Skip to main content
SpringerLink
Log in

A consensus reaching process with hesitant fuzzy elements considers the individuals best and worst consensus levels

  • Regular Paper
  • Published:
Knowledge and Information Systems Aims and scope Submit manuscript

Abstract

The purposes of the study: to address the situation where multi-criteria decision-making (MCDM) problems with hesitant fuzzy elements (HFEs), this study develops group decision-making method considering the individuals best and worst consensus levels simultaneously. Procedures: first, the concepts of individual best and worst consensus levels are proposed, and then, the concept of acceptable consensus level is developed. Second, several optimization models are constructed for improving the consensus levels. Third, the proposed consensus checking and improving processes are extended to incomplete evaluation information. Fourth, an algorithm is designed for deriving the priority weights of decision-makers. Finally, an illustrative example in conjunction with comparative analysis is provided. Findings: the concept of acceptable individual consensus level with HFEs not only overcomes the shortcoming of difficult to achieve owing to too restricted, but also the loss of information owing to too loose. The consensus improving process considers all the evaluation information and avoids the loss of information. Conclusions: Several programming models are constructed to improve the consensus level with HFEs. This provides the direction of the decision-makers to revise their evaluation values, and the consensus improving process is time-saving and easy to extend to incomplete evaluation information.

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. Akram M, Luqman A, Kahraman C (2021) Hesitant pythagorean fuzzy ELECTRE-II method for multi-criteria decision-making problems. Appl Soft Comput 108:107479

    Google Scholar 

  2. Atanassov K, Pasi G, Yager R (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 14:859–868

    MathSciNet  MATH  Google Scholar 

  3. Büyüközkan G, Güler M (2021) A combined hesitant fuzzy MCDM approach for supply chain analytics tool evaluation. Appl Soft Comput 112:107812

    Google Scholar 

  4. Bustince H, Kacprzyk J, Mohedano V (2000) Intuitionistic fuzzy generators application to intuitionistic fuzzy complementation. Fuzzy Sets Syst 114:485–504

    MathSciNet  MATH  Google Scholar 

  5. Deveci M, Oner S, Ciftci M et al (2022) Interval type-2 hesitant fuzzy entropy-based WASPAS approach for aircraft type selection. Appl Soft Comput 114:108076

    Google Scholar 

  6. Dombi J, Jónás T (2020) Ranking trapezoidal fuzzy numbers using a parametric relation pair. Fuzzy Sets Syst 399:20–43

    MathSciNet  MATH  Google Scholar 

  7. Dong Y, Xu Y, Li H et al (2010) The OWA-based consensus operator under linguistic representation models using position indexes. Eur J Oper Res 203:455–463

    MATH  Google Scholar 

  8. Li C, Rodríguez RM, Martínez L et al (2018) Consistency of hesitant fuzzy linguistic preference relations: an interval consistency index. Inf Sci 432:347–361

    MathSciNet  MATH  Google Scholar 

  9. Li H, Ji Y, Gong Z et al (2021a) Two-stage stochastic minimum cost consensus models with asymmetric adjustment costs. Inf Fusion 71:77–96

    Google Scholar 

  10. Li J, Chen Q (2020) An outranking method for multicriteria decision making with probabilistic hesitant information. Expert Syst 37:e12513

    Google Scholar 

  11. Li J, Niu L, Chen Q et al (2021b) Approaches for multicriteria decision-making based on the hesitant fuzzy best–worst method. Complex Intell Syst 7:2617–2634

    Google Scholar 

  12. Li J, Niu L, Chen Q et al (2022a) Group decision making method with hesitant fuzzy preference relations based on additive consistency and consensus. Complex Intell Syst 8:2023–2225

    Google Scholar 

  13. Li J, Niu L, Ye J et al (2022b) Decision-making models based on satisfaction degree with incomplete hesitant fuzzy preference relation. Soft Comput 26:3129–3145

