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

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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.

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References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 343–349 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15, 1179–1187 (2007)

    Article  Google Scholar 

  5. Xu, Z.S.: Intuitionistic preference relations and their application in group decision making. Inf. Sci. 177, 2363–2379 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Xu, Z.S., Cai, X.Q.: Intuitionistic Fuzzy Information Aggregation: Theory and Applications. Science Press/Springer, Beijing/Berlin (2012)

    Book  MATH  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  10. Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type 2. Inf. Control 31, 312–340 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dubois, D., Prade, H.: Fuzzy Sets and Systems-Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  12. Yager, R.R.: On the theory of bags. Int. J. General Syst. 13, 23–37 (1986)

    Article  MathSciNet  Google Scholar 

  13. Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets Syst. 158, 2429–2442 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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)

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

    MATH  Google Scholar 

  16. Xu, Z.S., Xia, M.M.: Distance and similarity measures for hesitant fuzzy sets. Inf. Sci. 181, 2128–2138 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Xu, Z.S., Xia, M.M.: On distance and correlation measures of hesitant fuzzy information. Int. J. Intell. Syst. 26, 410–425 (2011)

    Article  MATH  Google Scholar 

  18. Peng, D.H., Gao, C.Y., Gao, Z.F.: Generalized hesitant fuzzy synergetic weighted distance measures. Appl. Math. Model. 37, 5837–5850 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  21. Xia, M.M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision making. Int. J. Approx. Reason. 52, 395–407 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  23. Wei, G.W.: Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl.-Based Syst. 31, 176–182 (2012)

    Article  Google Scholar 

  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. 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. Zhu, B., Xu, Z.S., Xia, M.M.: Hesitant fuzzy geometric Bonferroni means. Inf. Sci. 205, 72–85 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhang, Z.M.: Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Inf. Sci. 234, 150–181 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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. Yu, D.J.: Group decision making under multiplicative hesitant fuzzy environment. Int. J. Fuzzy Syst. 16, 233–241 (2014)

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  34. Rodríguez, R.M., Martínez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 1, 109–119 (2012)

    Article  Google Scholar 

  35. Zhu, B., Xu, Z.S.: Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans. Fuzzy Syst. 22, 35–45 (2014)

    Article  MathSciNet  Google Scholar 

  36. Pei, Z., Yi, L.: A note on operations of hesitant fuzzy sets. Int. J. Comput. Intell. Syst. 8, 226–239 (2015)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  38. Bullen, P.S., Mitrinović, D.S., Vasić, P.M.: Means and Their Inequalities. Reidel, Dordrecht (1988)

    Book  MATH  Google Scholar 

  39. Xu, Z.S.: Fuzzy harmonic mean operators. Int. J. Intell. Syst. 24, 152–172 (2009)

    Article  MATH  Google Scholar 

  40. Liao, H.C., Xu, Z.S.: Subtraction and division operations over hesitant fuzzy sets. J. Intell. Fuzzy Syst. 27, 65–72 (2014)

    MathSciNet  MATH  Google Scholar 

  41. Arrow, K.J.: Social Choice and Individual Values, pp. 1–138. Wiley, New York (1963)

    Google Scholar 

  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)

    Article  Google Scholar 

  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 

Download references

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).

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Authors and Affiliations

  1. Institute of Sciences, PLA University of Science and Technology, Nanjing, 210007, China

    Hua Zhao

  2. Business School, Sichuan University, Chengdu, 610064, Sichuan, China

    Zeshui Xu

  3. College of Humanities & Social Sciences, Nanjing Agricultural University, Nanjing, 210095, China

    Feng Cui

Authors
  1. Hua Zhao
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  2. Zeshui Xu
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  3. Feng Cui
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Corresponding author

Correspondence to Feng Cui.

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Zhao, H., Xu, Z. & Cui, F. Generalized Hesitant Fuzzy Harmonic Mean Operators and Their Applications in Group Decision Making. Int. J. Fuzzy Syst. 18, 685–696 (2016). https://doi.org/10.1007/s40815-015-0099-z

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  • DOI: https://doi.org/10.1007/s40815-015-0099-z

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