Skip to main content
SpringerLink
Log in

Overview of Hesitant Linguistic Preference Relations for Representing Cognitive Complex Information: Where We Stand and What Is Next

  • Published:
Cognitive Computation Aims and scope Submit manuscript

Abstract

Hesitant fuzzy linguistic preference relations (HFLPRs) can be used to represent cognitive complex information in a situation in which people hesitate among several possible linguistic terms for the preference degrees of pairwise comparisons over alternatives. HFLPRs have attracted growing attention owing to their efficiency in dealing with increasingly cognitive complex decision-making problems. Due to the emergence of various studies on HFLPRs, it is necessary to make a comprehensive overview of the theory of HFLPRs and their applications. In this paper, we first review different types of linguistic representation models, including the hesitant fuzzy linguistic term set, hesitant 2-tuple fuzzy linguistic term set, probabilistic linguistic term set, and double-hierarchy hesitant fuzzy linguistic term set. The reasons for proposing these models are discussed in detail. Then, the hesitant linguistic preference relation models associated with the aforementioned linguistic representation models are addressed one by one. An overview is then provided in terms of their consistency properties, inconsistency-repairing processes, priority vector derivation methods, consensus measures, applications, and future directions. Basically, we try to answer to two questions: where we stand and what is next? The preference relations and consistency properties are discussed in detail. The inconsistency-repairing processes for those preference relations that are not acceptably consistent are summarized. Methods to derive the priorities from the HFLPRs and their extensions are further reviewed. The consensus measures and consensus-reaching processes for group decision making with HFLPRs and their extensions are discussed. The applications of HFLPRs and their extensions in different areas are highlighted. The future research directions regarding HFLPRs are given from different perspectives. This paper provides a comprehensive overview of the development and research status of HFLPRs for representing cognitive complex information. It can help researchers to identify the frontier of cognitive complex preference relation theory in the realm of decision analysis. Since the research on HFLPRs is still at its initial stage, this review has guiding significance for the later stage of study on this topic. Furthermore, this paper can engage further research or extend the research interests of scholars.

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

Similar content being viewed by others

References

  1. Chen M, Herrera F, Hwang K. Cognitive computing: human-centered computing with cognitive intelligence on clouds. IEEE Access. 2018;6:19774–83.

    Google Scholar 

  2. Juvina I, Larue O, Hough A. Modeling valuation and core affect in a cognitive architecture: the impact of valence and arousal on memory and decision-making. Cogn Syst Res. 2018;48:4–24.

    Google Scholar 

  3. Gudivada VN, Pankanti S, Seetharaman G, Zhang Y. Cognitive computing systems: their potential and the future. Computer. 2019;52(5):13–8.

    Google Scholar 

  4. Saaty TL, Vargas LG. Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res. 1987;32(1):107–17.

    Google Scholar 

  5. Orlorski SA. Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1978;1(3):155–67.

    Google Scholar 

  6. Bustince H, Burillo P. Mathematical analysis of interval-valued fuzzy relations: application to approximate reasoning. Fuzzy Sets Syst. 2000;113:205–19.

    Google Scholar 

  7. Xu ZS. Intuitionistic preference relations and their application in group decision making. Inf Sci. 2007;177:2363–79.

    Google Scholar 

  8. Xu ZS, Liao HC. A survey of approaches to decision making with intuitionistic fuzzy preference relations. Knowl-Based Syst. 2015;80:131–42.

    Google Scholar 

  9. Xia MM, Xu ZS, Liao HC. Preference relations based on intuitionistic multiplicative information. IEEE Trans Fuzzy Syst. 2013;21(1):113–33.

    Google Scholar 

  10. Herrera F, Herrera-Viedma E. Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst. 2000;115(1):67–82.

    Google Scholar 

  11. Xu ZS. Deviation measures of linguistic preference relations in group decision making. Omega. 2005;33(3):249–54.

    Google Scholar 

  12. Herrera F, Martínez L. A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst. 2008;8(6):746–52.

    Google Scholar 

  13. Rodríguez RM, Martínez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst. 2012;20(1):109–19.

    Google Scholar 

  14. Liao HC, Xu ZS, Zeng XJ, Merigó JM. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl-Based Syst. 2015;76(1):127–38.

