Skip to main content
SpringerLink
Log in

Similarity Measures for Hesitant Fuzzy Sets and Their Extensions

  • Chapter
  • First Online:
Book cover Information Measures for Hesitant Fuzzy Sets and Their Extensions

Part of the book series: Uncertainty and Operations Research ((UOR))

  • 300 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  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. 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)

    Article  Google Scholar 

  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. B. Farhadinia, Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf. Sci. 240, 129–144 (2013)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. 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. 263–271

    Google Scholar 

  11. Z.S. Xu, A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf. Sci. 180, 181–190 (2010)

    Article  Google Scholar 

  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. 272–282

    Google Scholar 

  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. R.R. Yager, Generalized OWA aggregation operators. Fuzzy Optim. Decis. Mak. 3, 93–107 (2004)

    Article  Google Scholar 

  15. B. Farhadinia, Distance and similarity measures for higher order hesitant fuzzy sets. Knowl.-Based Syst. 55, 43–48 (2014)

    Article  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Quchan University of Technology, Quchan, Iran

    Bahram Farhadinia

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

    Zeshui Xu

Authors
  1. Bahram Farhadinia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bahram Farhadinia .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Farhadinia, B., Xu, Z. (2019). Similarity Measures for Hesitant Fuzzy Sets and Their Extensions. In: Information Measures for Hesitant Fuzzy Sets and Their Extensions. Uncertainty and Operations Research. Springer, Singapore. https://doi.org/10.1007/978-981-13-3729-1_3

Download citation

Publish with us

Policies and ethics

Search

Navigation