A Method for Estimating the Least Number of Objects in Fuzzy Clusters

Dmitri A. Viattchenin, Aliaksandr Yaroma


The theoretical note deals with the problem of estimation of the value of the least number of objects in fuzzy clusters for following detection of the optimal number of objects in fuzzy clusters through heuristic possibilistic clustering. A technique for detecting the optimal maximal number of elements in the a priori unknown number of fuzzy clusters of the sought clustering structure is reminded and a procedure for finding the initial minimal value of the number of objects in fuzzy clusters is proposed. Numerical examples are considered and conclusions are formulated.

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L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965.

R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Transactions on Fuzzy Systems, vol. 1, no. 2, pp. 98–110, 1993.

J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981.

F. Höppner, F. Klawonn, R. Kruse, and T. Runkler, Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition, Wiley, Chichester, 1999.

J. C. Bezdek, J. M. Keller, R. Krishnapuram, and N. R. Pal, Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, Springer, New York, 2005.

D. A. Viattchenin, A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications, Springer, Heidelberg, 2013.

D. A. Viattchenin, “Heuristic possibilistic clustering for detecting optimal number of elements in fuzzy clusters,” Foundations of Computing and Decision Sciences, vol. 41, no. 1, pp. 45-76, 2016.

D. A. Viattchenin, A. Yaroma, and A. Damaratski, “A novel direct relational heuristic algorithm of possibilistic clustering,” International Journal of Computer Applications, vol. 107, no. 18, pp. 15-21, 2014.

D. A. Viattchenin, “A novel heuristic algorithm of possibilistic clustering for given minimal value of the tolerance threshold,” Journal of Information, Control and Management Systems, vol. 13, no. 2, pp. 161-174, 2015.

D. A. Viattchenin, E. Nikolaenya, and A. Damaratski, “A fuzzy graph-based heuristic algorithm of possibilistic clustering,” Communications on Applied Electronics, vol. 3, no. 7, pp. 13-23, 2015.

D. A. Viattchenin and A. Damaratski, “Direct heuristic algorithms of possibilistic clustering based on transitive approximation of fuzzy tolerance,” Informatica Economicá, vol. 17, no.3, pp. 5-15, 2013.

M. Sato-Ilic and L. C. Jain, Innovations in Fuzzy Clustering. Theory and Applications, Springer, Heidelberg, 2006.

M. Walesiak, Ugólniona Miara Odległości w Statystycznej Analizie Wielowymiarowej, Wydawnictwo Akademii Ekonomicznej im. Oskara Langego, Wrocław, 2002. (in Polish)

A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, 1975.

P. H. A. Sneath and R. Sokal, Numerical Taxonomy, Freeman, San Francisco, 1973.


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