    Google Scholar 

  15. Wang H, Xu ZS. Some consistency measures of extended hesitant fuzzy linguistic preference relations. Inf Sci. 2015;297:316–31.

    Google Scholar 

  16. Zhu B, Xu ZS. Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst. 2014;22(1):35–45.

    Google Scholar 

  17. Liao HC, Wu XL, Liang XD, Yang JB, Xu DL, Herrera F. A continuous interval-valued linguistic ORESTE method for multi-criteria group decision making. Knowl-Based Syst. 2018;153:65–77.

    Google Scholar 

  18. Wei CP, Liao HC. A multigranularity linguistic group decision-making method based on hesitant 2-tuple sets. Int J Intell Syst. 2016;31(6):612–34.

    Google Scholar 

  19. Pang Q, Wang H, Xu ZS. Probabilistic linguistic term sets in multi-attribute group decision-making. Inf Sci. 2016;369:128–43.

    Google Scholar 

  20. Gou XJ, Liao HC, Xu ZS, Herrera F. Double hierarchy hesitant fuzzy linguistic MULTIMOORA method for evaluating the implementation status of haze controlling measures. Information Fusion. 2017;38:22–34.

    Google Scholar 

  21. Liao HC, Xu ZS, Herrera-Viedma E, Herrera F. Hesitant fuzzy linguistic term set and its application in decision making: a state-of-the art survey. Int J Fuzzy Syst. 2018;20(7):2084–110.

    Google Scholar 

  22. Rodríguez RM, Martínez L, Herrera F. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf Sci. 2013;241(12):28–42.

    Google Scholar 

  23. Liu HB, Cai JF, Jiang L. On improving the additive consistency of the fuzzy preference relations based on comparative linguistic expressions. Int J Intell Syst. 2014;29(6):544–59.

    Google Scholar 

  24. Zhang ZM, Wu C. On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations. Knowl-Based Syst. 2014;72:13–27.

    Google Scholar 

  25. Xu YJ, Wang HM. A group consensus decision support model for hesitant 2-tuple fuzzy linguistic preference relations with additive consistency. J Intell Fuzzy Syst. 2017;33(1):41–54.

    Google Scholar 

  26. Wu ZB, Xu JP. Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega. 2016;65(3):28–40.

    Google Scholar 

  27. Li CC, Rodríguez RM, Martínez L, Dong YC, Herrera F. Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions. Knowl-Based Syst. 2018;145:156–65.

    Google Scholar 

  28. Li CC, Rodríguez RM, Martínez L, Dong YC, Herrera F. Consistency of hesitant fuzzy linguistic preference relations: an interval consistency index. Inf Sci. 2018;432:347–61.

    Google Scholar 

  29. Ren PJ, Zhu B, Xu ZS. Assessment of the impact of hydropower stations on the environment with a hesitant fuzzy linguistic hyperplane-consistency programming method. IEEE Trans Fuzzy Syst. 2018;26(5):2981–92.

    Google Scholar 

  30. Liu HB, Jiang L, Xu ZS. Improving the additive and multiplicative consistency of hesitant fuzzy linguistic preference relations. J Intell Fuzzy Syst. 2017;33:3677–93.

    Google Scholar 

  31. Wang LH, Gong ZW. Priority of a hesitant fuzzy linguistic preference relation with a normal distribution in meteorological disaster risk assessment. Int J Environ Res Public Health. 2017;14(10):1203. https://doi.org/10.3390/ijerph14101203.

    Article  PubMed Central  Google Scholar 

  32. Wu ZB, Xu JP. An interactive consensus reaching model for decision making under hesitation linguistic environment. J Intell Fuzzy Syst. 2016;31(3):1635–44.

    Google Scholar 

  33. Wu ZB. A consensus process for hesitant fuzzy linguistic preference relations, IEEE international conference on fuzzy systems. Turkey: Istanbul; 2015. https://doi.org/10.1109/FUZZ-IEEE.2015.7337827.

    Book  Google Scholar 

  34. Dong YC, Herrera XCF. Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making. Inf Sci. 2015;297:95–117.

    Google Scholar 

  35. Gou XJ, Xu ZS, Liao HC. Group decision making with compatibility measures of hesitant fuzzy linguistic preference relations. Soft Comput. 2017;6:1–17.

