Skip to main content
SpringerLink
Log in

A continuous interval-valued double hierarchy linguistic GLDS method and its application in performance evaluation of bus companies

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

The double hierarchy linguistic information is more close to people’s habits of expression and it can describe evaluation information more accurately, so it has been extensively utilized in multi-criteria decision-making (MCDM) problems in recent years. First of all, taking the advantage of the completeness of the double hierarchy linguistic information, this paper proposes the continuous interval-valued double hierarchy linguistic term set. It is vital that it not only can express more complex evaluation information but also can aggregate group opinions by continuous terms. At the same time, the gained and lost dominance score (GLDS) method is a outranking method that has emerged in recent years. It takes the perspective of individuals and groups more comprehensively, making the obtained ranking results more convincing and accurate. Therefore, we construct the GLDS method into the continuous interval-valued double hierarchy linguistic environment (named CIVDHL-GLDS method) based on the above considerations. Public transportation is an important part of urban transportation. A comprehensive and objective description of urban surface bus operation level is conductive to a more objective evaluation of urban traffic level. Afterwards, in order to justify its validity of our method, taking the performance evaluation of four subsidiaries of Chengdu Public Transport Group in Sichuan province as a case study. Finally, Some discussions and comparisons are provided to reveal our proposed method has some innovations and dominance.

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
Fig. 2
Fig. 3

Similar content being viewed by others

Abbreviations

MCDM:

Multi-criteria decision-making

HFLTS:

Hesitant fuzzy linguistic term set

DHLTS:

Double hierarchy linguistic term set

LTS:

Linguistic term set

DHHFL:

Double hierarchy hesitant fuzzy linguistic

DHHFLTS:

Double hierarchy hesitant fuzzy linguistic term set

CIVDHL:

Continuous interval-valued double hierarchy linguistic

GLDS:

Gained and lost dominance score

GDS:

Gained dominance score

LDS:

Lost dominance score

MULTIMOORA:

Multiobjective optimization by ratio analysis plus the full multiplicative form

ORESTE:

Organísation, rangement et Synthèse de données relarionnelles, in French

TOPSIS:

Technique for order preference by similarity to ideal solution

VIKOR:

VIse Kriterijumska Optimizacija I Kompromisno Resenje

TODIM:

Acronym in Portuguese of Interactive and Multicriteria Decision Making

References

  1. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    MATH  Google Scholar 

  2. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-part I. Inf Sci 8(3):199–249

    MATH  Google Scholar 

  3. Chen CT, Lin CT, Huang SF (2006) A fuzzy approach for supplier evaluation and selection in supply chain management. Int J Prod Econ 102(2):289–301

    Google Scholar 

  4. Mamdani EH, Assilian S (1999) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Hum-Comput Stud 51(2):135–147

    MATH  Google Scholar 

  5. Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752

    Google Scholar 

  6. Türkşen IB (2002) Type 2 representation and reasoning for CWW. Fuzzy Sets Syst 127:17–36

    MathSciNet  MATH  Google Scholar 

  7. Lin Y, Wang YM, Chin KS (2019) An enhanced approach for two-sided matching with 2-tuple linguistic multi-attribute preference. Soft Comput 23(17):7977–7990

    MATH  Google Scholar 

  8. Zhao XM, Mo H, Yan KF, Li LX (2020) Type-2 fuzzy control for driving state and behavioral decisions of unmanned vehicle. IEEE-CAA J Autom Sin 7(1):178–186

    MathSciNet  Google Scholar 

  9. Rodríguez RM, Martínez L, Herrera F (2012) HFLTSs for decision making. IEEE Trans Fuzzy Syst 20(1):109–119

    Google Scholar 

  10. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  11. Zhao N, Xu ZS, Ren ZL (2018) Some approaches to constructing distance measures for HFLTSs with applications in decision-making. Int J Inf Technol Decis Mak 17(1):103–132

    Google Scholar 

  12. Liao HC, Mi XM, Yu Q, Luo L (2019) Hospital performance evaluation by a hesitant fuzzy linguistic best worst method with inconsistency repairing. J Clean Prod 232:657–671

    Google Scholar 

  13. Gou XJ, Liao HC, Xu ZS, Herrera F (2017) Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: a case of study to evaluate the implementation status of haze controlling measures. Inf Fusion 38:22–34

    Google Scholar 

  14. Liu XY, Wang XL, Qu QX, Zhang L (2018) Double hierarchy hesitant fuzzy linguistic mathematical programming method for MAGDM based on Shapley values and incomplete preference information. IEEE Access 6:74162–74179

