Skip to main content
SpringerLink
Log in

Relationships among Fuzzy Entropy, Similarity Measure and Distance Measure of Intuitionistic Fuzzy Sets

  • Conference paper
Fuzzy Information and Engineering 2010

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 78))

  • 1111 Accesses

Abstract

Fuzzy entropy, similarity measure and distance measure are three important measures of intuitionistic fuzzy sets. Their relationships are studied in this paper through operations between intuitionistic fuzzy sets, and some formulas are given to transform a measure into another. Additionally, some examples are presented to show how to use the formulas above.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
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. Atanassov, K.: Intuititionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Atanassov, K.: Intuitionistic fuzzy sets. In: Sgurev, V. (ed.) VII ITKR’s Session, Sofia (1983)

    Google Scholar 

  4. Xuecheng, L.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems 52, 305–318 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fan, J.L., Xie, W.X.: Distance measure and induced fuzzy entropy. Fuzzy Sets and Systems 104, 305–314 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Zeng, W.Y., Li, H.X.: Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets and Systems 157, 1477–1484 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Zadeh, L.A.: Probability measures of fuzzy events. J. M. M. A. 23, 421–427 (1968)

    MATH  MathSciNet  Google Scholar 

  8. De Luca, A., Termini, S.: A definition of a nonprobabilityes entropy in the setting of fuzzy set theory. Inform. and Control 20, 301–312 (1972)

    Article  MATH  Google Scholar 

  9. Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79, 403–405 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  10. Deschrijver, G., Kerre, E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems 133, 227–235 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Wang, G.J., He, Y.Y.: Intuitionistic fuzzy sets and L-fuzzy sets. Fuzzy Sets and Systems 110, 271–274 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Shang, X.G., Jiang, W.S.: A note on fuzzy information measures. Patterns Recognition Letters 18, 425–432 (1997)

    Article  Google Scholar 

  13. Ghosh, A.: Use of fuzziness measures in layered networks for object extraction: a generalization. Fuzzy Sets and Systems 72, 331–348 (1995)

    Article  Google Scholar 

  14. Pal, S.K.: A note on the quantitative measures of image enhancement though fuzziness. IEEE Trans. Pattern Anal. Machine Intell. 14, 204–208 (1982)

    Article  Google Scholar 

  15. Pal, N.R., Pal, S.K.: Object-background segmentation using new definitions of entropy. IEEE. Proc. 36, 284–295 (1989)

    Google Scholar 

  16. Fan, J.L., Xie, W.X.: Subsethood measure: new definitons. Fuzzy Sets and Systems 106, 201–209 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Pappis, C., Karacapilidis, N.: A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems 56, 171–174 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  18. Lee, H.M., Wang, W.T.: A neural network architecture for classification of fuzzy inputs. Fuzzy Sets and Systems 63, 159–173 (1994)

    Article  Google Scholar 

  19. Sinha, D., Dougherty, E.R.: Fuzzification of set inclusion: theory and applications. Fuzzy Sets and System 55, 15–42 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  20. Cross, V.V., Sudkamp, T.A.: Similarity and Compatibility in Fuzzy Sets Theory. Physica-Verlag, Heidelberg (2002)

    Google Scholar 

  21. Kuncheva, L.I.: Fuzzy rough sets: application to feature selection. Fuzzy Sets and Systems 51, 147–153 (1992)

    Article  MathSciNet  Google Scholar 

  22. Wang, X.Z., De Baets, B., Kerre, E.: A comparative study of similarity measures. Fuzzy Sets and Systems 73, 259–268 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  23. Bustince, H., Buillo, P.: Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 75, 237–244 (1995)

    Article  Google Scholar 

  24. Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  25. Chen, S.M., Tan, J.M.: Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67, 163–172 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  26. Hong, D.H., Choi, C.H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy sets and Systems 114, 103–113 (2000)

    Article  MATH  Google Scholar 

  27. Bustince, H., Buillo, P.: Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 75, 237–244 (1995)

    Article  Google Scholar 

  28. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Systems Science, College of Science, Liaoning Technical University, Fuxin, 123000, China

    Yinchao Lv & Sizong Guo

Authors
  1. Yinchao Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sizong Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Mathematics and Information Science Guangzhou Higher Education Mega Center , Guangzhou University, 230Wai Huan Xi Road, ZIP 510006, Guangdong, China

    Bing-yuan Cao

  2. Shaanxi Normal University, China

    Guo-jun Wang

  3. Institute of Mathematics and Systems Science, Liaoning Technical University , 123000, China

    Si-zong Guo

  4. School of Science, Jimei University , 361021, Xiamen, Fujian, China

    Shui-li Chen

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lv, Y., Guo, S. (2010). Relationships among Fuzzy Entropy, Similarity Measure and Distance Measure of Intuitionistic Fuzzy Sets. In: Cao, By., Wang, Gj., Guo, Sz., Chen, Sl. (eds) Fuzzy Information and Engineering 2010. Advances in Intelligent and Soft Computing, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14880-4_59

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14880-4_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14879-8

  • Online ISBN: 978-3-642-14880-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation