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Entropy Measures for Extended Hesitant Fuzzy Linguistic Term Sets and Their Applications

  • Xia Liang
  • Cuiping WeiEmail author
  • Xiaoyan Cheng
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 660)

Abstract

As a useful format of assessment, hesitant fuzzy linguistic term set (HFLTS) comes to the fore because of its wide applications in decision making. Extended hesitant fuzzy linguistic term set (EHFLTS) is a generalized form of HFLTS, and applied to collect the hesitant fuzzy linguistic information of a group. In this paper, we focus on the problem of how to measure the uncertain information of an EHFLTS. We first establish axiomatic definition of entropy for EHFLTS. Then we propose a series of entropy measures for EHFLTSs, which are also applicable for measure the uncertainty of HFLTSs. Compared with the entropy measures for HFLTSs provided by Farhadinia, the proposed entropy measures can measure both fuzziness and hesitation of an EHFLTS or HFLTS. Finally, we present a method, based on entropy and distance of EHFLTS, to determine the weights of the criteria for multi-criteria group decision making problem.

Keywords

Multi-criteria group decision making Extended hesitant fuzzy linguistic term sets Entropy Weight 

Notes

Acknowledgements

The authors are most grateful to the referees and the editors for their constructive suggestions. The work was partly supported by the National Natural Science Foundation of China (71371107, 11271224), and the Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (No. PPZY2015B109).

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–356 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 78, 73–87 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning. Inf. Sci. Part I 8, 199–249; Part II 8, 301–357; Part III 9, 43–80 (1975)Google Scholar
  4. 4.
    Herrera, F., Martínez, L.: A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision-making. IEEE Trans. Syst. Man Cybern. Part B Cybern. 31, 227–234 (2001)CrossRefGoogle Scholar
  5. 5.
    Rodríguez, R.M., Martínez, L.: An analysis of symbolic linguistic computing models in decision making. Int. J. Gen. Syst. 42, 121–136 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Herrera, F., Martínez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8, 746–752 (2000)CrossRefGoogle Scholar
  7. 7.
    Rodriguez, R.M., Martínez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20, 109–119 (2012)CrossRefGoogle Scholar
  8. 8.
    Zhu, B., Xu, Z.S.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22, 35–45 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Montes, R., Snchez, 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. 35, 949–957 (2015)CrossRefGoogle Scholar
  10. 10.
    Wei, C.P., Zhao, N., Tang, X.J.: Operations and comparisons of hesitant fuzzy linguistic term sest. IEEE Trans. Fuzzy Syst. 22, 575–585 (2014)CrossRefGoogle Scholar
  11. 11.
    Wu, J.T., Wang, J.Q., Wang, J., Zhang, H.Y., Chen, X.H.: Hesitant fuzzy linguistic multicriteria decision-making method based on generalized prioritized aggregation operator. Sci. World J. 2014, 1–16 (2014)Google Scholar
  12. 12.
    Yang, S.H., Ju, Y.B.: Dual hesitant fuzzy linguistic aggregation operators and their applications to multi-attribute decision making. J. Intell. Fuzzy Syst. 27, 1935–1947 (2014)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Lin, R., Zhao, X.F., Wang, H.J., Wei, G.W.: Hesitant fuzzy linguistic aggregation operators and their application to multiple attribute decision making. J. Intell. Fuzzy Syst. 36, 49–63 (2014)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Hesamian, G., Shams, M.: Measuring similarity and ordering based on hesitant fuzzy linguistic term sets. J. Intell. Fuzzy Syst. 28, 983–990 (2015)MathSciNetGoogle Scholar
  15. 15.
    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, 5328–5336 (2015)CrossRefGoogle Scholar
  16. 16.
    Xu, Y.J., Xu, A.W., Merig, J.M., Wang, H.M.: Hesitant fuzzy linguistic ordered weighted distance operators for group decision making. J. Appl. Math. Comput. 49, 1–24 (2015)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Liao, H.C., Xu, Z.S., Zeng, X.J.: Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans. Fuzzy Syst. 23, 1343–1355 (2015)CrossRefGoogle Scholar
  18. 18.
    Beg, I., Rashid, T.: TOPSIS for hesitant fuzzy linguistic term sets. Int. J. Intell. Syst. 28, 1162–1171 (2013)CrossRefGoogle Scholar
  19. 19.
    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. 86, 224–236 (2015)CrossRefGoogle Scholar
  20. 20.
    Wei, C.P., Ren, Z.L., Rodrguez, R.M.: A hesitant fuzzy linguistic TODIM method based on a score function. Int. J. Comput. Intell. Syst. 8, 701–712 (2015)CrossRefGoogle Scholar
  21. 21.
    Wang, H.: Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making. Int. J. Comput. Intell. Syst. 8, 14–33 (2014)CrossRefGoogle Scholar
  22. 22.
    Wei, C.P., Zhao, N., Tang, X.J.: A novel linguistic group decision-making model based on extended hesitant fuzzy linguistic term sets. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 23, 379–398 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    De, L.A., Termini, S.: A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20, 301–312 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Liang, X., Wei, C.P., Xia, M.M.: New entropy, similarity measure of intuitionistic fuzzy sets and their applications in group decision making. Int. J. Comput. Intell. Syst. 6, 987–1001 (2013)CrossRefGoogle Scholar
  25. 25.
    Wei, C.P., Yan, F.F., Rodrígueza, R.M.: Entropy measures for hesitant fuzzy sets and their application in multi-criteria decision-making. J. Intell. Fuzzy Syst. 31, 673–685 (2016)CrossRefGoogle Scholar
  26. 26.
    Farhadinia, B.: Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl. Based Syst. 93, 135–144 (2015)CrossRefGoogle Scholar
  27. 27.
    Herrera, F., Herrera-Viedma, E., Verdegay, L.: A sequential selection process in group decision making with linguistic assessment approach. Inf. Sci. 85, 223–239 (1995)CrossRefzbMATHGoogle Scholar
  28. 28.
    Herrera, F., Herrera-Viedma, E.: A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 78, 73–87 (1996)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Hwang, C.L., Yoon, K.: Multiple Attributes Decision Making Methods and Applications. Springer, Heidelberg (1981)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  1. 1.School of Management Science and EngineeringShandong University of Finance and EconomicsJinanChina
  2. 2.College of Mathematical SciencesYangzhou UniversityYangzhouChina

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