| Title of paper:
|
On some issues related to the distances between the Atanassov intuitionistic fuzzy sets are described on universe with weights
|
| Author(s):
|
| Radoslav Tzvetkov
|
| Technical University of Sofia, Kliment Ohridski St. 8, Sofia-1000, Bulgaria
|
| rado_tzv8@hotmail.com
|
| 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
|
|
| Presented at:
|
14th ICIFS, Sofia, 15-16 May 2010
|
| Published in:
|
Conference proceedings, "Notes on IFS", Volume 16 (2010) Number 2, pages 22—30
|
| Download:
|
 PDF (63 Kb, Info)
|
| Abstract:
|
This paper is a continuation of our previous works on the concepts and properties of distances between the Atanassov intuitionistic fuzzy sets (A-IFSs, for short). We remind the necessity of taking into account all three terms (membership, non-membership and hesitation margin) describing A-IFSs while considering the distances that provides a foundation of our works. Next, we show that the considered three term continuous Hamming distance is the counterpart of the discrete Hamming distance, and is a metric.
|
| Keywords:
|
Intuitionistic fuzzy sets, distances.
|
| 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.
- Atanassov K., Taseva V., Szmidt E., Kacprzyk J. (2005), On the Geometrical Interpretations of the Intuitionistic Fuzzy Sets. In: K. T. Atanassov, J. Kacprzyk, M. Krawczak, E. Szmidt (Eds.): Issues in the Representation and Processing of Uncertain and Imprecise Information. Series: Problems of the Contemporary Science. EXIT, Warszawa 2005, 11–24.
- Fan J-L., Ma Y-L. and Xie W-X. (2001), On some properties of distance measures. Fuzzy Sets and Systems, 117, 355–361.
- 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.
- Szmidt E. and Baldwin J. (2004), Entropy for intuitionistic fuzzy set theory and mass assignment theory. Notes on IFSs, 10(3), 15-28.
- Szmidt E. and Kacprzyk J. (1996c) Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on IFS, 2(3), 22–31.
- Szmidt E. and Kacprzyk J. (1997) On measuring distances between intuitionistic fuzzy sets, Notes on IFS, 3(4), 1–13.
- Szmidt E. and Kacprzyk J. (1998a) Group Decision Making under Intuitionistic Fuzzy Preference Relations. IPMU’98, 172–178.
- Szmidt E. and Kacprzyk J. (1998b) Applications of Intuitionistic Fuzzy Sets in Decision Making. EUSFLAT’99, 150–158.
- Szmidt E. and Kacprzyk J. (2000), Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114(3), 505–518.
- Szmidt E. and Kacprzyk J. (2000) On Measures on Consensus Under Intuitionistic Fuzzy Relations. IPMU 2000, 1454–1461.
- Szmidt E. and Kacprzyk J. (2001), Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118(3), 467–477.
- Szmidt E. and Kacprzyk J. (2001) Analysis of Consensus under Intuitionistic Fuzzy Preferences. Proc. Int. Conf. in Fuzzy Logic and Technology. Leicester, UK, 79–82.
- Szmidt E. and Kacprzyk J. (2002) Analysis of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Preferences. IPMU 2002, Annecy, France, 1859–1865.
- Szmidt E. and J. Kacprzyk J. (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. and Kacprzyk J. (2004), Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. IPMU 2004, 1405–1412.
- 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.
- 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.
- Szmidt E. and Kacprzyk J. (2006) Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 3rd Int. IEEE Conf. Intelligent Systems IS06, London, 716–721.
- Szmidt E. and Kacprzyk J. (2006), Entropy and similarity of intuitionistic fuzzy sets. IPMU 2006, 2375–2382.
- Szmidt E. and Kacprzyk J. (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. and Kacprzyk J. (2007). Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. Applications of Fuzzy Sets Theory. Lecture Notes on Artificial Intelligence, 4578, 291–297. Springer-Verlag.
- Szmidt E. and Kacprzyk J. (2007a). A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 2007 IEEE Conference on Fuzzy Systems, 481–486.
- Szmidt E. and Kukier M. (2006). Classification of Imbalanced and Overlapping Classes using Intuitionistic Fuzzy Sets. 3rd International IEEE Conference on Intelligent Systems IS’06, London, 2006, 722-727.
- Szmidt E. and Kukier M. (2008) A New Approach to Classification of Imbalanced Classes via Atanassov’s Intuitionistic Fuzzy Sets. In: ”Intelligent Data Analysis: Developing New Methodologies Through Pattern Discovery and Recovery. (Ed. Hsiao-Fan Wang),IGI Global, 85–101.
- 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.
- Zadeh L.A. (1965), Fuzzy sets. Information and Control, 8, 338–353.
|
| 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.
|
|
