Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study

Dmitri A. Viattchenin; Stanislav Shiray

doi:doi:10.11648/j.ijsmit.20170306.11

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Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study

Dmitri A. Viattchenin, Stanislav Shiray

Published in International Journal of Sustainability Management and Information Technologies (Volume 3, Issue 6)

Received: 28 February 2017 Accepted: 22 March 2017 Published: 14 December 2017

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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.

Published in	International Journal of Sustainability Management and Information Technologies (Volume 3, Issue 6)
DOI	10.11648/j.ijsmit.20170306.11
Page(s)	57-62
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Clustering, Intuitionistic Fuzzy Data, Distance, Similarity Measure, Allotment Among Intuitionistic Fuzzy Clusters

References

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[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.
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Dmitri A. Viattchenin, Stanislav Shiray. (2017). Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study. International Journal of Sustainability Management and Information Technologies, 3(6), 57-62. https://doi.org/10.11648/j.ijsmit.20170306.11

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ACS Style

Dmitri A. Viattchenin; Stanislav Shiray. Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study. Int. J. Sustain. Manag. Inf. Technol. 2017, 3(6), 57-62. doi: 10.11648/j.ijsmit.20170306.11

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AMA Style

Dmitri A. Viattchenin, Stanislav Shiray. Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study. Int J Sustain Manag Inf Technol. 2017;3(6):57-62. doi: 10.11648/j.ijsmit.20170306.11

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@article{10.11648/j.ijsmit.20170306.11,
  author = {Dmitri A. Viattchenin and Stanislav Shiray},
  title = {Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study},
  journal = {International Journal of Sustainability Management and Information Technologies},
  volume = {3},
  number = {6},
  pages = {57-62},
  doi = {10.11648/j.ijsmit.20170306.11},
  url = {https://doi.org/10.11648/j.ijsmit.20170306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsmit.20170306.11},
  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.},
 year = {2017}
}

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TY  - JOUR
T1  - Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study
AU  - Dmitri A. Viattchenin
AU  - Stanislav Shiray
Y1  - 2017/12/14
PY  - 2017
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DO  - 10.11648/j.ijsmit.20170306.11
T2  - International Journal of Sustainability Management and Information Technologies
JF  - International Journal of Sustainability Management and Information Technologies
JO  - International Journal of Sustainability Management and Information Technologies
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PB  - Science Publishing Group
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VL  - 3
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Author Information

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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APA Style

Dmitri A. Viattchenin, Stanislav Shiray. (2017). Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study. International Journal of Sustainability Management and Information Technologies, 3(6), 57-62. https://doi.org/10.11648/j.ijsmit.20170306.11

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ACS Style

Dmitri A. Viattchenin; Stanislav Shiray. Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study. Int. J. Sustain. Manag. Inf. Technol. 2017, 3(6), 57-62. doi: 10.11648/j.ijsmit.20170306.11

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AMA Style

Dmitri A. Viattchenin, Stanislav Shiray. Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study. Int J Sustain Manag Inf Technol. 2017;3(6):57-62. doi: 10.11648/j.ijsmit.20170306.11

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@article{10.11648/j.ijsmit.20170306.11,
  author = {Dmitri A. Viattchenin and Stanislav Shiray},
  title = {Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study},
  journal = {International Journal of Sustainability Management and Information Technologies},
  volume = {3},
  number = {6},
  pages = {57-62},
  doi = {10.11648/j.ijsmit.20170306.11},
  url = {https://doi.org/10.11648/j.ijsmit.20170306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsmit.20170306.11},
  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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study
AU  - Dmitri A. Viattchenin
AU  - Stanislav Shiray
Y1  - 2017/12/14
PY  - 2017
N1  - https://doi.org/10.11648/j.ijsmit.20170306.11
DO  - 10.11648/j.ijsmit.20170306.11
T2  - International Journal of Sustainability Management and Information Technologies
JF  - International Journal of Sustainability Management and Information Technologies
JO  - International Journal of Sustainability Management and Information Technologies
SP  - 57
EP  - 62
PB  - Science Publishing Group
SN  - 2575-5110
UR  - https://doi.org/10.11648/j.ijsmit.20170306.11
AB  - 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.
VL  - 3
IS  - 6
ER  -

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