International Journal of Fuzzy Systems

, Volume 18, Issue 4, pp 685–696 | Cite as

Generalized Hesitant Fuzzy Harmonic Mean Operators and Their Applications in Group Decision Making

Article
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Abstract

In this paper, we propose the generalized hesitant fuzzy harmonic mean operators including the generalized hesitant fuzzy weighted harmonic mean operator (GHFWHM), the generalized hesitant fuzzy ordered weighted harmonic mean operator (GHFOWHM), and the generalized hesitant fuzzy hybrid harmonic mean operator (GHFHHM), using the technique of obtaining values in the interval. Then we apply the developed aggregation operators to group decision making under hesitant fuzzy environment. Considering the existing hesitant fuzzy group decision-making method does not distinguish the importance degrees of different experts, we present a new group decision-making algorithm which can consider the weight of every expert. Two numerical examples are used to illustrate the effectiveness of the proposed operators and the new group decision-making algorithm.

Keywords

Hesitant fuzzy set Harmonic mean Aggregation operator Weight Decision making 
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Notes

Acknowledgments

The work was supported by the National Natural Science Foundation of China (No. 61273209) and the Central University Basic Scientific Research Business Expenses Project (no.skgt201501).

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 343–349 (1989)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15, 1179–1187 (2007)CrossRefGoogle Scholar
  5. 5.
    Xu, Z.S.: Intuitionistic preference relations and their application in group decision making. Inf. Sci. 177, 2363–2379 (2007)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Xu, Z.S., Cai, X.Q.: Intuitionistic Fuzzy Information Aggregation: Theory and Applications. Science Press/Springer, Beijing/Berlin (2012)CrossRefMATHGoogle Scholar
  7. 7.
    Tao, Z.F., Chen, H.Y., Zhou, L.G., Liu, J.P.: A generalized multiple attributes group decision making approach based on intuitionistic fuzzy sets. Int. J. Fuzzy Syst. 16, 184–195 (2014)MathSciNetGoogle Scholar
  8. 8.
    Wang, X.F., Wang, J.Q., Deng, S.Y.: Some geometric operators for aggregating intuitionistic linguistic information. Int. J. Fuzzy Syst. 17, 268–278 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yu, D.J., Merigó, J.M., Zhou, L.G.: Interval-valued multiplicative intuitionistic fuzzy preference relations. Int. J. Fuzzy Syst. 15, 412–422 (2013)MathSciNetGoogle Scholar
  10. 10.
    Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type 2. Inf. Control 31, 312–340 (1976)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems-Theory and Applications. Academic Press, New York (1980)MATHGoogle Scholar
  12. 12.
    Yager, R.R.: On the theory of bags. Int. J. General Syst. 13, 23–37 (1986)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets Syst. 158, 2429–2442 (2007)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision, the 18th IEEE International Conference on Fuzzy Systems, Jeju Island, pp. 1378–1382 (2009)Google Scholar
  15. 15.
    Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25, 529–539 (2010)MATHGoogle Scholar
  16. 16.
    Xu, Z.S., Xia, M.M.: Distance and similarity measures for hesitant fuzzy sets. Inf. Sci. 181, 2128–2138 (2011)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Xu, Z.S., Xia, M.M.: On distance and correlation measures of hesitant fuzzy information. Int. J. Intell. Syst. 26, 410–425 (2011)CrossRefMATHGoogle Scholar
  18. 18.
    Peng, D.H., Gao, C.Y., Gao, Z.F.: Generalized hesitant fuzzy synergetic weighted distance measures. Appl. Math. Model. 37, 5837–5850 (2013)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Chen, N., Xu, Z.S., Xia, M.M.: Hierarchical hesitant fuzzy K-means clustering algorithm. Appl. Mathematics-A J. Chin. Univ. Ser. B 29, 1–17 (2014)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Chen, N., Xu, Z.S., Xia, M.M.: Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl. Math. Model. 37, 2197–2211 (2013)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Xia, M.M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52, 395–407 (2011)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Xia, M.M., Xu, Z.S., Chen, N.: Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negot. 22, 259–279 (2013)CrossRefGoogle Scholar
  23. 23.
    Wei, G.W.: Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl.-Based Syst. 31, 176–182 (2012)CrossRefGoogle Scholar
  24. 24.
    Yu, D.J., Wu, Y.Y., Zhou, W.: Multi-criteria decision making based on choquet integral under hesitant fuzzy environment. J. Comput. Inf. Syst. 12, 4506–4513 (2011)Google Scholar
  25. 25.
    Wei, G.W., Zhao, X.F., Wang, H.J., Lin, R.: Hesitant fuzzy choquet integral aggregation operators and their applications to multiple attribute decision making. Inf. Int. Interdiscip. J. 15, 441–448 (2012)Google Scholar
  26. 26.
    Zhu, B., Xu, Z.S., Xia, M.M.: Hesitant fuzzy geometric Bonferroni means. Inf. Sci. 205, 72–85 (2012)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Zhang, Z.M.: Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Inf. Sci. 234, 150–181 (2013)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Meng, F.Y., Chen, X.H., Zhang, Q.: Generalized hesitant fuzzy generalized shapley-choquet integral operators and their application in decision making. Int. J. Fuzzy Syst. 16, 400–410 (2014)Google Scholar
  29. 29.
    Yu, D.J.: Group decision making under multiplicative hesitant fuzzy environment. Int. J. Fuzzy Syst. 16, 233–241 (2014)Google Scholar
  30. 30.
    Liao, H.C., Xu, Z.S.: A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim. Decis. Mak. 12, 373–392 (2013)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Zhang, N., Wei, G.W.: A multiple criteria hesitant fuzzy decision making with Shapley value-based VIKOR method. J. Intell. Fuzzy Syst. 24, 789–803 (2013)Google Scholar
  32. 32.
    Liao, H.C., Xu, Z.S., Xia, M.M.: Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int. J. Inf. Technol. Decis. Mak. 13, 47–76 (2014)CrossRefGoogle Scholar
  33. 33.
    Liao, H.C., Xu, Z.S.: Satisfaction degree based interactive decision making method under hesitant fuzzy environment with incomplete weights. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 22, 553–572 (2014)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Rodríguez, R.M., Martínez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 1, 109–119 (2012)CrossRefGoogle Scholar
  35. 35.
    Zhu, B., Xu, Z.S.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22, 35–45 (2014)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Pei, Z., Yi, L.: A note on operations of hesitant fuzzy sets. Int. J. Comput. Intell. Syst. 8, 226–239 (2015)CrossRefGoogle Scholar
  37. 37.
    Rodríguez, R.M., Martínez, L., Torra, V., Xu, Z.S., Herrera, F.: Hesitant fuzzy sets: State of the art and future directions. Int. J. Intell. Syst. 29, 495–524 (2014)CrossRefGoogle Scholar
  38. 38.
    Bullen, P.S., Mitrinović, D.S., Vasić, P.M.: Means and Their Inequalities. Reidel, Dordrecht (1988)CrossRefMATHGoogle Scholar
  39. 39.
    Xu, Z.S.: Fuzzy harmonic mean operators. Int. J. Intell. Syst. 24, 152–172 (2009)CrossRefMATHGoogle Scholar
  40. 40.
    Liao, H.C., Xu, Z.S.: Subtraction and division operations over hesitant fuzzy sets. J. Intell. Fuzzy Syst. 27, 65–72 (2014)MathSciNetMATHGoogle Scholar
  41. 41.
    Arrow, K.J.: Social Choice and Individual Values, pp. 1–138. Wiley, New York (1963)Google Scholar
  42. 42.
    Zhou, L.G., Chen, H.Y., Liu, J.P.: Generalized multiple averaging operators and their applications to group decision making. Group Decis. Negot. 22, 331–358 (2013)CrossRefGoogle Scholar
  43. 43.
    Yang, T., Zuo, C.R.: A method of multi-attribute group decision making based on fuzzy distance and evidence theory. Value Eng. 7, 8–11 (2009)Google Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of SciencesPLA University of Science and TechnologyNanjingChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.College of Humanities & Social SciencesNanjing Agricultural UniversityNanjingChina

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