    Google Scholar 

  36. Zhao M, Liu T, Su J, Liu MY. A method adjusting consistency and consensus for group decision-making problems with hesitant fuzzy linguistic preference relations based on discrete fuzzy numbers. Complexity. 2018;2018:1–17. https://doi.org/10.1155/2018/9345609.

    Article  Google Scholar 

  37. Feng XQ, Zhang L, Wei CP. The consistency measures and priority weights of hesitant fuzzy linguistic preference relations. Appl Soft Comput. 2018;65:79–90.

    Google Scholar 

  38. Tang M, Liao HC, Li ZM, Xu ZS. Nature disaster risk evaluation with a group decision making method based on incomplete hesitant fuzzy linguistic preference relations. Int J Environ Res Public Health. 2018;15(4):751.

    PubMed Central  Google Scholar 

  39. Quirk R. A comprehensive grammar of the English language. General Grammar Series: Longman; 1985.

    Google Scholar 

  40. Durand M, Truck I. A new proposal to deal with hesitant linguistic expressions on preference assessments. Information Fusion. 2018;41:176–81.

    Google Scholar 

  41. Herrera F, Herrera-Viedma E, Verdegay JL. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 1996;78(1):73–87.

    Google Scholar 

  42. Torra V. Hesitant fuzzy sets. Int J Intell Syst. 2010;25:529–39.

    Google Scholar 

  43. Wei CP, Zhao N, Tang XJ. Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst. 2014;22(3):575–85.

    Google Scholar 

  44. Tang M, Liao HC. Managing information measures for hesitant fuzzy linguistic term sets and their applications in designing clustering algorithms. Information Fusion. 2019;50:30–42.

    Google Scholar 

  45. Liao HC, Yang LY, Xu ZS. Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets. Appl Soft Comput. 2018;63:223–34.

    Google Scholar 

  46. Tian ZP, Wang J, Wang JQ. A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cogn Comput. 2016;8(4):670–83.

    CAS  Google Scholar 

  47. Chen ZS, Chin KS, Li YL, Yang Y. Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making. Inf Sci. 2016;357:61–87.

    Google Scholar 

  48. Meng FY, Wang C, Chen XH. Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput. 2016;8(1):52–68.

    Google Scholar 

  49. Liu PD, Tang GL. Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cogn Comput. 2016;8(6):1036–56.

    Google Scholar 

  50. Ye J. Multiple attribute decision-making methods based on the expected value and the similarity measure of hesitant neutrosophic linguistic numbers. Cogn Comput. 2018;10(3):454–63.

    Google Scholar 

  51. Gou XJ, Liao HC, Xu ZS, Min R, Herrera F. Group decision making with double hierarchy hesitant fuzzy linguistic preference relations: consistency based measures, index and repairing algorithms and decision model. Inf Sci. 2019;489:93–112.

    Google Scholar 

  52. Zhang YX, Xu ZS, Wang H, Liao HC. Consistency-based risk assessment with probabilistic linguistic preference relation. Appl Soft Comput. 2016;49:817–33.

    Google Scholar 

  53. Zhang YX, Xu ZS, Liao HC. An ordinal consistency-based group decision making process with probabilistic linguistic preference relation. Inf Sci. 2018;467:179–98.

    Google Scholar 

  54. Gao J, Xu ZS, Ren PJ, Liao HC. An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations. Int J Mach Learn Cybern. 2018;10:1613–29. https://doi.org/10.1007/s13042-018-0839-0.

    Article  Google Scholar 

  55. Wu P, Zhou LG, Chen HY, Tao ZF. Additive consistency of hesitant fuzzy linguistic preference relation with a new expansion principle for hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst. 2019;27(4):716–30.

    Google Scholar 

  56. Liu HB, Ma Y, Jiang L. Managing incomplete preferences and consistency improvement in hesitant fuzzy linguistic preference relations with applications in group decision making. Information Fusion. 2019;51:19–29.

    Google Scholar 

  57. Song YM, Hu J. A group decision support model based on incomplete hesitant fuzzy linguistic preference relations for mine disaster rescue. Progr Artif Intell. 2018;7:213–24.

