Skip to main content

Advertisement

Springer Nature Link
Log in

Multi-criteria Group Decision-Making Approach Based on 2-Tuple Linguistic Aggregation Operators with Multi-hesitant Fuzzy Linguistic Information

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

In practice, when the frequency of a linguistic term in evaluation information is greater than one, a consensus has been reached and this frequency is regarded to be one by default. However, in case that the frequencies of several elements in a dataset are not identical, their respective importance that was initially distinguishable will become indifferent in a routine processing, which may distort the original intention of decision-makers. As an extension of hesitant fuzzy linguistic term sets (HFLTSs) and hesitant fuzzy linguistic sets (HFLSs), multi-hesitant fuzzy linguistic term sets (MHFLTSs) are thus proposed on the basis of multi-hesitant fuzzy sets (MHFSs) in this paper, and each multi-hesitant fuzzy linguistic term element (MHFLTE) can contain inconsecutive and repeatable linguistic terms. Besides, inspired by the 2-tuple linguistic model and linguistic scale functions, the transformation functions among linguistic terms, 2-tuples, and numerical data are constructed in a generalized form to cope with different semantics. According to practical conditions, decision-makers’ preferences, or experts’ suggestions, various functions can be chosen after some necessary adjustments. In this way, the original essence of vague evaluations can be retained properly and the accuracy and reliability of final results could be further improved. Furthermore, the basic operations and comparison method of MHFLTEs are given on the basis of the transformation functions, and some 2-tuple linguistic aggregation operators of MHFLTEs are also provided to deal with problems where the criteria weights are known or unknown. Based on these prerequisites, a multi-criteria group decision-making approach is established to process multi-hesitant fuzzy linguistic information. The validity and effectiveness of the proposed approach are finally demonstrated through illustration and comparison analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Dubois, D.: The role of fuzzy sets in decision sciences: Old techniques and new directions. Fuzzy Sets Syst. 184, 3–28 (2011)

    Article  MATH  Google Scholar 

  2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  3. Parreiras, R.O., Ekel, P.Y., Martini, J.S.C., Palhares, R.M.: A flexible consensus scheme for multicriteria group decision making under linguistic assessments. Inf. Sci. 180, 1075–1089 (2010)

    Article  Google Scholar 

  4. Chen, Y.H., Wang, T.C., Wu, C.Y.: Multi-criteria decision making with fuzzy linguistic preference relations. Appl. Math. Model. 35, 1322–1330 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Yang, W.E., Wang, J.Q.: Multi-criteria semantic dominance: a linguistic decision aiding technique based on incomplete preference information. Eur. J. Oper. Res. 231(1), 171–181 (2013)

    Article  Google Scholar 

  6. Liang, D., Pedrycz, W., Liu, D., Hu, P.: Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making. Appl. Soft Comput. 29, 256–269 (2015)

    Article  Google Scholar 

  7. Delgado, M., Verdegay, J., Vila, M.: On aggregation operations of linguistic labels. Int. J. Intel. Syst. 8, 351–370 (1993)

    Article  MATH  Google Scholar 

  8. Morente-Molinera, J.A., Perez, I.J., Urena, M.R., Herrera-Viedma, E.: On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends. Knowl. Based Syst. 74, 49–60 (2015)

    Article  Google Scholar 

  9. Türksen, I.B.: Type 2 representation and reasoning for CWW. Fuzzy Sets Syst. 127(1), 17–36 (2002)

    Article  MATH  Google Scholar 

  10. Mendel, J.M., Wu, D.R.: Perceptual Computing: Aiding People in Making Subjective Judgments. IEEE Press and John Wiley, New Jersey (2010)

    Book  Google Scholar 

  11. Wang, J., Chen, Q.H., Zhang, H.Y., Chen, X.H., Wang, J.Q.: Multi-criteria decision-making method based on type-2 fuzzy sets. FILOMAT (2015)

  12. Sepehriar, A., Eslamipoor, R., Nobari, A.: A new mixed fuzzy-LP method for selecting the best supplier using fuzzy group decision making. Neural Comput. Appl. 23(1), 345–352 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Martínez, L., Herrera, F.: An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf. Sci. 207, 1–18 (2012)

  15. Wang, J.H., Hao, J.Y.: A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 14, 435–445 (2006)

    Article  Google Scholar 

  16. Wang, J.Q., Lu, P., Zhang, H.Y., Chen, X.H.: Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information. Inf. Sci. 274, 177–191 (2014)

    Article  MathSciNet  Google Scholar 

  17. Wang, J.Q., Wang, P., Wang, J., Zhang, H.Y., Chen, X.H.: Atanassov’s interval-valued intuitionistic linguistic multi-criteria group decision-making method based on trapezium cloud model. IEEE Trans. Fuzzy Syst. 23(3), 542–554 (2015)

  18. Wang, J.Q., Wu, J.T., Wang, J., Zhang, H.Y., Chen, X.H.: Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers. Soft Comput. (2015). doi:10.1007/s00500-015-1609-5

    Google Scholar 

  19. Xu, Z.S.: A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci. 166(1), 19–30 (2004)

    Article  MATH  Google Scholar 

  20. Xu, Z.S.: Induced uncertain linguistic OWA operators applied to group decision making. Inf. Fusion 7, 231–238 (2006)

    Article  Google Scholar 

  21. Park, J.H., Gwak, M.G., Kwun, Y.C.: Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making. Computing 93, 47–64 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Peng, B., Ye, C.M., Zeng, S.Z.: Uncertain pure linguistic hybrid harmonic averaging operator and generalized interval aggregation operator based approach to group decision making. Knowl. Based Syst. 36, 175–181 (2012)

    Article  Google Scholar 

  23. Wang, J.Q., Peng, J.J., Zhang, H.Y., Liu, T., Chen, X.H.: An uncertain linguistic multi-criteria group decision-making method based on a cloud model. Group Decis. Negot. 24(1), 171–192 (2015)

    Article  Google Scholar 

  24. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—II. Inf. Sci. 8(4), 301–357 (1975)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  26. Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109–119 (2012)

    Article  Google Scholar 

  27. Liu, H., Rodriguez, R.M.: A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making. Inf. Sci. 258, 220–238 (2014)

    Article  MathSciNet  Google Scholar 

  28. Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhang, Z.M., Wu, C.: Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making. J. Intel. Fuzzy Syst. 26(5), 2185–2202 (2014)

    MATH  Google Scholar 

  30. Beg, I., Rashid, T.: TOPSIS for hesitant fuzzy linguistic term sets. Int. J. Intel. Syst. 28(12), 1162–1171 (2013)

    Article  Google Scholar 

  31. Liao, H.C., Xu, Z.S., Zeng, X.J.: Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf. Sci. 271, 125–142 (2014)

    Article  MathSciNet  Google Scholar 

  32. Liao, H.C., Xu, Z.S.: Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making. Expert Syst. Appl. 42(12), 5328–5336 (2015)

    Article  Google Scholar 

  33. Wang, J., Wang, J.Q., Zhang, H.Y., Chen, X.H.: Multi-criteria decision-making based on hesitant fuzzy linguistic term sets: an outranking approach. Knowl. Based Syst. (2015). doi:10.1016/j.knosys.2015.06.007

  34. Liao, H.C., Xu, Z.S., Zeng, X.J., Merigo, J.M.: Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl. Based Syst. 76, 127–138 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  36. Lee, L.W., Chen, S.M.: Fuzzy Decision Making Based on Hesitant Fuzzy Linguistic Term Sets, ACIIDS, pp. 21–30. Springer, Berlin (2013)

    Google Scholar 

  37. Montes, R., Sanchez, A.M., Villar, P., Herrera, F.: A web tool to support decision making in the housing market using hesitant fuzzy linguistic term sets. Appl. Soft Comput. (2015). doi:10.1016/j.asoc.2015.01.030

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Zhang, Y.J., Wang, Y.Z., Wang, J.P.: Hesitant fuzzy linguistic multiple attribute decision making. In: International Conference on Information Fusion, pp 1421–1426 (2013)

  41. Peng, J.J., Wang, J.Q., Wang, J., Yang, L.J., Chen, X.H.: An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets. Inf. Sci. 307, 113–126 (2015)

