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Intuitionistic Heuristic Prototype-based Algorithm of Possibilistic Clustering

Dmitri A. Viattchenin, Stanislau Shyrai Published in Fuzzy Systems

Communications on Applied Electronics
Year of Publication: 2015
© 2015 by CAE Journal

Dmitri A Viattchenin and Stanislau Shyrai. Article: Intuitionistic Heuristic Prototype-based Algorithm of Possibilistic Clustering. Communications on Applied Electronics 1(8):30-40, May 2015. Published by Foundation of Computer Science, New York, USA. BibTeX

	author = {Dmitri A. Viattchenin and Stanislau Shyrai},
	title = {Article: Intuitionistic Heuristic Prototype-based Algorithm of Possibilistic Clustering},
	journal = {Communications on Applied Electronics},
	year = {2015},
	volume = {1},
	number = {8},
	pages = {30-40},
	month = {May},
	note = {Published by Foundation of Computer Science, New York, USA}


This paper introduces a novel intuitionistic fuzzy set-based heuristic algorithm of possibilistic clustering. For the purpose, some remarks on the fuzzy approach to clustering are discussed and a brief review of intuitionistic fuzzy set-based clustering procedures is given, basic concepts of the intuitionistic fuzzy set theory and the intuitionistic fuzzy generalization of the heuristic approach to possibilistic clustering are considered, a general plan of the proposed clustering procedure is described in detail, two illustrative examples confirm good performance of the proposed algorithm, and some preliminary conclusions are formulated.


  1. Zadeh, L. A. 1965. Fuzzy Sets. Information and Control. 8, 338-353.
  2. Krishnapuram, R. and Keller, J. M. 1993. A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems. 1(1), 98-110.
  3. Bezdek, J. C. 1981. Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum Press.
  4. Höppner, F. , Klawonn, F. , Kruse, R. and Runkler, T. 1999. Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. Chichester: John Wiley & Sons.
  5. Sato-Ilic, M. and Jain, L. C. 2006. Innovations in Fuzzy Clustering. Theory and Applications. Heidelberg: Springer.
  6. Miyamoto, S. , Ichihashi, H. and Honda, K. 2008. Algorithms for Fuzzy Clustering. Methods in C-Means Clustering with Applications. Heidelberg: Springer.
  7. Viattchenin, D. A. 2013. A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications. Heidelberg: Springer.
  8. Atanassov, K. T. 1986. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems. 20, 87-96.
  9. Hung, W. -L. , Lee, J. -S. and Fuh, C. -D. 2004. Fuzzy Clustering Based on Intuitionistic Fuzzy Relations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 12, 513-529.
  10. Xu, Z. , Chen, J. and Wu, J. 2008. Clustering Algorithm for Intuitionistic Fuzzy Sets. Information Science. , 178, 3775-3790.
  11. Cai, R. , Lei, Y. J. and Zhao, X. J. 2009. Clustering Method Based on Intuitionistic Fuzzy Equivalent Dissimilarity Matrix. Journal of Computer Applications. 29, 123-126.
  12. Wang, Z. , Xu, Z. , Liu, S. and Tang, J. 2011. A Netting Clustering Analysis Method under Intuitionistic Fuzzy Environment. Applied Soft Computing. 11, 5558-5564.
  13. Pelekis, N. , Iakovidis, D. K. , Kotsifakos, E. E. and Kopanakis, I. 2008. Fuzzy Clustering of Intuitionistic Fuzzy Data. International Journal of Business Intelligence and Data Mining. 3, 45-65.
  14. Iakovidis, D. K. , Pelekis, N. , Kotsifakos, E. E. and Kopanakis, I. 2008. Intuitionistic Fuzzy Clustering with Applications in Computer Vision. In Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems (ACIVS'2008), 764-774.
  15. Torra, V. , Miyamoto, S. , Endo, Y. and Domingo-Ferrer, J. 2008. On Intuitionistic Fuzzy Clustering for its Application to Privacy. In Proceedings of the 2008 IEEE World Congress on Computational Intelligence (WCCI'2008) and the 17th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'08), 1042-1048.
  16. Karthikeyani Visalakshi, N. , Thangavel, K. and Parvathi, R. 2010. An Intuitionistic Fuzzy Approach to Distributed Fuzzy Clustering. International Journal of Computer Theory and Engineering. 2, 295-302.
  17. Todorova, L. and Vassilev, P. 2010. Algorithm for Clustering Data Set Represented by Intuitionistic Fuzzy Estimates. International Journal of Bioautomation. 14, 61-68.
  18. Xu, Z. 2009. Intuitionistic Fuzzy Hierarchical Clustering Algorithms. Journal of Systems Engineering and Electronics. 20, 1-8.
  19. Xu, Z. and Wu, J. 2010. Intuitionistic Fuzzy C-Means Clustering Algorithms. Journal of Systems Engineering and Electronics. 21, 580-590.
  20. Yan, C. and Chen, A. -D. 2012. A FCM Algorithm Based on Weighted Intuitionistic Fuzzy Set. International Journal of Digital Content Technology and Its Applications. 6, 95-101.
  21. Chaudhuri, A. 2015. Intuitionistic Fuzzy Possibilistic C Means Clustering Algorithms. Advances in Fuzzy Systems. 2015, 1-17.
  22. Pal, N. R. , Pal, K. and Bezdek, J. C. 1997. A Mixed C-Means Clustering Model. In Proceedings of the 6th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'97), Vol. 1, 11-21.
  23. Xu, Z. 2013. Intuitionistic Fuzzy Aggregation and Clustering. Heidelberg: Springer.
  24. Burillo, P. and Bustince, H. 1995. Intuitionistic Fuzzy Relations (Part I). Mathware and Soft Computing. 2, 5-38.
  25. Burillo, P. and Bustince, H. 1995. Intuitionistic Fuzzy Relations (Part II) Effect of Atanassov's Operators on the Properties of the Intuitionistic Fuzzy Relations. Mathware and Soft Computing. 2, 117-148.
  26. Zimmermann, H. -J. 1991. Fuzzy Set Theory and Its Applications. Boston: Kluwer Academic Publishers.
  27. Varlamov, O. O. 2002. Evolutional Data and Knowledge Bases for an Adaptive Synthesis of Intelligent Systems. MIVAR Information Space. Moscow: Radio I Svyaz. (in Russian)
  28. Varlamov, O. O. 2011. MIVAR Technologies of the Development of Intelligent Systems and the Creation of the Active Multi-Subject Online MIVAR Encyclopedia. In Proceedings of the 11th International Conference on Pattern Recognition and Information Processing (PRIP'2011), 326-329.


Intuitionistic Fuzzy Set, Possibilistic Clustering, Allotment among Intuitionistic Fuzzy Clusters, Typical Point.