    Google Scholar 

  58. Liu NN, He Y, Xu ZS. A new approach to deal with consistency and consensus issues for hesitant fuzzy linguistic preference relations. Appl Soft Comput. 2019;76:400–15.

    Google Scholar 

  59. Xu YJ, Wen XW, Sun H, Wang HM. Consistency and consensus models with local adjustment strategy for hesitant fuzzy linguistic preference relations. Int J Fuzzy Syst. 2018;20(7):2216–33.

    Google Scholar 

  60. Gao J, Xu ZS, Liang ZL, Liao HC. Expected consistency-based emergency decision making with incomplete probabilistic linguistic preference relations. Knowl-Based Syst. 2019;176:15–28.

    Google Scholar 

  61. Krishankumar R, Ravichandran KS, Ifjaz Ahmed M, et al. Probabilistic linguistic preference relation-based decision framework for multi-attribute group decision making. Symmetry. 2019;11(2). https://doi.org/10.3390/sym11010002.

    Google Scholar 

  62. Mi XM, Wu XL, Tang M, et al. Hesitant fuzzy linguistic analytic hierarchical process with prioritization, consistency checking, and inconsistency repairing. IEEE Access. 2019;7:44135–49.

    Google Scholar 

  63. Gong KX, Chen CF, Wei Y. The consistency improvement of probabilistic linguistic hesitant fuzzy preference relations and their application in venture capital group decision making. J Intell Fuzzy Syst. 2019:1–12. https://doi.org/10.3233/JIFS-190052.

    Google Scholar 

  64. Zhang ZM, Chen SM. A consistency and consensus-based method for group decision making with hesitant fuzzy linguistic preference relations. Inf Sci. 2019;501:317–36.

    Google Scholar 

  65. Faizi S, Rashid T, Zafar S. Additive consistency-based approach for group decision making with hesitant 2-tuple linguistic preference relations. J Intell Fuzzy Syst. 2018;35:4657–72.

    Google Scholar 

  66. Luo SZ, Zhang HY, Wang JQ, Li L. Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. J Oper Res Soc. 2019:1–17. https://doi.org/10.1080/01605682.2018.1510806.

    Google Scholar 

  67. Liang WZ, Zhao GY, Luo SZ. Selecting the optimal mine ventilation system via a decision making framework under hesitant linguistic environment. Symmetry. 2018;10(7):283.

    Google Scholar 

  68. Wu XL, Liao HC. A consensus-based probabilistic linguistic gained and lost dominance score method. Eur J Oper Res. 2019;272:1017–27.

    Google Scholar 

  69. Xu YJ, Herrera F. Visualizing and rectifying different inconsistencies for fuzzy reciprocal preference relations. Fuzzy Sets Syst. 2019;362:85–109.

    Google Scholar 

  70. Mikhailov L. A fuzzy programming method for deriving priorities in the analytic hierarchy process. J Oper Res Soc. 2000;51:341–9.

    Google Scholar 

  71. Saaty TL. A scaling method for priorities in hierarchical structures. J Math Psychol. 1977;15(3):234–81.

    Google Scholar 

  72. Ness J, Hoffman C. Putting sense into consensus: solving the puzzle of making team decisions. Tacoma, WA: VISTA Associates; 1998.

    Google Scholar 

  73. Zhang HJ, Dong YC, Chiclana F, Shui Y. Consensus efficiency in group decision making: a comprehensive comparative study and its optimal design. Eur J Oper Res. 2019;275(2):580–98.

    Google Scholar 

  74. Cabrerizo FJ, Morente-Molinera JA, Pedrycz W, Taghavi A, Herrera-Viedma E. Granulating linguistic information in decision making under consensus and consistency. Expert Syst Appl. 2018;99:83–92.

    Google Scholar 

  75. Zhang YX, Xu ZS, Liao HC. A consensus process for group decision-making with probabilistic linguistic preference relations. Inf Sci. 2017;414:260–75.

    Google Scholar 

  76. Tang M, Liao HC. Multiple criteria group decision making based on hesitant fuzzy linguistic consensus model for fashion sales forecasting, in: artificial intelligence on fashion and textile conference. 2018. https://doi.org/10.1007/978-3-319-99695-0_40

    Google Scholar 

  77. Wu HY, Ren PJ, Xu ZS. Hesitant fuzzy linguistic consensus model based on trust-recommendation mechanism for hospital expert consultation. IEEE Trans Fuzzy Syst. 2019. https://doi.org/10.1109/TFUZZ.2019.2896836.

