Skip to main content

A comparative analysis of probabilistic linguistic preference relations and distributed preference relations for decision making

Abstract

When a decision-maker prefers to compare different alternatives in pairs to handle real situations, there are many different expression styles that can be used. Two representative expression styles are the probabilistic linguistic preference relation (PLPR), which originates from the fuzzy linguistic approach and the distributed preference relation (DPR), which originates from the evidential reasoning approach. Although these two expression styles look quite similar, their meanings, operations, and relevant decision making processes are significantly different. This presents the decision-maker with the challenge of selecting either PLPRs or DPRs in different real cases. To address this issue, this paper provides a detailed analysis of the similarities and differences between PLPRs and DPRs. The analysis is conducted from five perspectives, including modeling of decision making problems, handling of uncertainty, consistency between preference relations, information aggregation, and elicitation process. An engineer selection problem for an automobile manufacturing enterprise is investigated to demonstrate how to appropriately select PLPRs or DPRs to model and analyze decision making problems in real situations with consideration for the preferences of decision-makers.

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

Fig. 1

References

  • Fu, C., Chang, W. J., Xue, M., & Yang, S. L. (2019). Multiple criteria group decision making with belief distributions and distributed preference relations. European Journal of Operational Research, 273, 623–633.

    MathSciNet  Article  Google Scholar 

  • Fu, C., Xu, D. L., & Yang, S. L. (2016). Distributed preference relations for multiple attribute decision analysis. Journal of the Operational Research Society, 67, 457–473.

    Article  Google Scholar 

  • Gou, X. J., & Xu, Z. S. (2016). Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic terms sets, and probabilistic linguistic term sets. Information Sciences, 372, 407–427.

    Article  Google Scholar 

  • Herrera, F., Herrera-Viedma, E., & Chiclana, F. (2001). Multiperson decision-making based on multiplicative preference relations. European Journal of Operational Research, 129(2), 372–385.

    MathSciNet  Article  Google Scholar 

  • Huang, W. C., Liu, Y. K., Zhang, Y., Zhang, R., Xu, M. H., Dieu, G. J., Antwi, E., & Shuai, B. (2020). Fault tree and fuzzy D-S evidential reasoning combined approach: An application in railway dangerous goods transportation system accident analysis. Information Science, 520, 117–129.

    Article  Google Scholar 

  • Li, C. C., Dong, Y. C., Xu, Y. J., Chiclana, F., Herrera-Viedma, E., & Herrera, F. (2019). An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: taxonomy and future directions. Information Fusion, 52, 143–156.

    Article  Google Scholar 

  • Liang, P., Hu, J. H., Li, B., Liu, Y. M., & Chen, X. H. (2020). A group decision making with probabilistic linguistic preference relations based on nonlinear optimization model and fuzzy cooperative games. Fuzzy Optimization and Decision making, 19, 499–528.

    MathSciNet  Article  Google Scholar 

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

    Article  Google Scholar 

  • Liao, H. C., Mi, X. M., & Xu, Z. S. (2020a). A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optimization and Decision Making, 19, 81–134.

    MathSciNet  Article  Google Scholar 

  • Liao, H. C., Wu, X. L., Mi, X. M., & Herrera, F. (2020b). An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule. Omega, 93, 102052.

    Article  Google Scholar 

  • Ölçer, A. İ, & Odabaşi, A. Y. (2005). A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem. European Journal of Operational Research, 166(1), 93–114.

    Article  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 

  • Peng, H. G., & Wang, J. Q. (2020). Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic information. Fuzzy Optimization and Decision Making, 19, 435–470.

    MathSciNet  Article  Google Scholar 

  • Saaty, T. L. (1980). The analytic hierarchy process. McGraw Hill International.

    MATH  Google Scholar 

  • Simon, H. A. (1982). Models of bounded rationality: Empirically grounded economic reason. . MIT Press.

    Google Scholar 

  • Wu, J., Chiclana, F., & Liao, H. C. (2018b). Isomorphic multiplicative transitivity for intuitionistic and interval-valued fuzzy preference relations and its application in deriving their priority vectors. IEEE Transactions on Fuzzy Systems, 26, 193–202.

    Article  Google Scholar 

  • Wu, X. L., & Liao, H. C. (2019). A consensus-based probabilistic linguistic gained and lost dominance score method. European Journal of Operational Research, 272, 1017–1027.

    MathSciNet  Article  Google Scholar 

  • Wu, X. L., Liao, H. C., Xu, Z. S., Hafezalkotob, A., & Herrera, F. (2018a). Probabilistic linguistic MULTIMOORA: A multicriteria 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 

  • Xu, Y. J., Sun, H., & Wang, H. M. (2015). Optimal consensus models for group decision making under linguistic preference relations. International Journal of Operational Research, 23, 1201–1228.

    MathSciNet  Article  Google Scholar 

  • Xu, Z. S. (2005). Deviation measure of linguistic preference relations in group decision making. Omega, 33, 249–254.

    Article  Google Scholar 

  • Xu, Z. S., He, Y., & Wang, X. Z. (2019). An overview of probabilistic-based expressions for qualitative decision-making: techniques, comparisons and developments. International Journal of Machine Learning and Cybernetics, 10, 1513–1528.

    Article  Google Scholar 

  • Yang, J. B., & Xu, D. L. (2002). On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty. IEEE Transaction on Systems, and Cybernetics-Part A: Systems and Humans, 32(3), 289–304.

    Article  Google Scholar 

  • Yue, N., Wu, D. R., Xie, J. L., & Chen, S. L. (2020). Probabilistic linguistic multi-criteria decision-making based on double information under imperfect conditions. Fuzzy Optimization and Decision making, 19, 391–433.

    MathSciNet  Article  Google Scholar 

  • Zadeh, L. A. (1975). The concept of a linguistic variable and its applications for linguistic preference relations based on distribution assessments. Part 1. Information Sciences, 8, 199–249.

    Article  Google Scholar 

  • Zhang, Y. X., Xu, Z. S., Wang, H., & Liao, H. C. (2016). Consistency-based risk assessment with probabilistic linguistic preference relation. Applied Soft Computing, 49, 817–833.

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant Nos. 72001063, 71571060, 71690235, and 71690230) and by the Fundamental Research Funds for the Central Universities (JZ2020HGTA0082). In addition, this research is supported by NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization (U1709215).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chao Fu.

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

Xue, M., Fu, C. & Yang, S. A comparative analysis of probabilistic linguistic preference relations and distributed preference relations for decision making. Fuzzy Optim Decis Making 21, 71–97 (2022). https://doi.org/10.1007/s10700-021-09357-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10700-021-09357-w

Keywords

  • Decision making
  • Probabilistic linguistic preference relations
  • Distributed preference relations
  • Consistency
  • Information aggregation
  • Comparative analysis