    Article  MathSciNet  Google Scholar 

  42. Xia, M.M., Xu, Z.S., Chen, N.: Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negot. 22(2), 259–279 (2013)

    Article  Google Scholar 

  43. Zhou, L., Tao, Z., Chen, H., Liu, J.: Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making. Appl. Math. Model. 38(7–8), 2190–2205 (2014)

    Article  MathSciNet  Google Scholar 

  44. Wang, J.Q., Nie, R.R., Zhang, H.Y., Chen, X.H.: New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis. Inf. Sci. 251, 79–95 (2013)

    Article  MathSciNet  Google Scholar 

  45. Lan, J., Sun, Q., Chen, Q., Wang, Z.: Group decision making based on induced uncertain linguistic OWA operators. Decis. Support Syst. 55(1), 296–303 (2013)

    Article  Google Scholar 

  46. Xu, Z.S.: Linguistic aggregation operators: an overview. In: Bustince, H., Herrera, F., Montero, J. (eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, pp. 163–181. Springer, Berlin (2008)

    Chapter  Google Scholar 

  47. Yang, W., Chen, Z.P.: New aggregation operators based on the Choquet intergral and 2-tuple linguistic information. Expert Syst. Appl. 39, 2662–2668 (2012)

    Article  Google Scholar 

  48. Wang, X.F., Wang, J.Q., Yang, W.E.: Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators. J. Intel. Fuzzy Syst. 26(1), 115–125 (2014)

    MATH  Google Scholar 

  49. Yu, S., Zhou, H., Chen, X., Wang, J.Q.: A multi-criteria decision-making method based on Heronian mean operators under linguistic hesitant fuzzy environment. Asia Pac. J. Oper. Res. (2015)

  50. Sang, X., Liu, X., Chen, L.: Parametric weighting function for WOWA operator and its application in decision making. Int. J. Intel. Syst. 29(2), 119–136 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  52. Herrera, F., Herrera-Viedma, E., Martínez, L.: A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst. 114(1), 43–58 (2000)

    Article  MATH  Google Scholar 

  53. Xu, Z.S.: Group decision making based on multiple types of linguistic preference relations. Inf. Sci. 178(2), 452–467 (2008)

    Article  MATH  Google Scholar 

  54. Wang, J.Q., Wang, D.D., Zhang, H.Y., Chen, X.H.: Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators. Soft Comput. 19(2), 389–405 (2015)

    Article  Google Scholar 

  55. Bao, G.Y., Lian, X.L., He, M., Wang, L.L.: Improved two-tuple linguistic representation model based on new linguistic evaluation scale. Control Decis. 25(5), 780–784 (2010)

    MathSciNet  Google Scholar 

  56. Schweizer, B., Sklar, A.: Statistical metric spaces. Pac. J. Math. 10(1), 314–334 (1960)

    Article  Google Scholar 

  57. Yager, R.R.: Generalized OWA aggregation operators. Fuzzy Optim. Decis. Mak. 3(1), 93–107 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  58. Wikipedia, International English Language Testing System. http://en.wikipedia.org/wiki/IELTS (2014). Accessed 18 Aug 2014

Download references

Acknowledgments

The author would like to thank the editors and the anonymous referees for their valuable and constructive comments and suggestions that greatly help the improvement of this paper. This work was supported by the National Natural Science Foundation of China (Nos. 71271218, 71221061, and 71431006).

Author information

Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, China

    Jing Wang, Jian-qiang Wang, Hong-yu Zhang & Xiao-hong Chen

  2. International College, Central South University of Forestry and Technology, Changsha, 410004, China

    Jing Wang

Authors
  1. Jing Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jian-qiang Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Hong-yu Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Xiao-hong Chen
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jian-qiang Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Wang, Jq., Zhang, Hy. et al. Multi-criteria Group Decision-Making Approach Based on 2-Tuple Linguistic Aggregation Operators with Multi-hesitant Fuzzy Linguistic Information. Int. J. Fuzzy Syst. 18, 81–97 (2016). https://doi.org/10.1007/s40815-015-0050-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-015-0050-3

Keywords