    Google Scholar 

  78. Song YM, Li GX. A mathematical programming approach to manage group decision making with incomplete hesitant fuzzy linguistic preference relations. Comput Ind Eng. 2019;135:467–75.

    Google Scholar 

  79. Xie WY, Ren ZL, Xu ZS, Wang H. The consensus of probabilistic uncertain linguistic preference relations and the application on the virtual reality industry. Knowl-Based Syst. 2018;162:14–28.

    Google Scholar 

  80. Montserrat-Adell J, Agell N, Sánchez M, Ruiz FJ. Consensus, dissension and precision in group decision making by means of an algebraic extension of hesitant fuzzy linguistic term sets. Information Fusion. 2018;42:1–11.

    Google Scholar 

  81. Zhao M, Gao Q, Fang JY, Xiao QR. An approach to consensus measure based on possibility degrees of PLTSs in group decision making. Int J Fuzzy Syst. 2018;20(7):2257–72.

    Google Scholar 

  82. Gou XJ, Xu ZS, Herrera F. Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations. Knowl-Based Syst. 2018;157:20–33.

    Google Scholar 

  83. Wu P, Zhou LG, Chen HY, Tao ZF. Multi-stage optimization model for hesitant qualitative decision making with hesitant fuzzy linguistic preference relations. Appl Intell. 2019. https://doi.org/10.1007/s10489-019-01502-8.

    Google Scholar 

  84. Zhang HJ, Xiao J, Palomares I, Liang HM, Dong YC. Linguistic distribution-based optimization approach for large-scale GDM with comparative linguistic information. An application on the selection of wastewater disinfection technology. IEEE Trans Fuzzy Syst. 2019:1. https://doi.org/10.1109/TFUZZ.2019.2906856.

  85. Song YM. Deriving the priority weights from probabilistic linguistic preference relation with unknown probabilities. PLoS One. 2018;13(12):e0208855.

    CAS  PubMed  PubMed Central  Google Scholar 

  86. Song YM, Hu J. Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation. Appl Soft Comput J. 2019;80:712–22.

    Google Scholar 

  87. Song YM, Li GX. A large-scale group decision-making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection. J Oper Res Soc. 2019;70(5):827–41.

    Google Scholar 

  88. Chen XL, Ding F, Wang YL. Knowledge fusion based on the group argumentation theory in Web 2.0 environment. Int J Commun Syst. 2018;31(16):e3466.

    Google Scholar 

  89. Wang XQ, Wang ZR, Shi ZJ. A conflict assessment model for the decision making process of mega projects based on Euclidean. J Eng Manag. 2018;32(2):92–6.

    Google Scholar 

Download references

Funding

The work was supported by the National Natural Science Foundation of China (71771156), the 2018 Key Project of the Key Research Institute of Humanities and Social Sciences in Sichuan Province (No. LYC18-02, No. DSWL18-2), and the Spark Project of Innovation at Sichuan University (No. 2018hhs-43).

Author information

Authors and Affiliations

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

    Huchang Liao, Ming Tang, Rui Qin & Xiaomei Mi

  2. Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI), University of Granada, 18071, Granada, Spain

    Huchang Liao & Francisco Herrera

  3. Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Huchang Liao, Abdulrahman Altalhi & Francisco Herrera

  4. Faculty of Computing and Information Technology, University of Jeddah, Jeddah, 21589, Saudi Arabia

    Saleh Alshomrani

Authors
  1. Huchang Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ming Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaomei Mi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Abdulrahman Altalhi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Saleh Alshomrani
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Francisco Herrera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ming Tang.

Ethics declarations

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed Consent

As this article does not contain any studies with human participants or animals performed by any of the authors, the informed consent is not applicable.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Table 5 Summary of the HFLPR-related publications
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liao, H., Tang, M., Qin, R. et al. Overview of Hesitant Linguistic Preference Relations for Representing Cognitive Complex Information: Where We Stand and What Is Next. Cogn Comput 12, 25–48 (2020). https://doi.org/10.1007/s12559-019-09681-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12559-019-09681-9

Keywords

Search

Navigation