Skip to main content
SpringerLink
Log in

A preference structure in multi-attribute decision making: an algorithmic approach based on hesitant fuzzy sets

  • Optimization
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper introduces a new methodology for solving multi-attribute decision making (MADM) problems under hesitant fuzzy environment. The uncertainty in hesitant fuzzy elements (HFE) is derived by means of entropy. The resulting uncertainty is subsequently used in HFE to derive a single representative value (RV) of alternatives in each attribute. Our work transforms the RVs into their linguistic counterparts and then formulates a methodology for pairwise comparison of the alternatives via their linguistically defines RVs. The Eigen vector corresponding to maximum Eigen value of the pairwise comparison matrix prioritizes the alternatives in each attribute. The priority vectors of the alternatives are aggregated to derive the weights of the attributes using Quadratic programming. The weighted aggregation of the attribute values provides the ranking of the alternatives in MADM. An algorithm is written to validate the procedure developed. The proposed methodology is compared with similar existing methods, and the advantages of our method are presented. The robustness of our methodology is demonstrated through sensitivity analysis. To highlight the procedure, a car purchasing problem is illustrated.

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
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability

Enquiries about data availability should be directed to the authors.

References

  • Alcantud JCR, de Andrés Calle R, Torrecillas MJM (2016) Hesitant fuzzy worth: an innovative ranking methodology for hesitant fuzzy subsets. Appl Soft Comput 38:232–243

    Article  Google Scholar 

  • Bozoki S, Fulop J (2018) Efficient weight vectors from pairwise comparison matrices. Eur J Oper Res 264:419–427

    Article  MathSciNet  Google Scholar 

  • Chen S-M, Hong J-A (2014) Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf Sci 286:63–74

    Article  Google Scholar 

  • Cohon J (2004) Multiobjective programming and planning. Dover, Mineola

    MATH  Google Scholar 

  • Crawford G, Williams C (1985) A note on the analysis of subjective judgement matrices. J Math Psychol 29:387–405

    Article  Google Scholar 

  • Gou X, Xu Z, Liao H (2017) Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queing method for multiple criteria decision making. Inf Sci 388–389:225–246

    Article  Google Scholar 

  • Herrera F, Martinez L (2000) An approach for combining linguistic and numeric information based on 2-tuple fuzzy linguistic representation model in decision-making. Internat J Uncertain Fuzziness Knowl-Based Syst 8(5):539–562

    Article  Google Scholar 

  • Herrera F, Herrera Viedma E, Martinez L (2000) A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst 114:43–58

    Article  Google Scholar 

  • Hu J, Yang Y, Zhang X, Chen X (2018) Similarity and entropy measures for hesitant fuzzy sets. Int Trans Oper Res 25:857–886

    Article  MathSciNet  Google Scholar 

  • Jibin Lan RJ (2017) Priority degrees for hesitant fuzzy sets: application to multiple attribute decision making. Oper Res Prespect 4:67–73

    MathSciNet  Google Scholar 

  • Kaufmann A (1975) Introduction to the theory of fuzzy subsets, vol I. Academic, New York

    MATH  Google Scholar 

  • Kosko B (1986) Fuzzy entropy and conditioning. Inf Sci 40:165–174

    Article  MathSciNet  Google Scholar 

  • Li D, Zeng W, Li J (2015) New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision making. Eng Appl Artif Intell 40:11–16

    Article  Google Scholar 

  • Liao H, Xu Z (2016) Hesitant fuzzy decision making methodologies and applications. Springer, Singapore

    Google Scholar 

  • Liao H, Wu X, Liang X, Xu J, Herrera F (2018) A new hesitant fuzzy linguistic ORESTE method for hybrid multicriteria decision making. IEEE Trans Fuzzy Syst 26(6):3793–3807

    Article  Google Scholar 

  • Liao H, Gou X, Xu Z, Zeng X-J, Herrera F (2020) Hesitancy degree-based correlation measures for hesitant fuzzy linguistic term sets and their applications in multiple criteria decision making. Inf Sci 508:275–292

