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:
|
Conference proceedings, "Notes on IFS", Volume 17 (2011) Number 2, pages 25—34
|
Download:
|
PDF (210 Kb, File info)
|
Abstract:
|
We address the problem of assessing information and knowledge conveyed by an Atanassov's intuitionistic fuzzy set (A-IFS for short). We pay particular attention to the relationship between positive and negative knowledge (expressed by entropy which may be seen as a dual measure to information), and take into account also reliability of the information expressed by the hesitation margin.
|
Keywords:
|
Intuitionistic fuzzy sets, amount of information, entropy, hesitation margin.
|
References:
|
- Atanassov, K. (1983) Intuitionistic fuzzy sets. VII ITKR Session. Sofia (Centr. Sci.-Techn. Libr. of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
- Atanassov, K. (1999), Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag.
- Bustince, H., P. Burillo (1995) Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 74, 237–244.
- 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.
- 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.
- Chiang, D-A., N. P. Lin (1999) Correlation of fuzzy sets. Fuzzy Sets and Systems, 102, 221–226.
- Gersternkorn, T., J. Manko (1991), Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems 44, 39–43.
- Hong, D. H., S. Y. Hwang (1995), Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets and Systems 75, 77–81.
- Hong, D. H., S. Y. Hwang (1996), A note on the correlation of fuzzy numbers. Fuzzy Sets and Systems 79, 401–402.
- 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.
- Hung, W.L., J. W. Wu (2002) Correlation of intuitionistic fuzzy sets by centroid method. Information Sciences 144, 219–225.
- Kendler, K.S., J. Parnas (2008) Philosophical Issues in Psychiatry: Explanation, Phenomenology, and Nosology. Johns Hopkins University Press.
- Liu, S-T., Ch. Kao (2002) Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems 128, 267–275.
- Rodgers, J. L., W. Alan Nicewander (1988) Thirteen Ways to Look at the Correlation Coefficient. The American Statistician, 42(1), 59–66.
- 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.
- Szmidt, E., J. Kacprzyk. (1996c) Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on IFS, 2(3), 22–31.
- Szmidt, E., J. Kacprzyk. (1997) On measuring distances between intuitionistic fuzzy sets, Notes on IFS, 3(4), 1–13.
- Szmidt, E., J. Kacprzyk. (1998) Group Decision Making under Intuitionistic Fuzzy Preference Relations. IPMU’98, 172–178.
- Szmidt, E., J. Kacprzyk. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114(3), 505–518.
- Szmidt, E., J. Kacprzyk. (2000) On Measures on Consensus Under Intuitionistic Fuzzy Relations. IPMU 2000, 1454–1461.
- Szmidt, E., J. Kacprzyk. (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118 (3), 467–477.
- 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.
- 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.
- 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.
- 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.
- Szmidt, E., J. Kacprzyk. (2006) Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. IEEE IS’06, 716–721.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Szmidt, E., M. Kukier (2006) Classification of Imbalanced and Overlapping Classes using Intuitionistic Fuzzy Sets. IEEE IS’06, London, 722-727.
- 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.
- 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.
- Zadeh, L.A. (1965) Fuzzy sets. Information and Control, 8, 338–353.
- Zeng, W., H. Li (2007) Correlation coefficient of intuitionistic fuzzy sets. Journal of Industrial Engineering International, 3(5), 33–40.
- http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data
- http://www.cs.waikato.ac.nz/˜ml/weka/
|
Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|