    Google Scholar 

  14. Li J, Wang J, Hu J (2019) Consensus building for hesitant fuzzy preference relations with multiplicative consistency. Comput Ind Eng 128:387–400

    Google Scholar 

  15. Liang D, Darko A, Xu Z et al (2019a) Aggregation of dual hesitant fuzzy heterogenous related information with extended Bonferroni mean and its application to MULTIMOORA. Comput Ind Eng 135:156–176

    Google Scholar 

  16. Liang W, Zhao G, Wang X et al (2019b) Assessing the rockburst risk for deep shafts via distance-based multi-criteria decision making approaches with hesitant fuzzy information. Eng Geol 260:105211

    Google Scholar 

  17. Liao Z, Liao H, Tang M et al (2020) A Choquet integral-based hesitant fuzzy gained and lost dominance score method for multi-criteria group decision making considering the risk preferences of experts: case study of higher business education evaluation. Inf Fusion 62:121–133

    Google Scholar 

  18. Liu H, Jiang L (2020) Optimizing consistency and consensus improvement process for hesitant fuzzy linguistic preference relations and the application in group decision making. Inf Fusion 56:114–127

    Google Scholar 

  19. Liu H, Xu Z, Liao H (2016) The multiplicative consistency index of hesitant fuzzy preference relation. IEEE Trans Fuzzy Syst 24:82–93

    Google Scholar 

  20. Liu P, Zhang X, Pedrycz W (2021a) A consensus model for hesitant fuzzy linguistic group decision-making in the framework of Dempster–Shafer evidence theory. Knowl-Based Syst 212:106559

    Google Scholar 

  21. Liu X, Wang Z, Zhang S et al (2021b) Novel correlation coefficient between hesitant fuzzy sets with application to medical diagnosis. Expert Syst Appl 183:115393

    Google Scholar 

  22. Liu X, Xu Y, Gong Z et al (2022) Democratic consensus reaching process for multi-person multi-criteria large scale decision making considering participants’ individual attributes and concerns. Inf Fusion 77:220–232

    Google Scholar 

  23. Lu Y, Xu Y, Huang J et al (2022) Social network clustering and consensus-based distrust behaviors management for large-scale group decision-making with incomplete hesitant fuzzy preference relations. Appl Soft Comput 117:108373

    Google Scholar 

  24. Meng F, An Q (2017) A new approach for group decision making method with hesitant fuzzy preference relations. Knowl-Based Syst 127:1–15

    Google Scholar 

  25. Meng F, Chen S, Tang J (2020) Group decision making based on acceptable multiplicative consistency of hesitant fuzzy preference relations. Inf Sci 524:77–96

    MathSciNet  MATH  Google Scholar 

  26. Mishra A, Rani P, Pardasani K et al (2019) A novel hesitant fuzzy WASPAS method for assessment of green supplier problem based on exponential information measures. J Clean Prod 238:117901

    Google Scholar 

  27. Mo X, Zhao H, Xu Z (2020) Feature-based hesitant fuzzy aggregation method for satisfaction with life scale. Appl Soft Comput 94:106493

    Google Scholar 

  28. Mu Z, Zeng S, Baležentis T (2015) A novel aggregation principle for hesitant fuzzy elements. Knowl-Based Syst 84:134–143

    Google Scholar 

  29. Phu N, Hung N, Ahmadian A et al (2022) Limit properties in the metric semi-linear space of picture fuzzy numbers. Soft Comput 26:5481–5496

    Google Scholar 

  30. Rodríguez R, Labella Á, Sesma-Sara M et al (2021) A cohesion-driven consensus reaching process for large scale group decision making under a hesitant fuzzy linguistic term sets environment. Comput Ind Eng 155:107158

    Google Scholar 

  31. Sen S, Patra K, Mondal S (2016) Fuzzy risk analysis in familial breast cancer using a similarity measure of interval-valued fuzzy numbers. Pac Sci Rev A Nat Sci Eng 18:203–221

    Google Scholar 

  32. Song Y, Li G (2019) Handling group decision-making model with incomplete hesitant fuzzy preference relations and its application in medical decision. Soft Comput 23:6657–6666

    MATH  Google Scholar 

  33. Tan X, Zhu J, Palomares I et al (2022) On consensus reaching process based on social network analysis in uncertain linguistic group decision making: exploring limited trust propagation and preference modification attitudes. Inf Fusion 78:180–198

    Google Scholar 

  34. Tang J, An Q, Meng F et al (2017) A natural method for ranking objects from hesitant fuzzy preference relations. Int J Inf Technol Decis Mak 16:1611–1646

    Google Scholar 

  35. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: IEEE International Conference on Fuzzy Systems, Fuzz-Ieee

  36. Vassilev P, Atanassov K (2019) Extensions and modifications of intuitionistic fuzzy sets. "Prof. Marin Drinov" Academic Publishing House, Sofia

  37. Wan S, Yan J, Dong J (2022a) Personalized individual semantics based consensus reaching process for large-scale group decision making with probabilistic linguistic preference relations and application to COVID-19 surveillance. Expert Syst Appl 191:116328

    Google Scholar 

  38. Wan S, Zou W, Dong J et al (2022b) A consensual method for multi-criteria group decision-making with linguistic intuitionistic information. Inf Sci 582:797–832

    Google Scholar 

  39. Wang F (2021) Preference degree of triangular fuzzy numbers and its application to multi-attribute group decision making. Expert Syst Appl 178:114982

    Google Scholar 

  40. Wang Z, Rodríguez R, Wang Y et al (2021) A two-stage minimum adjustment consensus model for large scale decision making based on reliability modeled by two-dimension 2-tuple linguistic information. Comput Ind Eng 151:106973

    Google Scholar 

  41. Wu J, Dai L, Chiclana F et al (2018a) A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust. Inf Fusion 41:232–242

    Google Scholar 

  42. Wu N, Xu Y, Liu X et al (2020) Water–energy–food nexus evaluation with a social network group decision making approach based on hesitant fuzzy preference relations. Appl Soft Comput 93:106363

    Google Scholar 

  43. Wu Q, Liu X, Qin J et al (2021) Multi-criteria group decision-making for portfolio allocation with consensus reaching process under interval type-2 fuzzy environment. Inf Sci 570:668–688

    MathSciNet  Google Scholar 

  44. Wu Z, Xu J (2018b) A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Inf Fusion 41:217–231

    Google Scholar 

  45. Xia M, Xu Z (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395–407

    MathSciNet  MATH  Google Scholar 

  46. Xiao J, Wang X, Zhang H (2022) Coping with diversity ratings in prioritizing design requirements in quality function deployment: a consensus-based approach with minimum-maximum adjustments. Comput Ind Eng 163:107799

    Google Scholar 

  47. Xu Y, Cabrerizo F, Herrera-Viedma E (2017) A consensus model for hesitant fuzzy preference relations and its application in water allocation management. Appl Soft Comput 58:265–284

    Google Scholar 

  48. Xu Y, Dai W, Huang J et al (2022) Some models to manage additive consistency and derive priority weights from hesitant fuzzy preference relations. Inf Sci 586:450–467

    Google Scholar 

  49. Xu Y, Liu X, Xu L (2020) A dynamic expert contribution-based consensus model for hesitant fuzzy group decision making with an application to water resources allocation selection. Soft Comput 24:4693–4708

    MATH  Google Scholar 

  50. Zeng W, Cui H, Liu Y et al (2022) Novel distance measure between intuitionistic fuzzy sets and its application in pattern recognition. Iran J Fuzzy Syst 19:127–137

    MathSciNet  Google Scholar 

  51. Zhang H, Zhao S, Kou G et al (2020a) An overview on feedback mechanisms with minimum adjustment or cost in consensus reaching in group decision making: research paradigms and challenges. Inf Fusion 60:65–79

