Skip to main content

Attribute Selection for Atanassov’s Intuitionistic Fuzzy Sets by the Three Term Attribute Description

  • Conference paper
  • First Online:
Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives (IWIFSGN 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1081))

  • 263 Accesses

Abstract

This paper is a continuation of our previous considerations on attribute selection while a data set is expressed via Atanassov’s intuitionistic fuzzy sets (IFSs). The main goal is the dimension reduction for sets of data represented as the IFSs. We propose a simple, yet powerful algorithm which makes use of the three term attribute description. Next, we provide an illustrative example using the real Income data set and analyze in detail the results obtained by a new algorithm. The results are compared with other results from the literature, and the results are promising.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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

References

  1. Atanassov, K.: Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia (Centr. Sci.-Techn. Libr. of Bulg. Acad. of Sci., 1697/84) (1983). (in Bulgarian)

    Google Scholar 

  2. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg (1999)

    Book  Google Scholar 

  3. Atanassov, K.T.: On Intuitionistic Fuzzy Sets Theory. Springer, Heidelberg (2012)

    Book  Google Scholar 

  4. Atanassova, V.: Strategies for decision making in the conditions of intuitionistic fuzziness. In: International Conference 8th Fuzzy Days, Dortmund, Germany, pp. 263–269 (2004)

    Google Scholar 

  5. Baldwin, J.F., Lawry, J., Martin, T.P.: The application of generalized fuzzy rules to machine learning and automated knowledge discovery. Int. J. Uncertainty Fuzzyness Knowl.-Based Syst. 6(5), 459–487 (1998)

    Article  Google Scholar 

  6. Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)

    Article  Google Scholar 

  7. Bujnowski, P., Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy decision trees - a new approach. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., urada, J. (eds.) Artificial Intelligence and Soft Computing, Part I, pp. 181-192. Springer, Switzerland (2014)

    Google Scholar 

  8. Bustince, H., Mohedano, V., Barrenechea, E., Pagola, M.: An algorithm for calculating the threshold of an image representing uncertainty through A-IFSs. In: IPMU 2006, pp. 2383–2390 (2006)

    Google Scholar 

  9. Hand, D.J., Till, R.J.: A simple generalization of the area under the ROC curve for multiple class classification problems. Mach. Learn. 45, 171–186 (2001)

    Article  Google Scholar 

  10. Jackson, J.E.: A User’s Guide to Principal Components. Wiley, New York (1991)

    Book  Google Scholar 

  11. Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (1986)

    Book  Google Scholar 

  12. Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  13. Landwehr, N., Hall, M., Frank, E.: Logistic model trees. Mach. Learn. 95(1–2), 161–205 (2005)

    Article  Google Scholar 

  14. Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis, Probability and Mathematical Statistics. Academic Press, Cambridge (1995)

    Google Scholar 

  15. Roeva, O., Michalikova, A.: Generalized net model of intuitionistic fuzzy logic control of genetic algorithm parameters. In: Notes on Intuitionistic Fuzzy Sets, vol. 19, no. 2, pp. 71–76. Academic Publishing House, Sofia (2013). ISSN 1310-4926

    Google Scholar 

  16. Szmidt, E.: Distances and Similarities in Intuitionistic Fuzzy Sets. Springer, Heidelberg (2014)

    Book  Google Scholar 

  17. Szmidt, E., Baldwin, J.: Intuitionistic fuzzy set functions, mass assignment theory, possibility theory and histograms. IEEE World Congr. Comput. Intell. 2006, 237–243 (2006)

    Google Scholar 

  18. Szmidt, E., Kacprzyk, J.: On measuring distances between intuitionistic fuzzy sets. Notes IFS 3(4), 1–13 (1997)

    MathSciNet  MATH  Google Scholar 

  19. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114(3), 505–518 (2000)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets: straightforward approaches may not work. In: IEEE IS 2006, pp. 716–721 (2006)

    Google Scholar 

  22. Szmidt, E., Kacprzyk, J.: Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. In: Applications of Fuzzy Sets Theory, LNAI, vol. 4578, pp. 291–297. Springer, Heidelberg (2007)

    Google Scholar 

  23. Szmidt, E., Kacprzyk, J.: A new similarity measure for intuitionistic fuzzy sets: straightforward approaches may not work. In: 2007 IEEE Conference on Fuzzy Systems, pp. 481–486 (2007a)

    Google Scholar 

  24. Szmidt, E., Kacprzyk, J.: A new approach to principal component analysis for intuitionistic fuzzy data sets. In: Greco, S., et al. (eds.) IPMU 2012, Part II, CCIS, vol. 298, pp. 529–538. Springer, Heidelberg (2012)

    Google Scholar 

  25. Szmidt, E., Kukier, M.: Classification of imbalanced and overlapping classes using intuitionistic fuzzy sets. In: IEEE IS 2006, London, pp. 722–727 (2006)

    Google Scholar 

  26. Szmidt, E., Kukier, M.: A new approach to classification of imbalanced classes via Atanassov’s intuitionistic fuzzy sets. In: Wang, H.F. (ed.) Intelligent Data Analysis: Developing New Methodologies Through Pattern Discovery and Recovery, pp. 85–101. Idea Group (2008)

    Google Scholar 

  27. Szmidt, E., Kukier, M.: Atanassov’s intuitionistic fuzzy sets in classification of imbalanced and overlapping classes. In: Chountas, P., Petrounias, I., Kacprzyk, J. (eds.) Intelligent Techniques and Tools for Novel System Architectures, pp. 455–471. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  28. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eulalia Szmidt .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Szmidt, E., Kacprzyk, J., Bujnowski, P. (2021). Attribute Selection for Atanassov’s Intuitionistic Fuzzy Sets by the Three Term Attribute Description. In: Atanassov, K., et al. Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives. IWIFSGN 2018. Advances in Intelligent Systems and Computing, vol 1081. Springer, Cham. https://doi.org/10.1007/978-3-030-47024-1_10

Download citation

Publish with us

Policies and ethics