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Additive Consistency-Based Decision-Making with Incomplete Probabilistic Linguistic Preference Relations

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Abstract

Probabilistic linguistic term set (PLTS), an efficient tool to describe decision information, can sufficiently express decision makers’ hesitation and preference. Probabilistic linguistic preference relation (PLPR) is based on PLTSs to describe the preference information of experts for paired alternatives. However, in practice, due to the complexity of the problem, the incompleteness of information and the lack of professional knowledge, the incomplete PLPR (InPLPR) with missing information often appears. Therefore, this paper proposes a decision-making method under InPLPR. Firstly, in order to fully consider the specific situation of missing values, missing linguistic term-InPLTS (MLT-InPLTS) is subdivided into missing single linguistic term-InPLTS (MSLT-InPLTS) and missing multiple linguistic terms-InPLTS (MMLT-InPLTS). Then, a two-stage mathematical optimization model of missing information estimation based on additive consistency, fuzzy entropy and hesitation entropy is established. Subsequently, aiming at the unacceptable consistency of complete PLPR (CPLPR) after filling in the missing values, a consistency improvement method based on the idea of gradient descent is proposed. Afterward, probabilistic linguistic weighted averaging (PLWA) operator is used to rank alternatives. Finally, medical supplier selection is taken as an example to verify the effectiveness of the proposed decision-making method, and the robustness and advantages of this method are illustrated by sensitivity analysis and comparison with other methods.

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References

  1. Chen, Z.-Y., Wang, X.-K., Peng, J.-J., et al.: An integrated probabilistic linguistic projection method for MCGDM based on ELECTRE III and the weighted convex median voting rule. Expert Syst. (2020). https://doi.org/10.1111/exsy.12593

    Article  Google Scholar 

  2. Koksalmis, E., Kabak, O.: Deriving decision makers’ weights in group decision making: an overview of objective methods. Inf. Fusion 49, 146–160 (2019). https://doi.org/10.1016/j.inffus.2018.11.009

    Article  Google Scholar 

  3. Wang, X., Wang, S.-H., Zhang, H.-Y., et al.: The recommendation method for hotel selection under traveller preference characteristics: a cloud-based multi-criteria group decision support model. Group Decis. Negot. (2021). https://doi.org/10.1007/s10726-021-09735-0

    Article  Google Scholar 

  4. Wang, X.K., Zhang, H.Y., Wang, J.Q., et al.: Extended TODIM‐PROMETHEE II method with hesitant probabilistic information for solving potential risk evaluation problems of water resource carrying capacity. Expert Syst. e12681 (2021). https://doi.org/10.1111/exsy.12681

  5. Zadeh, L.A.: Fuzzy sets *. Inf. Control. 8(3), 338–353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X

    Article  MATH  Google Scholar 

  6. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986). https://doi.org/10.1016/S0165-0114(86)80034-3

    Article  MATH  Google Scholar 

  7. Turksen, I.B.: Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 20(2), 191–210 (1986). https://doi.org/10.1016/0165-0114(86)90077-1

    Article  MathSciNet  MATH  Google Scholar 

  8. Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989). https://doi.org/10.1016/0165-0114(89)90205-4

    Article  MathSciNet  MATH  Google Scholar 

  9. Tian, Z.-P., Wang, J., Wang, J.-Q., et al.: Multicriteria decision-making approach based on gray linguistic weighted Bonferroni mean operator. Int. Trans. Oper. Res. 25(5), 1635–1658 (2018). https://doi.org/10.1111/itor.12220

    Article  MathSciNet  MATH  Google Scholar 

  10. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I ☆. Inf. Sci. 8(3), 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5

    Article  MathSciNet  MATH  Google Scholar 

  11. Rodríguez, R.M., Martínez, L. and Herrera, F., Hesitant Fuzzy Linguistic Term Sets. IEEE Press, (2011).

  12. Wang, J., Wang, J.Q., Tian, Z.P., et al.: A multihesitant fuzzy linguistic multicriteria decision-making approach for logistics outsourcing with incomplete weight information. Int. Trans. Oper. Res. 25(3), 831–856 (2018). https://doi.org/10.1111/itor.12448

    Article  MathSciNet  MATH  Google Scholar 

  13. Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 369, 128–143 (2016). https://doi.org/10.1016/j.ins.2016.06.021

    Article  Google Scholar 

  14. Zhang, Y., Xu, Z., Wang, H., et al.: Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft. Comput. 49, 817–833 (2016). https://doi.org/10.1016/j.asoc.2016.08.045

    Article  Google Scholar 

  15. Wang, P., Liu, P., Chiclana, F.: Multi-stage consistency optimization algorithm for decision making with incomplete probabilistic linguistic preference relation. Inf. Sci. (2020). https://doi.org/10.1016/j.ins.2020.10.004

    Article  Google Scholar 

  16. Gao, J., Xu, Z., Liang, Z., et al.: Expected consistency-based emergency decision making with incomplete probabilistic linguistic preference relations. Knowledge-Based Syst. 176, 15–28 (2019). https://doi.org/10.1016/j.knosys.2019.03.020

    Article  Google Scholar 

  17. Krishankumar, R., Ravichandran, K., Ahmed, M., et al.: Probabilistic linguistic preference relation-based decision framework for multi-attribute group decision making. Symmetry. (2018). https://doi.org/10.3390/sym11010002

    Article  MATH  Google Scholar 

  18. Gao, J., Xu, Z., Ren, P., et al.: An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations. Int. J. Mach. Learn. Cybern. 10(7), 1613–1629 (2019). https://doi.org/10.1007/s13042-018-0839-0

