Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study
International Journal of Sustainability Management and Information Technologies
Volume 3, Issue 6, December 2017, Pages: 57-62
Received: Feb. 28, 2017; Accepted: Mar. 22, 2017; Published: Dec. 14, 2017
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Authors
Dmitri A. Viattchenin, Laboratory of System Identification, United Institute of Informatics Problems of the National Academy of Sciences of Belarus, Minsk, Belarus
Stanislav Shiray, Department of Software Information Technology, Belarusian State University of Informatics and Radio-Electronics, Minsk, Belarus
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Abstract
The note deals with the problem of heuristic possibilistic clustering the intuitionistic fuzzy data. Different distances between intuitionistic fuzzy sets are considered in the paper. Similarity measures for intuitionistic fuzzy sets for constructing intuitionistic fuzzy tolerance relations are also considered. A numerical example of application of these distances and similarity measures for clustering the intuitionistic fuzzy data is presented. Some preliminary conclusions are formulated.
Keywords
Clustering, Intuitionistic Fuzzy Data, Distance, Similarity Measure, Allotment Among Intuitionistic Fuzzy Clusters
To cite this article
Dmitri A. Viattchenin, Stanislav Shiray, Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study, International Journal of Sustainability Management and Information Technologies. Vol. 3, No. 6, 2017, pp. 57-62. doi: 10.11648/j.ijsmit.20170306.11
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Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
L. A. Zadeh, “Fuzzy sets”, Information and Control, 8 (3), pp. 338-353, 1965.
[2]
L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility”, Fuzzy Sets and Systems, 1 (1), pp. 3-28, 1978.
[3]
R. Krishnapuram, J. M. Keller, “A possibilistic approach to clustering”, IEEE Transactions on Fuzzy Systems, vol. 1 (2), pp. 98-110, 1993.
[4]
J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum Press, 1981.
[5]
F. Höppner, F. Klawonn, R. Kruse, T. Runkler, Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. Chichester: Wiley, 1999.
[6]
J. C. Bezdek, J. M. Keller, R. Krishnapuram, N. R. Pal, Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. New York: Springer, 2005.
[7]
D. A. Viattchenin, A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications. Heidelberg: Springer, 2013.
[8]
K. T. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20 (1), pp. 87-96, 1986.
[9]
Z. Xu, Intuitionistic Fuzzy Aggregation and Clustering. Heidelberg: Springer, 2013.
[10]
J. Kacprzyk, J. W. Owsinski, D. A. Viattchenin, S. Shyrai, “A new heuristic algorithm of possibilistic clustering based on intuitionistic fuzzy relations,” Nowel Developments in Uncertainty Representation and Processing: Advances in Intuitionistic Fuzzy Sets and Generalized Nets – Proceedings of 14th International Conference on Intuitionistic Fuzzy Sets and Generalized Nets IWIFSGN’2015 (Cracow, Poland, October 26-28, 2015), K. T. Atanassov, O. Castillo, J. Kacprzyk, M. Krawczak, P. Melin, S. Sotirov, E. Sotirova, E. Szmidt, G. De Tré, eds., Heidelberg: Springer, 2015, 199-214.
[11]
D. A. Viattchenin, S. Shyrai, “Intuitionistic heuristic prototype-based algorithm of possibilistic clustering”, Communications on Applied Electronics, 1 (8), pp. 30-40, 2015.
[12]
S. Shyrai, D. A. Viattchenin, “Clustering the intuitionistic fuzzy data. Detection of an unknown number of intuitionistic fuzzy clusters in the allotment”, Proceedings of the International Conference on Information and Digital Technologies IDT’2015 (Zilina, Slovakia, July 7-9, 2015), Piscataway: IEEE Service Center, 2015, 302-311.
[13]
W.-L. Hung, J.-S. Lee, C.-D. Fuh, “Fuzzy clustering based on intuitionistic fuzzy relations”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12 (4), pp. 513-529, 2004.
[14]
K. T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications. Heidelberg: Springer, 1999.
[15]
K. T. Atanassov, On Intuitionistic Fuzzy Sets Theory. Heidelberg: Springer, 2012.
[16]
E. Szmidt, Distances and Similarities in Intuitionistic Fuzzy Sets, Heidelberg: Springer, 2014.
[17]
A. Kaufmann, Introduction to the Theory of Fuzzy Sets, New York: Academic Press, 1975.
[18]
Z. Wang, Z. Xu, S. Liu, J. Tang, “A netting clustering analysis method under intuitionistic fuzzy environment”, Applied Soft Computing, 11 (8), pp. 5558-5564, 2011.
[19]
D. A. Viattchenin, “A method of construction of intuitionistic fuzzy tolerances based on a similarity measure between intuitionistic fuzzy sets”, New Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics – Proceedings of 10th International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets IWIFSGN’2011 (Warsaw, Poland, September 30, 2011), Vol. I: Foundations, K. T. Atanassov, M. Baczyński, J. Drewniak, J. Kacprzyk, M. Krawczak, E. Szmidt, M. Wygralak, S. Zadrożny eds., Warsaw: IBS PAN, 2012, pp. 191-202.
[20]
J. Kacprzyk, D. A. Viattchenin, S. Shyrai, E. Szmidt, “A nowel similarity measure between intuitionistic fuzzy sets for constructing intuitionistic fuzzy tolerance,” Nowel Developments in Uncertainty Representation and Processing: Advances in Intuitionistic Fuzzy Sets and Generalized Nets – Proceedings of 14th International Conference on Intuitionistic Fuzzy Sets and Generalized Nets IWIFSGN’2015 (Cracow, Poland, October 26-28, 2015), K. T. Atanassov, O. Castillo, J. Kacprzyk, M. Krawczak, P. Melin, S. Sotirov, E. Sotirova, E. Szmidt, G. De Tré, eds., Heidelberg: Springer, 2015, 175-183.
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