Skip to main content
SpringerLink
Log in

Distance and Aggregation-Based Methodologies for Hesitant Fuzzy Decision Making

  • Published:
Cognitive Computation Aims and scope Submit manuscript

Abstract

Hesitant fuzzy set (HFS) as an effective tool to reflect human’s hesitancy has received great attention in recent years. The importance weights of possible values in hesitant fuzzy elements (HFEs), which are the basic units of a HFS, have not been taken into account in the existing literature. Thus, the frequently used HFEs cannot deal with the situations where all the possible values are provided by experts with different levels of expertise. Consequently, in this paper, we propose an extension of typical HFS called the ordered weighted hesitant fuzzy set (OWHFS). The basic units of an OWHFS allow the membership of a given element to be defined in terms of several possible values together with their importance weights. Moreover, in order to indicate that the OWHFS has a good performance in decision making, we first present some information measures and several aggregation operators for OWHFSs. Then, we apply them to multi-attribute decision making with ordered weighted hesitant fuzzy 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

Similar content being viewed by others

References

  1. Akusok A, Miche Y, Hegedus J, Nian R, Lendasse A. A two stage methodology using K-NN and false-positive minimizing ELM for nominal data classification. Cogn Comput 2014;6:432–445.

    Article  Google Scholar 

  2. Atanassov K. Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag. Heidelberg: NewYork; 1999.

    Book  Google Scholar 

  3. Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96.

    Article  Google Scholar 

  4. Atanassov K, Gargov G. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1989;31:343–349.

    Article  Google Scholar 

  5. Bustince H. Indicator of inclusion grade for interval-valued fuzzy sets: application to approximate reasoning based on interval-valued fuzzy sets. Int J Approx Reason 2000;23(3):137–209.

    Article  Google Scholar 

  6. Bustince H, Burillo P. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 1996;79:403–405.

    Article  Google Scholar 

  7. Czubenko M, Kowalczuk Z, Ordys A. Autonomous driver based on an intelligent system of decision-making. Cogn Comput 2015;7:569–581.

    Article  Google Scholar 

  8. Dubois D, Prade H. Fuzzy Sets and Systems Theory and Applications. New York: Kluwer Academic; 1980.

    Google Scholar 

  9. Farhadinia B. A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 2013;28:752–767.

    Article  Google Scholar 

  10. Farhadinia B. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 2013; 240:129–144.

    Article  Google Scholar 

  11. Farhadinia B. Distance and similarity measures for higher order hesitant fuzzy sets. Knowl-Based Syst 2014; 55:43–48.

    Article  Google Scholar 

  12. Farhadinia B. Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int J Intell Syst 2014;29:184–205.

    Article  Google Scholar 

  13. Farhadinia B. A series of score functions for hesitant fuzzy sets. Inf Sci 2014;277:102–110.

    Article  Google Scholar 

  14. Farhadinia B. Multi criteria decision making method based on the higher order hesitant fuzzy soft set. Int Scholar Research Notices 2014. Hindawi.

  15. Farhadinia B. Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making. Inf Sci 2016;327:233–245.

    Article  Google Scholar 

  16. Farhadinia B. Multiple criteria decision making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl-Based Syst 2016;93:135–144.

    Article  Google Scholar 

  17. Rodriguez RM, Bedregal B, Bustince H, Dong YC, Farhadinia B, Kahraman C, Martinez L, Torra V, Xu YJ, Xu ZS, Herrera F. A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf Fusion 2016;29:89–97.

    Article  Google Scholar 

  18. Goguen JA. L-fuzzy sets. J Math Anal Appl 1967;18:145–174.

    Article  Google Scholar 

  19. Gorzalczany MB. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 1987;21:1–17.

    Article  Google Scholar 

  20. Kahraman C, Kaya I. A fuzzy multicriteria methodology for selection among energy alternatives. Expert Syst Appl 2010;37:6270–6281.

    Article  Google Scholar 

  21. Klir GJ, Yuan B. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River: Prentice-Hall; 1995.

    Google Scholar 

  22. Meng FY, Chen XH. Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput 2015;7:445–463.

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Mitchell HB. Pattern recognition using type-II fuzzy sets. Inf Sci 2005;2-4:409–418.

