Skip to main content

Modified Cosine Similarity Measure between Intuitionistic Fuzzy Sets

  • Conference paper
Artificial Intelligence and Computational Intelligence (AICI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7530))

Abstract

Similarity of intuitionistic fuzzy sets (IFSs) is an important measure to indicate the similarity degree between IFSs. Recently, Ye (2011) proposed a similarity measure between IFSs based on the cosine concept. Although this cosine similarity measure has good concept and merit, the measure is not satisfied the definition of a similarity between IFSs and not presented well for analyzing IFS data. In this paper, we modify the cosine similarity measure between IFSs. This modified similarity measure between IFSs is not only to satisfy the definition of a similarity between IFSs, but also to improve the efficiency of the Ye’s measure. An example is used to demonstrate this phenomenon.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–356 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Atanassov, K.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg (1999)

    MATH  Google Scholar 

  4. Atanassov, K., Georgeiv, G.: Intuitionistic Fuzzy Prolog. Fuzzy Sets and Systems 53, 121–128 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pankowska, A., Wygralak, M.: General IF-Sets with Triangular Norms and Their Applications to Group Decision Making. Information Sciences 176, 2713–2754 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. De, S.K., Biswas, R., Roy, A.R.: An Application of Intuitionistic Fuzzy Sets in Medical Diagnosis. Fuzzy Sets and Systems 117, 209–213 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hung, W.L., Yang, M.S.: On the J-Divergence of Intuitionistic Fuzzy Sets with Its Application to Pattern Recognition. Information Sciences 178, 1641–1650 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dengfeng, L., Chuntian, C.: New Similarity Measures of Intuitionistic Fuzzy Sets and Application to Pattern Recognition. Pattern Recognition Letters 23, 221–225 (2002)

    Article  MATH  Google Scholar 

  9. Liang, Z., Shi, P.: Similarity Measures on Intuitionistic Fuzzy Sets. Pattern Recognition Letters 24, 2687–2693 (2003)

    Article  MATH  Google Scholar 

  10. Mitchell, H.B.: On the Dengfeng-Chuntian Similarity Measure and Its Application to Pattern Recognition. Pattern Recognition Letters 24, 3101–3104 (2003)

    Article  Google Scholar 

  11. Hung, W.L., Yang, M.S.: Similarity Measures of Intuitionistic Fuzzy Sets Based on Hausdorff Distance. Pattern Recognition Letters 25, 1603–1611 (2004)

    Article  Google Scholar 

  12. Xu, Z.S., Chen, J.: An Overview of Distance and Similarity Measures of Intuitionistic Fuzzy Sets. International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems 16, 529–555 (2008)

    Article  MATH  Google Scholar 

  13. Ye, J.: Cosine Similarity Measures for Intuitionistic Fuzzy Sets and Their Applications. Mathematical and Computer Modelling 53, 91–97 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Li, Y., Olson, D.L., Qin, Z.: Similarity Measures between Intuitionistic Fuzzy (Vague) Sets: A Comparative Analysis. Pattern Recognition Letters 28, 2687–2693 (2007)

    Google Scholar 

  15. Chen, S.M.: Measures of Similarity between Vague Sets. Fuzzy Sets and Systems 74, 217–223 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hong, D.H., Kim, C.: A Note on Similarity Measures between Vague Sets and between Elements. Information Science 115, 83–96 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hwang, CM., Yang, MS. (2012). Modified Cosine Similarity Measure between Intuitionistic Fuzzy Sets. In: Lei, J., Wang, F.L., Deng, H., Miao, D. (eds) Artificial Intelligence and Computational Intelligence. AICI 2012. Lecture Notes in Computer Science(), vol 7530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33478-8_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33478-8_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33477-1

  • Online ISBN: 978-3-642-33478-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics