 5694–5702.

    Article  Google Scholar 

  • Wen, X., Yan, M., Xian, J., Yue, R., & Peng, A. (2016). Supplier selection in supplier chain management using Choquet integral-based linguistic operators under fuzzy heterogeneous environment. Fuzzy Optimization and Decision Making, 15(3), 307–330.

    MathSciNet  Article  Google Scholar 

  • Wu, X. L., Liao, H. C., Xu, Z. S., Hafezalkotob, A., & Herrera, F. (2018). Probabilistic linguistic MULTIMOORA: A multi-criteria decision making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Transactions on Fuzzy Systems, 26(6), 3688–3702.

    Article  Google Scholar 

  • Xia, M. M., & Xu, Z. S. (2011). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3), 395–407.

    MathSciNet  Article  Google Scholar 

  • Xu, Z. S. (2015). Uncertain multiple attribute decision making: Methods and applications. . Springer.

    MATH  Google Scholar 

  • Xu, Z. S., & Wang, H. (2016). On the syntax and semantics of virtual linguistic terms for information fusion in decision making. Information Fusion, 34, 43–48.

    Article  Google Scholar 

  • Yamazaki, M., Ishibe, K., Yamashita, S., Miyamoto, I., Kurihara, M., & Shindo, H. (1997). An analysis of obstructive factors to welfare service using DEMATEL method. Reports of the Faculty of Engineering, 48, 25–30.

    Google Scholar 

  • Yazdani, M., Alidoosti, A., & Zavadskas, E. K. (2011). Risk analysis of critical infrastructures using fuzzy COPRAS. Economic research-Ekonomska istraživanja, 24(4), 27–40.

    Article  Google Scholar 

  • Yu, P. L. (1973). A class of solutions for group decision problems. Management Science, 19(8), 936–946.

    MathSciNet  Article  Google Scholar 

  • Zavadskas, E. K., & Kaklauskas, A. (1996). Multiple criteria evaluation of buildings. . Vilnius.

    Google Scholar 

  • Zhang, X., & Xing, X. (2017). Probabilistic linguistic VIKOR method to evaluate green supply chain initiatives. Sustainability, 9(7), 1231.

    Article  Google Scholar 

  • Zhang, Y. X., Xu, Z. S., & Liao, H. C. (2018). An ordinal consistency-based group decision making process with probabilistic linguistic preference relation. Information Sciences, 467, 179–198.

    MathSciNet  Article  Google Scholar 

  • Zheng, Y. H., Xu, Z. S., He, Y., & Liao, H. C. (2018). Severity assessment of chronic obstructive pulmonary disease based on hesitant fuzzy linguistic COPRAS method. Applied Soft Computing, 69, 60–71.

    Article  Google Scholar 

Download references


This study was funded by the National Natural Science Foundation of China (Nos. 72071135, 71771155), the scholarship under the UK-China Joint Research and Innovation Partnership Fund PhD Placement Programme (No. 201806240416) and the Teacher-Student Joint Innovation Research Fund of Business School of Sichuan University (No. H2018016).

Author information

Authors and Affiliations


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

Verify currency and authenticity via CrossMark

Cite this article

Yuan, Y., Xu, Z. & Zhang, Y. The DEMATEL–COPRAS hybrid method under probabilistic linguistic environment and its application in Third Party Logistics provider selection. Fuzzy Optim Decis Making 21, 137–156 (2022).

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Probabilistic lingustic term sets
  • DEMATEL method
  • COPRAS method
  • Multiple criteria group decision making
  • Third Party Logistics providers