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Similarity Measures for Hesitant Fuzzy Sets and Their Extensions

  • Bahram FarhadiniaEmail author
  • Zeshui Xu
Chapter
Part of the Uncertainty and Operations Research book series (UOR)

Abstract

The similarity measure has become an important tool for a variety of different applications ranging from the clustering analysis, pattern recognition to medical diagnosis. What is remarkable in analysing similarity measures for HFSs is the existing relationships between the axioms for similarity measures and those for distance measures. Indeed, by the help of them, any distance measure formulation can be used to produce its counterpart similarity measure, and vice versa. Due to this close relationship with distance measures, the HFS similarity measures can be naturally applied to many real-world situations where the distance measures of HFSs and their extensions have been applied.

References

  1. 1.
    X.L. Zhang, Z.S. Xu, Novel distance and similarity measures on hesitant fuzzy sets with applications to clustering analysis. J. Intell. Fuzzy Syst. 28, 2279–2296 (2015)Google Scholar
  2. 2.
    F. Jin, Z. Ni, H. Chen, Y. Li, L. Zhou, Multiple attribute group decision making based on interval valued hesitant fuzzy information measures. Comput. Ind. Eng. 101, 103–115 (2016)CrossRefGoogle Scholar
  3. 3.
    P. Singh, Distance and similarity measures for multiple-attribute decision making with dual hesitant fuzzy sets. Comput. Appl. Math. 36, 1–16 (2015)Google Scholar
  4. 4.
    B. Farhadinia, Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf. Sci. 240, 129–144 (2013)CrossRefGoogle Scholar
  5. 5.
    H.C. Liao, Z.S. Xu, X.J. Zeng, Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf. Sci. 271, 125–142 (2014)CrossRefGoogle Scholar
  6. 6.
    D.F. Li, C.T. Cheng, New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit. Lett. 23, 221–225 (2002)CrossRefGoogle Scholar
  7. 7.
    M.S. Yang, D.C. Lin, On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput. Math. Appl. 57, 896–907 (2009)CrossRefGoogle Scholar
  8. 8.
    T.J. Wang, Z.D. Lu, F. Li, Bidirectional approximate reasoning based on weighted similarity measures of vague sets. J. Comput. Eng. Sci. 24, 96–100 (2002)Google Scholar
  9. 9.
    S.K. Pal, R.A. King, Image enhancement using smoothing with fuzzy sets. IEEE Trans. Syst. Man Cybern. 11, 495–501 (1981)Google Scholar
  10. 10.
    E. Szmidt, J. Kacprzyk, Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis, in ICCS 2001, ed. by V.N. Alexandrov, J. Dongarra, B.A. Juliano, R.S. Renner, C.J.K. Tan. LNCS, 2074 (Springer, Heidelberg, 2001), pp. 263–271Google Scholar
  11. 11.
    Z.S. Xu, A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf. Sci. 180, 181–190 (2010)CrossRefGoogle Scholar
  12. 12.
    E. Szmidt, J. Kacprzyk, A new concept of a similarity measure for intuitionistic fuzzy sets and its use in group decision making, in Modelling Decision for Artificial Intelligence, LNAI, vol. 3558, ed. by V. Torra, Y. Narukawa, S. Miyamoto (Springer, 2005), pp. 272–282Google Scholar
  13. 13.
    G. Wei, R. Lin, H. Wang, Distance and similarity measures for hesitant interval-valued fuzzy sets. J. Intell. Fuzzy Syst. 27, 19–36 (2014)Google Scholar
  14. 14.
    R.R. Yager, Generalized OWA aggregation operators. Fuzzy Optim. Decis. Mak. 3, 93–107 (2004)CrossRefGoogle Scholar
  15. 15.
    B. Farhadinia, Distance and similarity measures for higher order hesitant fuzzy sets. Knowl.-Based Syst. 55, 43–48 (2014)CrossRefGoogle Scholar
  16. 16.
    B. Farhadinia, Z.S. Xu, Novel hesitant fuzzy linguistic entropy and cross-entropy measures in multiple criteria decision making. Appl. Intell. 1–13 (2018)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Quchan University of TechnologyQuchanIran
  2. 2.Business SchoolSichuan UniversityChengduChina

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