    Article  Google Scholar 

  19. Zhang, Z., Chen, S.-M.: Group decision making based on acceptable multiplicative consistency and consensus of hesitant fuzzy linguistic preference relations. Inf. Sci. 541, 531–550 (2020). https://doi.org/10.1016/j.ins.2020.07.024

    Article  MathSciNet  MATH  Google Scholar 

  20. Liao, H., Peng, X., Gou, X.: Medical supplier selection with a group decision-making method based on incomplete probabilistic linguistic preference relations. Int. J. Fuzzy Syst. (2020). https://doi.org/10.1007/s40815-020-00885-y

    Article  Google Scholar 

  21. Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning-Part I. Inf. Sci. 8, 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5

    Article  MATH  Google Scholar 

  22. Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A sequential selection process in group decision making with a linguistic assessment approach. Inf. Sci. 85(4), 223–239 (1995). https://doi.org/10.1016/0020-0255(95)00025-k

    Article  MATH  Google Scholar 

  23. Xu, Z.S.: Deviation measures of linguistic preference relations in group decision making. Omega 33(3), 249–254 (2005). https://doi.org/10.1016/j.omega.2004.04.008

    Article  Google Scholar 

  24. Wang, J.-Q., Wu, J.-T., Wang, J., et al.: Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf. Sci. 288, 55–72 (2014). https://doi.org/10.1016/j.ins.2014.07.034

    Article  MathSciNet  MATH  Google Scholar 

  25. Liao, H.C., Xu, Z.S., Zeng, X.J.: Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf. Sci. 271, 125–142 (2014). https://doi.org/10.1016/j.ins.2014.02.125

    Article  MathSciNet  MATH  Google Scholar 

  26. Xu, Z.S.: EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 12(6), 791–810 (2004). https://doi.org/10.1142/S0218488504003211

  27. Fama, E.F., French, K.R.: A five-factor asset pricing model. J. Financ. Econ. 116(1), 1–22 (2015). https://doi.org/10.1016/j.jfineco.2014.10.010

    Article  Google Scholar 

  28. Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978). https://doi.org/10.1016/0165-0114(78)90001-5

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhang, G., Dong, Y., Xu, Y.: Consistency and consensus measures for linguistic preference relations based on distribution assessments. Inf. Fusion 17, 46–55 (2014). https://doi.org/10.1016/j.inffus.2012.01.006

    Article  Google Scholar 

  30. Herrera-Viedma, E., Herrera, F., Chiclana, F., et al.: Some issues on consistency of fuzzy preference relations. Eur. J. Oper. Res. 154(1), 98–109 (2004). https://doi.org/10.1016/s0377-2217(02)00725-7

    Article  MathSciNet  MATH  Google Scholar 

  31. Xu, Z.: Incomplete linguistic preference relations and their fusion. Inf. Fusion 7(3), 331–337 (2006). https://doi.org/10.1016/j.inffus.2005.01.003

    Article  Google Scholar 

  32. Gupta, S., Deep, K., Mirjalili, S.: An efficient equilibrium optimizer with mutation strategy for numerical optimization. Appl. Soft. Comput. 96, 106542 (2020). https://doi.org/10.1016/j.asoc.2020.106542

    Article  Google Scholar 

  33. Rabehi, A., Nail, B., Helal, H., et al.: Optimal estimation of Schottky diode parameters using a novel optimization algorithm: equilibrium optimizer. Superlattices Microstruct. 146, 106665 (2020). https://doi.org/10.1016/j.spmi.2020.106665

    Article  Google Scholar 

  34. Faramarzi, A., Heidarinejad, M., Stephens, B., et al.: Equilibrium optimizer: a novel optimization algorithm. Knowledge-Based Syst. 191, 105190 (2020). https://doi.org/10.1016/j.knosys.2019.105190

    Article  Google Scholar 

  35. Tharwat, A., Schenck, W.: A conceptual and practical comparison of PSO-style optimization algorithms. Expert Syst. Appl. 167, 114430 (2021). https://doi.org/10.1016/j.eswa.2020.114430

    Article  Google Scholar 

  36. Dhiman, G., Singh, K.K., Soni, M., et al.: MOSOA: A new multi-objective seagull optimization algorithm. Expert Syst. Appl. 191, 114150 (2020). https://doi.org/10.1016/j.eswa.2020.114150

    Article  Google Scholar 

  37. Liu, H., Jiang, L., Xu, Z.: Entropy measures of probabilistic linguistic term sets. Int. J. Comput. Intell. Syst. 11(1), 45–57 (2018). https://doi.org/10.2991/ijcis.11.1.4

    Article  Google Scholar 

  38. Zhu, B., Xu, Z.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22(1), 35–45 (2014). https://doi.org/10.1109/tfuzz.2013.2245136

    Article  Google Scholar 

  39. Wright, S.E., Lim, S.: Solving nested-constraint resource allocation problems with an interior point method. Oper. Res. Lett. 48(3), 297–303 (2020). https://doi.org/10.1016/j.orl.2020.04.001

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are very grateful to the anonymous reviewers for their valuable comments and suggestions to help improve the overall quality of this paper. This work was supported by the National Natural Science Foundation of China (No. 71962005).

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Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, People’s Republic of China

    Zi-yu Chen, Fei Xiao, Min-hui Deng & Jian-qiang Wang

  2. School of Business, Guilin University of Technology, Guilin, 541004, People’s Republic of China

    Min-hui Deng & He-wei Liu

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  1. Zi-yu Chen
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  2. Fei Xiao
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Correspondence to He-wei Liu or Jian-qiang Wang.

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Chen, Zy., Xiao, F., Deng, Mh. et al. Additive Consistency-Based Decision-Making with Incomplete Probabilistic Linguistic Preference Relations. Int. J. Fuzzy Syst. 24, 405–424 (2022). https://doi.org/10.1007/s40815-021-01144-4

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