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JACIII Vol.12 No.5 pp. 461-466
doi: 10.20965/jaciii.2008.p0461
(2008)

Paper:

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Fuzzy c-Means for Data with Rectangular Maximum Tolerance Range

Yasunori Endo*, Yasushi Hasegawa**, Yukihiro Hamasuna**, and Sadaaki Miyamoto*

*Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba
Email: endo@risk.tsukuba.ac.jp

**Graduate School of Systems and Information Engineering, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

Received:
October 10, 2007
Accepted:
February 15, 2008
Published:
September 20, 2008
Creative Commons License
Keywords:
clustering, uncertainty, tolerance, optimization, Lagrange function
Abstract
This paper provides new clustering algorithms for data with tolerance. Tolerance is understood in a broad sense, e.g., calculation errors and loss of attribute of data. The concept of tolerance is modified by using new concept of tolerance vector. First, the concept is explained and optimization problems of clustering are formulated using the vectors. Second, the problems are solved using Karush-Kuhn-Tucker conditions. Third, the new clustering algorithms are constructed by using the solutions of the problems. Moreover, the effectiveness of proposed algorithms is verified through some numerical examples.
Cite this article as:
Y. Endo, Y. Hasegawa, Y. Hamasuna, and S. Miyamoto, “Fuzzy c-Means for Data with Rectangular Maximum Tolerance Range,” J. Adv. Comput. Intell. Intell. Inform., Vol.12 No.5, pp. 461-466, 2008.
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Last updated on Dec. 01, 2023