    Article  Google Scholar 

  25. Miyamoto S. Fuzzy multisets and their generalizations. Multiset Processing 2001;2235:225–235.

    Article  Google Scholar 

  26. Mizumoto M, Tanaka K. Some properties of fuzzy sets of type-2. Inf Control 1976;31:312–340.

    Article  Google Scholar 

  27. Torra V. Hesitant fuzzy sets. Int J Intell Syst 2010;25:529– 539.

    Google Scholar 

  28. Peng DH, Gao CY, Gao ZF. Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision making. Appl Math Model 2013;37:5837– 5850.

    Article  Google Scholar 

  29. Rodriguez RM, Martinez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Syst 2012;20:109–119.

    Google Scholar 

  30. Turksen IB. Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 1986;20:191–210.

    Article  Google Scholar 

  31. Wei GW. Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl-Based Syst 2012;31:176–182.

    Article  CAS  Google Scholar 

  32. Wei GW, Lan G. Grey relational analysis method for interval-valued intuitionistic fuzzy multiple attribute decision making. 5th International Conference on Fuzzy Systems and Knowledge Discovery; 2008. p. 291–295.

  33. Wei GW, Zhao XF, Lin v. Some hesitant interval-valued aggregation operators and their applications to multiple attribute decision making. Knowl-Based Syst 2013;46:43–53.

    Article  Google Scholar 

  34. Wu D, Mendel JM. A vector similarity measure for linguistic approximation: interval type-2 and type-1 fuzzy sets. Inf Sci 2008;178(2):381–402.

    Article  Google Scholar 

  35. Xia MM, Xu ZS. Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 2011; 52:395–407.

    Article  Google Scholar 

  36. Xu ZS. Deviation measures of linguistic preference relations in group decision making. Omega 2005;17:432–445.

    Google Scholar 

  37. Xu ZS, Xia MM. Distance and similarity measures for hesitant fuzzy sets. Inf Sci 2011;181:2128–2138.

    Article  Google Scholar 

  38. Yager RR. On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 1988;18:183–190.

    Article  Google Scholar 

  39. Yang J, Gong LY, Tang YF, Yan J, He HB, Zhang LQ, Li G. An improved SVM-based cognitive diagnosis algorithm for operation states of distribution grid. Cogn Comput 2015;7:582–593.

    Article  Google Scholar 

  40. Yu DJ. Some hesitant fuzzy information aggregation operators based on Einstein operational laws. Int J Intell Syst 2014;00:1– 21.

    Google Scholar 

  41. Zadeh LA. Fuzzy sets. Inf Comput 1965;8:338–353.

    Google Scholar 

  42. Zhang Z, Wu C. Weighted hesitant fuzzy sets and their application to multi-criteria decision making. British J Math Comput Sci 2014;4:1091–1123.

    Article  Google Scholar 

  43. Tian ZP, Wang J, Wang JQ, Zhang HY. A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cogn Comput 2016. doi:10.1007/s12559-016-9400-1.

  44. Zhu B, Xu ZS. Hesitant fuzzy Bonferroni means for multi-criteria decision making. J Oper Res Soc 2013; 64:1831–1840.

    Article  Google Scholar 

  45. Zhu B, Xu ZS, Xia MM. Dual hesitant fuzzy sets. J Appl Math 2012;2012:1–13.

    Google Scholar 

  46. Zhu B, Xu ZS, Xia MM. Hesitant fuzzy geometric Bonferroni means. Inf Sci 2012:72–85.

Download references

Acknowledgments

The work was partly supported by the National Natural Science Foundation of China (Nos. 61273209, 71571123).

Author information

Authors and Affiliations

  1. Department of Mathematics, Quchan University of Advanced Technology, Quchan, Iran

    B. Farhadinia

  2. Business School, Sichuan University, Chengdu, 610064, People’s Republic of China

    Zeshui Xu

Authors
  1. B. Farhadinia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Farhadinia.

Ethics declarations

Conflict of interests

Authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Farhadinia, B., Xu, Z. Distance and Aggregation-Based Methodologies for Hesitant Fuzzy Decision Making. Cogn Comput 9, 81–94 (2017). https://doi.org/10.1007/s12559-016-9436-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12559-016-9436-2

Keywords

Search

Navigation