Measuring the Amount of Knowledge for Atanassov’s Intuitionistic Fuzzy Sets

  • Eulalia Szmidt
  • Janusz Kacprzyk
  • Paweł Bujnowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6857)

Abstract

We address the problem of how to measure amount of knowledge conveyed by an Atanassov’s intuitionistic fuzzy set (A-IFS for short). The problem is useful from the point of view of a specific purpose, notably related to decision making. An amount of knowledge is strongly linked to its related amount of information. We pay particular attention to the relationship between the positive and negative information and a lack of information expressed by the hesitation margin.

Keywords

Negative Information Entropy Measure Informative Attribute Imprecise Information Saturday Morning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Atanassov, K.: Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia (Deposed in Centr. Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (1983) (in Bulgarian)Google Scholar
  2. 2.
    Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  3. 3.
    Atanassov, K., Tasseva, V., Szmidt, E., Kacprzyk, J.: On the geometrical interpretations of the intuitionistic fuzzy sets. In: Atanassov, K., Kacprzyk, J., Krawczak, M., Szmidt, E. (eds.) Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics. EXIT, Warsaw (2005)Google Scholar
  4. 4.
    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
  5. 5.
    Bustince, H., Mohedano, V., Barrenechea, E., Pagola, M.: Image thresholding using intuitionistic fuzzy sets. In: Atanassov, K., Kacprzyk, J., Krawczak, M., Szmidt, E. (eds.) Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics. EXIT, Warsaw (2005)Google Scholar
  6. 6.
    De Luca, A., Termini, S.: A definition of a non-probabilistic entropy in the setting of fuzzy sets theory. Inform. And Control 20, 301–312 (1972)CrossRefMATHGoogle Scholar
  7. 7.
    Narukawa, Y., Torra, V.: Non-monotonic fuzzy measure and intuitionistic fuzzy set. In: Torra, V., Narukawa, Y., Valls, A., Domingo-Ferrer, J. (eds.) MDAI 2006. LNCS (LNAI), vol. 3885, pp. 150–160. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Quinlan, J.R.: Induction of decision trees. Machine Learning 1, 81–106 (1986)Google Scholar
  9. 9.
    Stewart, T.: Wealth of Knowledge, Doubleday, New York (2001)Google Scholar
  10. 10.
    Szmidt, E., Baldwin, J.: New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes on IFSs 9(3), 60–76 (2003)MathSciNetMATHGoogle Scholar
  11. 11.
    Szmidt, E., Baldwin, J.: Entropy for intuitionistic fuzzy set theory and mass assignment theory. Notes on IFSs 10(3), 15–28 (2004)Google Scholar
  12. 12.
    Szmidt, E., Baldwin, J.: Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. IEEE World Congress on Computational Intelligence, 237–243 (2006)Google Scholar
  13. 13.
    Szmidt, E., Kacprzyk, J.: On measuring distances between intuitionistic fuzzy sets. Notes on IFS 3(4), 1–13 (1997)MathSciNetMATHGoogle Scholar
  14. 14.
    Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114(3), 505–518 (2000)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Szmidt, E., Kacprzyk, J.: Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. In: IPMU 2004, pp. 1405–1412 (2004)Google Scholar
  17. 17.
    Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets: straightforward approaches may not work. In: 3rd International IEEE Conference Intelligent Systems IS 2006, London, pp. 716–721 (2006)Google Scholar
  18. 18.
    Szmidt, E., Kreinovich, V.: Symmetry between true, false, and uncertain: An explanation. Notes on IFS 15(4), 1–8 (2009)MATHGoogle Scholar
  19. 19.
    Szmidt, E., Kukier, M.: Classification of imbalanced and overlapping classes using intuitionistic fuzzy sets. In: 3rd International IEEE Conference Intelligent Systems IS 2006, London, pp. 722–727 (2006)Google Scholar
  20. 20.
    Szmidt, E., Kacprzyk, J.: Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. In: Masulli, F., Mitra, S., Pasi, G. (eds.) WILF 2007. LNCS (LNAI), vol. 4578, pp. 291–297. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  21. 21.
    Szmidt, E., Kacprzyk, J.: A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. In: IEEE Conf. on Fuzzy Systems, pp. 481–486 (2007a)Google Scholar
  22. 22.
    Szmidt, E., Kacprzyk, J.: A new approach to ranking alternatives expressed via intuitionistic fuzzy sets. In: Ruan, D., et al. (eds.) Computational Intelligence in Decision and Control, pp. 265–270. World Scientific, Singapore (2008)CrossRefGoogle Scholar
  23. 23.
    Szmidt, E., Kacprzyk, J.: Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. In: Rakus-Andersson, E., Yager, R., Ichalkaranje, N., Jain, L.C. (eds.) Recent Advances in Decision Making. SCI, vol. 222, pp. 7–19. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Szmidt, E., Kacprzyk, J.: Dealing with typical values via Atanassov’s intuitionistic fuzzy sets. Int. J. of General Systems 39(5), 489–506 (2010)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    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. 65–102. Idea Group, USA (2008)Google Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inform. Sciences 8, 199–249 (1975)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Eulalia Szmidt
    • 1
    • 2
  • Janusz Kacprzyk
    • 1
    • 2
  • Paweł Bujnowski
    • 1
    • 2
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Warsaw School of Information TechnologyWarsawPoland

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