    Google Scholar 

  52. Zhang X, Li J, Mi J (2022a) Dynamic updating approximations approach to multi-granulation interval-valued hesitant fuzzy information systems with time-evolving attributes. Knowl-Based Syst 238:107809

    Google Scholar 

  53. Zhang Y, Chen X, Gao L et al (2022b) Consensus reaching with trust evolution in social network group decision making. Expert Syst Appl 188:116022

    Google Scholar 

  54. Zhang Z (2016) Deriving the priority weights from incomplete hesitant fuzzy preference relations based on multiplicative consistency. Appl Soft Comput 46:37–59

    Google Scholar 

  55. Zhang Z, Kou X, Dong Q (2018a) Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Syst Appl 98:118–128

    Google Scholar 

  56. Zhang Z, Kou X, Yu W et al (2018b) On priority weights and consistency for incomplete hesitant fuzzy preference relations. Knowl-Based Syst 143:115–126

    Google Scholar 

  57. Zhang Z, Pedrycz W (2020b) Iterative algorithms to manage the consistency and consensus for group decision-making with hesitant multiplicative preference relations. IEEE Trans Fuzzy Syst 28:2944–2957

    Google Scholar 

  58. Zhang Z, Wang C, Tian X (2015a) A decision support model for group decision making with hesitant fuzzy preference relations. Knowl-Based Syst 86:77–101

    Google Scholar 

  59. Zhang Z, Wang C, Tian X (2015b) Multi-criteria group decision making with incomplete hesitant fuzzy preference relations. Appl Soft Comput 36:1–23

    Google Scholar 

  60. Zhou X, Wang L, Liao H et al (2019) A prospect theory-based group decision approach considering consensus for portfolio selection with hesitant fuzzy information. Knowl-Based Syst 168:28–38

    Google Scholar 

  61. Zhu B, Xu Z (2014a) Analytic hierarchy process-hesitant group decision making. Eur J Oper Res 239:794–801

    MathSciNet  MATH  Google Scholar 

  62. Zhu B, Xu Z, Xu J (2014b) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans Cybern 44:1328–1337

    Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous reviewers and the editor for their insightful and constructive comments and suggestions that have led to an improved version of this paper. This work was supported by the National Natural Science Foundation of China (No.72061026), the Natural Science Foundation of Guangxi (No. 2020GXNSFAA297239), the Science and Technology Plan of Guangxi (No. gui ke AD20238006) and Young Teachers’ Basic Scientific Research Ability in Universities of Guangxi (Nos. 2022KY0387, 2021KY1563 and 2021KY1560).

Author information

Authors and Affiliations

  1. School of Logistics Management and Engineering, Nanning Normal University, Nanning, 530001, People’s Republic of China

    Jian Li & Qiongxia Chen

  2. Guangxi Agricultural Vocational and Technical University, Nanning, 530007, People’s Republic of China

    Li-li Niu & Limei Wei

  3. Guangxi Key Lab of Human-Machine Interaction and Intelligent Decision, Nanning, 530001, People’s Republic of China

    Jian Li

  4. Guangxi Medical University Cancer Hospital, Nanning, 530021, People’s Republic of China

    Feilong Li

  5. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, People’s Republic of China

    Zhong-xing Wang

Authors
  1. Jian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li-li Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiongxia Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Feilong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Limei Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhong-xing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiongxia Chen.

Ethics declarations

Conflict of interest

Authors Jian Li, Li-li Niu, Qiongxia Chen, Feilong Li, Limei Wei and Zhong-xing Wang declare that they have no conflict of interest.

Ethical approval

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

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Niu, Ll., Chen, Q. et al. A consensus reaching process with hesitant fuzzy elements considers the individuals best and worst consensus levels. Knowl Inf Syst 65, 3665–3693 (2023). https://doi.org/10.1007/s10115-023-01874-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10115-023-01874-x

Keywords

Search

Navigation