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Issue:Two- and three-parameter representation of intuitionistic fuzzy sets in the context of entropy and similarity

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Title of paper: Two- and three-parameter representation of intuitionistic fuzzy sets in the context of entropy and similarity
Author(s):
Eulalia Szmidt
Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, OL-447 Warsaw, Poland
szmidt@ibspan.waw.pl
Janusz Kacprzyk
Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, OL-447 Warsaw, Poland
kacprzyk@ibspan.waw.pl
Presented at: 11th ICIFS, Sofia, Bulgaria, 28-30 April 2007
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 13 (2007) Number 2, pages 8—17
Download:  PDF (193  Kb, File info)
Abstract: This paper is a continuation of our previous papers on entropy and similarity of the Atanassov intuitionistic fuzzy sets (A-IFSs, for short). We discuss the usefulness of taking into account all three functions (membership, non-membership and hesitation margin) describing A-IFSs while considering the entropy and similarity measures. We demonstrate on the examples that the omitting of the hesitation margins in both entropy and similarity measures considered leads sometimes to the counterintuitive results.
Keywords: Intuitionistic fuzzy sets, Entropy, Similarity
References:
  1. Atanassov K. (1983), Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia (Centr. Sci.-Techn. Libr. of Bulg.Acad. of Sci., 1697/84) (in Bulgarian).
  2. Atanassov K. (1999), Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag.
  3. Bouchon-Meunier B., Rifgi M., and Bothorel S. (1996). General measures of comparison of objects. Fuzzy Sets and Systems, Vol. 84, No. 2, 143—153.
  4. Chen S., Yeh M. and Hsiao P. (1995). A comparison of similarity measures of fuzzy values. Fuzzy Sets and Systems, Vol. 72, No. 1, 79—89.
  5. Cross V. and Sudkamp T. (2002) Similarity and Compatibility in Fuzzy Set Theory. Assessment and Applications.(Series: Studies in Fuzziness and Soft Computing). Physica-Verlag.
  6. Burillo P. and Bustince H. (1996). Entropy of intuitionistic fuzzy sets and on interval-valued fuzzy sets.Fuzzy Sets and Systems, 78, 305—316.
  7. Dengfeng L. and Chuntian C. (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, Vol. 23, 221-225.
  8. Higashi M. and Klir G. (1982). On measures of fuzziness and fuzzy complements. Int. J. Gen. Syst., 8,169—180.
  9. De Luca A. and Termini S. (1972). A definition of a non-probabilistic entropy in the setting of fuzzy sets theory. Inform. and Control, 20, 301—312.
  10. Fan J. and W. Xie (1999). Distance measure and induced fuzzy entropy. Fuzzy Sets and Systems, 104,305—314.
  11. Fan J-L., Ma Y-L. and Xie W-X. (2001). On some properties of distance measures. Fuzzy Sets and Systems,117, 355—361.
  12. Fan J-L. and Ma Y-L. (2002). Some new fuzzy entropy formulas. Fuzzy Sets and Systems, 128, 277—284.
  13. Hu Q. and Yu D. (2004). Entropies of fuzzy indiscernibility relation and its operations. Int. J. of Uncertainty,Knowledge-Based Systems, 12 (5), 575—589.
  14. Hung W-L. (2003). A note on entropy of intuitionistic fuzzy sets. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 11 (5), 627—633.
  15. Kosko B. (1986) Fuzzy entropy and conditioning. Inform. Sciences, 40, 165—174.
  16. Pal N.R. and Bezdek J.C. (1994). Measuring fuzzy uncertainty. IEEE Trans. on Fuzzy Systems, 2 (2),107—118.
  17. Pal N.R. and Pal S.K. (1991). Entropy: a new definition and its applications. IEEE Trans. on Systems, Man,and Cybernetics, 21 (5), 1260—1270.
  18. Pappis C., and Karacapilidis N. (1993). A comparative assessment of measures of similarity of fuzzy values.Fuzzy Sets and Systems, Vol. 56, 171—174.
  19. Szmidt E. and Baldwin J. (2003) New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes on IFSs, 9 (3), 60—76.
  20. Szmidt E. and Baldwin J. (2004) Entropy for intuitionistic fuzzy set theory and mass assignment theory.Notes on IFSs, 10, 3, 15-28.
  21. Szmidt E. and Kacprzyk J. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114(3), 505—518.
  22. Szmidt E. and Kacprzyk J. (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118 (3),467—477.
  23. Szmidt E. and Kacprzyk J. (2002). An Intuitionistic Fuzzy Set Base Approach to Intelligent Data Analysis(an application to medical diagnosis). In A. Abraham, L. Jain, J. Kacprzyk (Eds.): Recent Advances in Intelligent Paradigms and Applications. Springer-Verlag, 57—70.
  24. Szmidt E. and Kacprzyk J. (2004) Similarity of intuitionistic fuzzy sets and the Jaccard coeHcient. IPMU2004, 1405—1412.
  25. Szmidt E., Kacprzyk J. (2004) A Concept of Similarity for Intuitionistic Fuzzy Sets and its use in Group Decision Making. 2004 IEEE Conf. on Fuzzy Systems, Budapest, 1129—1134.
  26. Szmidt E. and Kacprzyk J. (2005) A New Concept of a Similarity Measure for Intuitionistic Fuzzy Sets and its Use in Group Decision Making. In V. Torra, Y. Narukawa, S. Miyamoto (Eds.): Modelling Decisions for AI. LNAI 3558, Springer 2005, 272—282.
  27. Szmidt E. and Kacprzyk J. (2006) Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 3rd Int. IEEE Conf. ”Intelligent Systems”, 716—721.
  28. Szmidt E. and Kacprzyk J. (2006) Entropy and similarity of intuitionistic fuzzy sets. IPMU 2006, 2375—2382.
  29. Szmidt E. and Kacprzyk J. A new similarity measure for intuitionistic fuzzy sets: straightforward approaches may not work. Submitted.
  30. Tasseva V., Szmidt E. and Kacprzyk J. (2005) On one of the geometrical interpretations of the intuitionistic fuzzy sets. Notes on IFSs, 11 (3), 21—27.
  31. Veltkamp R.C. (2001) Shape matching: similarity measures and algorithms. Proc. Shape Modelling International,Genova, Italy, IEEE Press, 188—197.
  32. Vlachos I.K. and Sergiadis G.D. (2007) The Role of Entropy in Intuitionistic Fuzzy Contrast Enhancement.Accepted.
  33. Tversky A. (1977). Features of similarity. Psychol. Rev., 84, 327—352.
  34. Wang X., De Baets B., and Kerre E. (1995). A comparative study of similarity measures. Fuzzy Sets and Systems, 73 (2), 259—268.
  35. Yager R.R. (1997). On measures of fuzziness and negation. Part I: Membership in the unit interval. Int. J.Gen. Syst., 5, 221—229.
  36. Zadeh L.A. (1965). Fuzzy sets. Information and Control, 8, 338—353.
  37. Zeng W. and H. Li (2006) Relationship between similarity measure and entropy of interval valued fuzzy sets.Fuzzy Sets and Systems 157, 1477—1484.
  38. Zwick R., Carlstein E., Budescu D. (1987). Measures of similarity among fuzzy concepts: A comparative analysis. Int. J. of Approx. Reasoning, 1, 221—242.
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