Advertisement

Some New Distance Measures for Generalized Hesitant Fuzzy Sets

  • Chen BinEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

Abstract

Distance and similarity measures are very important topics in fuzzy set theory. In this paper, we propose some new distance measures for generalized hesitant fuzzy sets. We investigate the connections of the aforementioned distance measures and further develop a number of generalized hesitant ordered weighted distance measures.

Keywords

Fuzzy set Generalized hesitant fuzzy set Distance measure 

Notes

Acknowledgment

This paper is supported by the Project of Shandong Province Higher Educational Science and Technology Program 2016 (J16LI08).

References

  1. 1.
    Xu, Z.S., Xia, M.M.: Distance and similarity measures for hesitant fuzzy sets. Inf. Sci. 181(11), 2128–2138 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Xu, Z.S., Xia, M.M.: On distance and correlation measures of hesitant fuzzy information. Int. J. Intell. Syst. 26(5), 410–425 (2011)CrossRefGoogle Scholar
  3. 3.
    Farhadinia, B.: Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inform. Sci. 240, 129–144 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chen, N., Xu, Z., Xia, M.: Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl. Math. Model. 37(4), 2197–2211 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bedregal, B., Reiser, R., Bustince, H., Lopez-Molina, C., Torra, V.: Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms. Inform. Sci. 255, 82–99 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Qian, G., Wanga, H., Feng, X.: Generalized hesitant fuzzy sets and their application in decision support system. Knowl.-Based Syst. 37, 357–365 (2013)CrossRefGoogle Scholar
  7. 7.
    Li, D.F., Cheng, C.T.: New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recogn. Lett. 23, 221–225 (2002)CrossRefGoogle Scholar
  8. 8.
    Yang, M.S., Lin, D.C.: On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput. Math. Appl. 57, 896–907 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Wang, T.J., Lu, Z.D., Li, F.: Bidirectional approximate reasoning based on weighted similarity measures of vague sets. J. Comput. Eng. Sci. 24, 96–100 (2002)Google Scholar
  10. 10.
    Pal, S.K., King, R.A.: Image enhancement using smoothing with fuzzy sets. IEEE Trans. Syst. Man Cybern. 11, 495–501 (1981)Google Scholar
  11. 11.
    Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis. In: Alexandrov, V.N., Dongarra, J., Juliano, B.A., Renner, R.S., Tan, C.J.K. (eds.) ICCS 2001. LNCS, vol. 2074, pp. 263–271. Springer, Heidelberg (2001)Google Scholar
  12. 12.
    Xu, Z.S.: A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf. Sci. 180, 181–190 (2010)CrossRefGoogle Scholar
  13. 13.
    Liang, Z.Z., Shi, P.F.: Similarity measures on intuitionistic fuzzy sets. Pattern Recogn. Lett. 24, 2687–2693 (2003)CrossRefGoogle Scholar
  14. 14.
    Mitchell, H.B.: On the Dengfeng-Chuntian similarity measure and its application to pattern recognition. Pattern Recogn. Lett. 24, 3101–3104 (2003)CrossRefGoogle Scholar
  15. 15.
    Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114, 505–518 (2000)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Wang, W.Q., Xin, X.L.: Distance measure between intuitionistic fuzzy sets. Pattern Recogn. Lett. 26, 2063–2069 (2005)CrossRefGoogle Scholar
  17. 17.
    Hung, W.L., Yang, M.S.: Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recogn. Lett. 25, 1603–1611 (2004)CrossRefGoogle Scholar
  18. 18.
    Bin, C.: Distance and similarity measures for generalized hesitant fuzzy soft sets. In: Advances in Computational Science and Computing. ISCSC 2018. Advances in Intelligent Systems and Computing, vol. 877, pp. 396–403. Springer (2019)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of JinanJinanChina

Personalised recommendations