    Google Scholar 

  15. Zhang WY, Yang FX, Fan HY, Yu Q, Yang Y, Liu J (2018) Comprehensive evaluation of haze governance based on double hierarchy hesitant fuzzy language and entropy method integrated weight. Softw Eng Serv Sci 2:279–285

    Google Scholar 

  16. Montserrat-Adell J, Xu ZS, Gou XJ, Agell N (2019) Free double hierarchy hesitant fuzzy linguistic term sets: An application on ranking alternatives in GDM. Inf Fusion 47:45–59

    Google Scholar 

  17. Fu ZG, Liao HC (2019) Unbalanced double hierarchy linguistic term set: The TOPSIS method for multi-expert qualitative decision making involving green mine selection. Inf Fusion 51:271–286

    Google Scholar 

  18. Liu NN, He Y, Xu ZS (2019) Evaluate public-private-partnership’s advancement using double hierarchy hesitant fuzzy linguistic PROMETHEE with subjective and objective information from stakeholder perspective. Technol Econ Dev Econ 25:386–420

    Google Scholar 

  19. Mardani A, Nilashi M, Zakuan N, Loganathan N, Soheilirad S, Saman MZM, Ibrahim O (2017) A systematic review and meta-Analysis of SWARA and WASPAS methods: Theory and applications with recent fuzzy developments. Appl Soft Comput 57:265–292

    Google Scholar 

  20. Krishankumar R, Subrajaa LS, Ravichandran KS, Kar S, Saeid AB (2019) A framework for multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic term set. Int J Fuzzy Syst 21(4):1130–1143

    MathSciNet  Google Scholar 

  21. Krishankumar R, Ravichandran KS, Shyam V, Sneha SV, Kar S, Garg H (2020) Multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic preference information. Neural Comput Applic 32:14031–14045

    Google Scholar 

  22. Zhang L, Liu R, Jiang S, Luo G, Liu HC (2020) Identification of key performance indicators for hospital management using an extended hesitant linguistic DEMATEL approach. Healthcare. https://doi.org/10.3390/healthcare8010007

  23. Liu ZM, Zhao XL, Li L, Wang XY, Wang D, Liu PD (2020) Selecting a public service outsourcer based on the improved ELECTRE II method with unknown weight information under a double hierarchy hesitant linguistic environment. Sustainability. https://doi.org/10.3390/su12062315

  24. Liu PD, Shen MJ, Teng F, Zhu BY, Rong LL, Geng YS (2020) Double hierarchy hesitant fuzzy linguistic entropy-based TODIM approach using evidential theory. Inf Sci 547:223–243

    Google Scholar 

  25. Zhang RC, Xu ZS, Gou XJ (2020) An integrated method for multi-criteria decision-making based on the best-worst method and Dempster-Shafer evidence theory under double hierarchy hesitant fuzzy linguistic environment. Appl Intell 51(2):713–735

    Google Scholar 

  26. Li X, Wang H, Xu ZS (2021) Work resumption after epidemic using three-way decisions. Int J Fuzzy Syst 23:630–641. https://doi.org/10.1007/s40815-020-01006-5

    Article  Google Scholar 

  27. Liu ZM, Zhao XL, Li L, Wang XY, Wang D (2019) A novel multi-attribute decision making method based on the double hierarchy hesitant fuzzy linguistic generalized power aggregation operator. Information 10(11):339

    Google Scholar 

  28. Krishankumar R, Ravichandran KS, Liao HC, Kar S (2020) An integrated decision framework for group decision-making with double hierarchy hesitant fuzzy linguistic information and unknown weights. Int J Comput Intell Syst 13(1):624–637

    Google Scholar 

  29. Krishankumar R, Ravichandran KS, Kar S, Gupta P, Mehlawat MK (2020) Double-hierarchy hesitant fuzzy linguistic term set-based decision framework for multi-attribute group decision-making. Soft Comput 25:2665–2685. https://doi.org/10.1007/s00500-020-05328-2

    Article  Google Scholar 

  30. Liu X, Han B, Chen HY, Zhou LG (2018) Interval-valued 2-tuple linguistic induced continuous ordered weighted distance measure and its application to multiple attribute group decision making. Informatica 29(2):321–352

    MathSciNet  Google Scholar 

  31. Zeng SZ, Chen SM, Fan KY (2020) Interval-valued intuitionistic fuzzy multiple attribute decision making based on nonlinear programming methodology and TOPSIS method. Inf Sci 506:424–442