    Article  MathSciNet  Google Scholar 

  • Peng J-J, Wang J-Q, Wu X-H (2016) Novel multi-criteria decision making approaches based on hesitant fuzzy sets and prospect theory. Int J Inf Technol Decis Mak 15(3):621–643

    Article  Google Scholar 

  • Qian G, Wang H, Feng X (2013) Generalized hesitant fuzzy sets and their application in decision support system. Knowl-Based Syst 37:357–365

    Article  Google Scholar 

  • Rao J, Tiwari R, Mohanty B (1988) A method for finding numerical compensation for fuzzy multicriteria decision problem. Fuzzy Sets Syst 25:33–41

    Article  MathSciNet  Google Scholar 

  • Riera JV, Massanet S, Herrera-Viedma E, Torrens J (2015) Some interesting properties of the fuzzy linguistic model based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information. Appl Soft Comput 36:383–391

    Article  Google Scholar 

  • Sellak H, Ouhbi B, Frikh B (2018) A knowledge based outranking approach for multi-criteria decision making with hesitant fuzzy linguistic term sets. Appl Soft Comput 67:625–640

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Wang Y-M, Parkan C (2005) Multiple attribute decision making based on fuzzy preference information on alternatives: ranking and weighting. Fuzzy Sets Syst 153:331–346

    Article  MathSciNet  Google Scholar 

  • Wang J-Q, Wang J, Chen Q-H, Zhang H-Y, Chen X-H (2014) An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf Sci 280:338–351

    Article  MathSciNet  Google Scholar 

  • Wang J, Wang J-X, Zhang H-Y, Chen X-H (2015) Multi criteria decision making based on hesitant fuzzy linguistic term sets: an outranking approach. Knowl Based Syst 86:224–236

    Article  Google Scholar 

  • Wei C, Zhao N, Tang X (2014) Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 22(3):575–585

    Article  Google Scholar 

  • Xu Y, Da X, Liu L (2009) Normalizing rank aggregation method for priority of a fuzzy preference relation and its effectiveness. Int J Approx Reason 50:1287–1297

    Article  MathSciNet  Google Scholar 

  • Xu Y, Wang H, Sun H, Yu D (2014) A distance based aggregation approach for group decision making with interval preference orderings. Comput Ind Eng 72:178–186

    Article  Google Scholar 

  • Yager RR (1995) Measures of entropy and fuzziness related to aggregation operators. Inf Sci 82:147–166

    Article  MathSciNet  Google Scholar 

  • Yager RR (2003) Induced aggregation operators. Fuzzy Sets Syst 137:59–69

    Article  MathSciNet  Google Scholar 

  • Yager RR (2004) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3:93–107

    Article  MathSciNet  Google Scholar 

  • Yang MS, Hussain Z (2019) Distance and similarity measures of hesitant fuzzy sets based on Hausdorff metric with applications to multi-criteria decision making and clustering. Soft Comput 23(14):5835–5848

    Article  Google Scholar 

  • Zimmermann H-J (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We thank the anonymous reviewers for their valuable comments and suggestions by which our work is significantly improved.

Funding

The authors have not used any funding/grant to carry out this research work.

Author information

Authors and Affiliations

  1. Indian Institute of Management, Lucknow, 226 013, India

    B. K. Mohanty & Eshika Aggarwal

Authors
  1. B. K. Mohanty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eshika Aggarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. K. Mohanty.

Ethics declarations

Conflict of interest

All authors declare that they have no conflict of interest.

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

Mohanty, B.K., Aggarwal, E. A preference structure in multi-attribute decision making: an algorithmic approach based on hesitant fuzzy sets. Soft Comput 26, 7259–7277 (2022). https://doi.org/10.1007/s00500-022-07112-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-022-07112-w

Keywords

Search

Navigation