| Title of paper:
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A new similarity measure and new distances for intuitionistic fuzzy sets
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| Author(s):
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| Radoslav Tzvetkov
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| Technical University of Sofia, Boulevard Kliment Ohridski 8 Sofia, Bulgaria
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| rado_tzv@tu-sofia.bg
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| Eulalia Szmidt
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| Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
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| szmidt@ibspan.waw.pl
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| Janusz Kacprzyk
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| Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
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| kacprzyk@ibspan.waw.pl
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| Presented at:
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5th International Workshop on Intuitionistic Fuzzy Sets, 19 October 2009, Banská Bystrica, Slovakia.
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 15, Number 4, pages 33—39
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| Download:
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 PDF (80 Kb, File info)
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| Abstract:
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This paper is a continuation of our previous works on similarity measures of Atanassov’s intuitionistic fuzzy sets (to be called A-IFSs, for short). The similarity measures we considered used all three functions (membership, non-membership and hesitation) to represent A-IFSs, and examined two kinds of distances – one to an object to be compared, and one to its complement. In this paper we propose some new distances between A-IFSs, and new similarity measures preserving all the advantages of the previously proposed similarity measures and using the new distance functions.
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| References:
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- 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.
- Bouchon-Meunier B., Rifgi M., and Bothorel S. (1996). General measures of comparison of objects. Fuzzy Sets and Systems, 84 (2), 143–153.
- Chen S., Yeh M. and Hsiao P. (1995). A comparison of similarity measures of fuzzy values. Fuzzy Sets and Systems,72 (1), 79–89.
- 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.
- Dengfeng L. and Chuntian C. (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23, 221-225.
- Pappis C., and Karacapilidis N. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems, 56, 171–174.
- 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. (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. (2002a) Analysis of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Preferences. Proc. IPMU’2002, Annecy, 1859–1865.
- 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.
- Szmidt E. and Kacprzyk J. (2002c) Evaluation of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Sets. Proc. IEEE-IS’2002 – Int. IEEE Symposium: Intelligent Systems, Varna, 166–170.
- 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, 272–282.
- Szmidt E. and Kacprzyk J. (2006) Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 3rd Int. IEEE Conf. ”Intelligent Systems”, 716–721.
- Szmidt E. and Kacprzyk J. (2007). A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 2007 IEEE Conf. on Fuzzy Systems, 481–486.
- Tasseva V., Szmidt E. and Kacprzyk J. (2005) On one of the geometrical interpretations of the intuitionistic fuzzy sets. Notes on IFS, 11 (3), 21–27.
- Tversky A. (1977). Features of similarity. Psychol. Rev., 84, 327–352.
- Veltkamp R.C. (2001) Shape matching: similarity measures and algorithms. Proc. Shape Modelling International, Genova, Italy, IEEE Press, 188–197.
- Wang X., De Baets B., and Kerre E. (1995). A comparative study of similarity measures. Fuzzy Sets and Systems, 73 (2), 259–268.
- Zeng W. and H. Li (2006) Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets and Systems 157, 1477–1484.
- 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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