    Google Scholar 

  32. Zhou H, Ma XY, Zhou LG, Chen HY, Ding WR (2018) A novel approach to group decision-making with interval-valued intuitionistic fuzzy preference relations via shapley value. Int J Fuzzy Syst 20(4):1172–1187

    MathSciNet  Google Scholar 

  33. Meng FY, Chen XH, Zhang Q (2014) Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making. Appl Math Model 38:2543–2557

    MathSciNet  MATH  Google Scholar 

  34. Liu HC, You JX, Lu C, Shan MM (2014) Application of interval 2-tuple linguistic MULTIMOORA method for health-care waste treatment technology evaluation and selection. Waste Manag 34:2355–2364

    Google Scholar 

  35. Liu HC, You JX, You XY (2014) Evaluating the risk of healthcare failure modes using interval 2-tuple hybrid weighted distance measure. Comput Ind Eng 78:249–258

    Google Scholar 

  36. Zhang HM (2013) Some interval-valued 2-tuple linguistic aggregation operators and application in multi-attribute group decision making. Appl Math Model 37:4269–4282

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  38. Zhang Z, Kou XY, Palomares I, Yu WY, Gao JL (2019) Stable two-sided matching decision making with incomplete fuzzy preference relations: a disappointment theory based approach. Appl Soft Comput 84:105730. https://doi.org/10.1016/j.asoc.2019.105730

    Article  Google Scholar 

  39. Chen N, Xu ZS (2015) Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems. Inf Sci 292:175–197

    Google Scholar 

  40. Xu ZS (2007) Multiple-attribute group decision making with different formats of preference information on attributes. IEEE Trans Syst Man Cybern Part B-Cybern 37(6):1500–1511

    Google Scholar 

  41. Hwang CL, Yoon K (1981) Multiple attributes decision making methods and applications. Springer, Heidelberg

    MATH  Google Scholar 

  42. Opricovic S (1998) Multicriteria optimization of civil engineering systems. Faculty Civil Eng Belgrade 2(1):5–21 (in Serbian)

    MathSciNet  Google Scholar 

  43. Gomes LFAM, Lima MMPP (1992) TODIM: basic and application to multicriteria ranking of projects with environmental impacts. Fund Comput Decis Sci 16(4):113–127

    MATH  Google Scholar 

  44. Wu XL, Liao HC (2019) A consensus-based probabilistic linguistic gained and lost dominance score method. Eur J Oper Res 272:1017–1027

    MathSciNet  MATH  Google Scholar 

  45. Fu ZG, Liao HC, Wu XL, Herrera F (2018) Underground mining method selection with the hesitant fuzzy linguistic gained and lost dominance score method. IEEE Access 6:66442–66458

    Google Scholar 

  46. H.C. Liao, J.Y. Yu, X.L. Wu, A. Al-Barakati, A. Altalhi and F. Herrera, Life satisfaction evaluation in earthquake-hit area by the probabilistic linguistic GLDS method integrated with the logarithm-multiplicative analytic hierarchy process, Int J Disaster Risk Reduction 38(2019) 101190 https://doi.org/10.1016/j.ijdrr.2019.101190

  47. Xu ZS (2004) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168(1–4):171–184

    MATH  Google Scholar 

  48. Dunstan FD, Nix AB (1991) Estimation of the mean and standard-deviation using order-statistics. Stat Med 10(6):855–869

    Google Scholar 

  49. Wang YM (1997) Using the method of maximizing deviation to make decision for multi-indices. J Syst Eng Electron 8(3):21–26

    Google Scholar 

  50. Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15:234–281

    MathSciNet  MATH  Google Scholar 

  51. Yeh CH, Deng HP, Chang YH (2000) Fuzzy multicriteria analysis for performance evaluation of bus companies. Eur J Oper Res 126:459–473

    MATH  Google Scholar 

  52. Wang JQ, Wu JT, Wang J, Zhang HY, Chen XH (2014) Interval-valued hesitant fuzzy linguistic sets and their applications in MCDM problems. Inf Sci 288:55–72

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Xindi Wang, Xunjie Gou & Zeshui Xu

Authors
  1. Xindi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xunjie Gou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Gou, X. & Xu, Z. A continuous interval-valued double hierarchy linguistic GLDS method and its application in performance evaluation of bus companies. Appl Intell 52, 4511–4526 (2022). https://doi.org/10.1007/s10489-021-02581-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-02581-2

Keywords

Search

Navigation