Call for Paper

CAE solicits original research papers for the July 2021 Edition. Last date of manuscript submission is June 30, 2021.

Read More

A Fuzzy Graph-based Heuristic Algorithm of Possibilistic Clustering

Dmitri A. Viattchenin, Evgeny Nikolaenya, Aliaksandr Damaratski. Published in Fuzzy Systems.

Communications on Applied Electronics
Year of Publication: 2015
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors: Dmitri A. Viattchenin, Evgeny Nikolaenya, Aliaksandr Damaratski

Dmitri A Viattchenin, Evgeny Nikolaenya and Aliaksandr Damaratski. Article: A Fuzzy Graph-based Heuristic Algorithm of Possibilistic Clustering. Communications on Applied Electronics 3(7):13-23, December 2015. Published by Foundation of Computer Science (FCS), NY, USA. BibTeX

	author = {Dmitri A. Viattchenin and Evgeny Nikolaenya and Aliaksandr Damaratski},
	title = {Article: A Fuzzy Graph-based Heuristic Algorithm of Possibilistic Clustering},
	journal = {Communications on Applied Electronics},
	year = {2015},
	volume = {3},
	number = {7},
	pages = {13-23},
	month = {December},
	note = {Published by Foundation of Computer Science (FCS), NY, USA}


In this paper, a heuristic algorithm of possibilistic clustering based on fuzzy graph decomposition is proposed. For the purpose, concepts of fuzzy graph and fuzzy tolerance relation are considered and basic definitions of the heuristic approach to possibilistic clustering are described. An application of the proposed algorithm to the Tamura’s portrait data set is provided and some concluding remarks are stated.


  1. 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.
  2. Krishnapuram, R. and Keller, J.M. 1993. A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems. 1, 98-110.
  3. Mandel, I.D. 1988. Clustering Analysis. Moscow: Finansy i Statistica. (in Russian)
  4. Viattchenin, D.A. 2013. A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications. Heidelberg: Springer.
  5. Schaeffer, S. 2007. Graph Clustering. Computer Science Review. 1, 27-64.
  6. Fortunato, S. 2010. Community Detection in Graphs. Physics Reports. 486, 75-174.
  7. Zadeh, L.A. 1965. Fuzzy Sets. Information and Control. 8, 338-353.
  8. Kaufmann, A. 1975. Introduction to the Theory of Fuzzy Subsets. New York: Academic Press.
  9. Rosenfeld, A. 1975. Fuzzy Graphs. In Fuzzy Sets and Their Applications to Cognitive and Decision Processes. New York: Academic Press, 77-95.
  10. Devillez, A., Billaudel, P. and Villermain Lecolier, G. 2002. A Fuzzy Hybrid Hierarchical Clustering Method with a New Criterion Able to Find the Optimal Partition. Fuzzy Sets and Systems. 128, 77-95.
  11. Dong, Y., Zhuang, Y., Chen, K. and Tai, X. 2006. A Hierarchical Clustering Algorithm Based on Graph Connectedness. Fuzzy Sets and Systems. 157, 1760-1774.
  12. Tamura, S., Higuchi, S. and Tanaka, K. 1971. Pattern Classification Based on Fuzzy Relations. IEEE Transactions on Systems, Man, and Cybernetics. 1, 61-66.
  13. Dawyndt, P., De Meyer, H. and De Baets, B. 2006. UPGMA Clustering Revisited: A Weight-Driven Approach to Transitive Approximation. International Journal of Approximate Reasoning. 42, 174-191.


Fuzzy Graph, Fuzzy Tolerance, Heuristic Possibilistic Clustering, Fuzzy Cluster, Allotment, Tolerance Threshold, Typical Point.