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Issue:Pearson's coefficient between intuitionistic fuzzy sets

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Title of paper: Pearson's coefficient between intuitionistic fuzzy sets
Author(s):
Eulalia Szmidt
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
szmidt@ibspan.waw.pl
Janusz Kacprzyk
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
kacprzyk@ibspan.waw.pl
Paweł Bujnowski
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
Presented at: 15th ICIFS, Burgas, 11-12 May 2011
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 17 (2011) Number 2, pages 25—34
Download:  PDF (210  Kb, File info)
Abstract: The correlation coefficient (Pearson's [math]\displaystyle{ r }[/math]) is one of the most frequently used tools in statistics. In this paper we discuss a correlation coefficient between Atanassov's intuitionistic fuzzy sets (A-IFSs). We have constructed the coefficient so it provides the strength of the relationship between A-IFSs and also shows if the considered sets are positively or negatively correlated. Next, the proposed correlation coefficient takes into account not only the amount of information related to the A-IFS data (expressed by the membership and non-membership values) but also the reliability of the data expressed by a so-called hesitation margin.
Keywords: Intuitionistic fuzzy sets, Correlation coefficient, Hesitation margin
AMS Classification: 03E72
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. Bustince, H., P. Burillo (1995) Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 74, 237–244.
  4. Bustince, H., V. Mohedano, E. Barrenechea, M. Pagola (2005) Image thresholding using intuitionistic fuzzy sets. In: Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics. (Eds. Atanassov K., Kacprzyk J., Krawczak M., Szmidt E.), EXIT, Warsaw 2005.
  5. Bustince, H., V. Mohedano, E. Barrenechea, M. Pagola (2006) An algorithm for calculating the threshold of an image representing uncertainty through A-IFSs. IPMU’2006, 2383–2390.
  6. Chiang, D-A., N. P. Lin (1999) Correlation of fuzzy sets. Fuzzy Sets and Systems, 102, 221–226.
  7. Gersternkorn, T., J. Manko (1991), Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems 44, 39–43.
  8. Hong, D. H., S. Y. Hwang (1995), Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets and Systems 75, 77–81.
  9. Hong, D. H., S. Y. Hwang (1996), A note on the correlation of fuzzy numbers. Fuzzy Sets and Systems 79, 401–402.
  10. Hung, W. L. (2001) Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. Int. Journal of Uncertainty, Fuzziness and Knowledge-Based systems, 9(4), 509–516.
  11. Hung, W.L., J. W. Wu (2002) Correlation of intuitionistic fuzzy sets by centroid method. Information Sciences 144, 219–225.
  12. Kendler, K.S., J. Parnas (2008) Philosophical Issues in Psychiatry: Explanation, Phenomenology, and Nosology. Johns Hopkins University Press.
  13. Liu, S-T., Ch. Kao (2002) Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems 128, 267–275.
  14. Rodgers, J. L., W. Alan Nicewander (1988) Thirteen Ways to Look at the Correlation Coefficient. The American Statistician, 42(1), 59–66.
  15. Szmidt, E., J. Baldwin (2006) Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. 2006 IEEE World Congress on Computational Intelligence, 237–243.
  16. Szmidt, E., J. Kacprzyk. (1996c) Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on IFS, 2(3), 22–31.
  17. Szmidt, E., J. Kacprzyk. (1997) On measuring distances between intuitionistic fuzzy sets, Notes on IFS, 3(4), 1–13.
  18. Szmidt, E., J. Kacprzyk. (1998) Group Decision Making under Intuitionistic Fuzzy Preference Relations. IPMU’98, 172–178.
  19. Szmidt, E., J. Kacprzyk. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114(3), 505–518.
  20. Szmidt, E., J. Kacprzyk. (2000) On Measures on Consensus Under Intuitionistic Fuzzy Relations. IPMU 2000, 1454–1461.
  21. Szmidt, E., J. Kacprzyk. (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118 (3), 467–477.
  22. Szmidt, E., J. Kacprzyk. (2001) Analysis of Consensus under Intuitionistic Fuzzy Preferences. Proc. Int. Conf. in Fuzzy Logic and Technology. De Montfort Univ. Leicester, UK, 79–82.
  23. Szmidt, E., J. Kacprzyk. (2002a) Analysis of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Preferences. Proc. 9th Int. Conf. IPMU 2002, 1859–1865.
  24. Szmidt, E., J. Kacprzyk. (2002b) An Intuitionistic Fuzzy Set Based 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.
  25. Szmidt, E., J. Kacprzyk. (2002c) An Intuitionistic Fuzzy Set Based 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.
  26. Szmidt, E., J. Kacprzyk. (2006) Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. IEEE IS’06, 716–721.
  27. Szmidt, E., J. Kacprzyk. (2006) An Application of Intuitionistic Fuzzy Set Similarity Measures to a Multi-criteria Decision Making Problem. ICAISC 2006, LNAI 4029, Springer-Verlag, 314–323.
  28. Szmidt, E., J. Kacprzyk. (2007). Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. Applications of Fuzzy Sets Theory. LNAI 4578, 291–297. Springer-Verlag.
  29. Szmidt, E., J. Kacprzyk. (2007a). A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 2007 IEEE Conf. on Fuzzy Systems, 481–486.
  30. Szmidt, E., J. Kacprzyk. (2008) A new approach to ranking alternatives expressed via intuitionistic fuzzy sets. In: D. Ruan et al. (Eds.) Computational Intelligence in Decision and Control. World Scientific, 265–270.
  31. Szmidt, E., J. Kacprzyk. (2009). Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. In: Recent Advances in decision Making, SCI 222. E. Rakus-Andersson, R. Yager, N. Ichalkaranje, L.C. Jain (Eds.), Springer-Verlag, 7–19.
  32. Szmidt, E., J. Kacprzyk. Ranking of Intuitionistic Fuzzy Alternatives in a Multi-criteria Decision Making Problem. In: Proceedings of the conference: NAFIPS 2009, Cincinnati, USA, June 14- 17, 2009, IEEE, ISBN: 978-1-4244-4577-6.
  33. Szmidt, E., M. Kukier (2006) Classification of Imbalanced and Overlapping Classes using Intuitionistic Fuzzy Sets. IEEE IS’06, London, 722-727.
  34. Szmidt, E., M. Kukier (2008) A New Approach to Classification of Imbalanced Classes via Atanassov’s Intuitionistic Fuzzy Sets. In: Hsiao-Fan Wang (Ed.): Intelligent Data Analysis: Developing New Methodologies Through Pattern Discovery and Recovery. Idea Group, 85–101.
  35. Szmidt, E., M. Kukier (2008) Atanassov’s intuitionistic fuzzy sets in classification of imbalanced and overlapping classes. In: Panagiotis Chountas, Ilias Petrounias, Janusz Kacprzyk (Eds.): Intelligent Techniques and Tools for Novel System Architectures. Springer, Berlin Heidelberg 2008, 455–471. Seria: Studies in Computational Intelligence.
  36. Zadeh, L.A. (1965) Fuzzy sets. Information and Control, 8, 338–353.
  37. Zeng, W., H. Li (2007) Correlation coefficient of intuitionistic fuzzy sets. Journal of Industrial Engineering International, 3(5), 33–40.
  38. http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data
  39. http://www.cs.waikato.ac.nz/˜ml/weka/
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