Fuzzy classification function of fuzzy c-means algorithms for data with tolerance

Yuchi Kanzawa; Yasunori Endo; Sadaaki Miyamoto

doi:10.1109/FUZZY.2008.4630504

Fuzzy classification function of fuzzy c-means algorithms for data with tolerance

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, two fuzzy classification functions of fuzzy c-means for data with tolerance are proposed. First, two clustering algorithms for data with tolerance are introduced. One is based on the standard method and the other is on the entropy-based one. Second, the fuzzy classification function for fuzzy c-means without tolerance is discussed as the solution of a certain optimization problem. Third, two optimization problems are shown so that the solutions are the fuzzy classification function values for fuzzy c-means algorithms with respect to data with tolerance, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, and two iterative algorithms are proposed for the optimization problems, respectively. Through some numerical examples, the proposed algorithms are discussed.

Original language	English
Title of host publication	2008 IEEE International Conference on Fuzzy Systems, FUZZ 2008
Pages	1081-1088
Number of pages	8
DOIs	https://doi.org/10.1109/FUZZY.2008.4630504
Publication status	Published - 2008 Nov 7
Event	2008 IEEE International Conference on Fuzzy Systems, FUZZ 2008 - Hong Kong, China Duration: 2008 Jun 1 → 2008 Jun 6

Publication series

Name	IEEE International Conference on Fuzzy Systems
ISSN (Print)	1098-7584

Conference

Conference	2008 IEEE International Conference on Fuzzy Systems, FUZZ 2008
Country/Territory	China
City	Hong Kong
Period	08/6/1 → 08/6/6

ASJC Scopus subject areas

Software
Theoretical Computer Science
Artificial Intelligence
Applied Mathematics

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10.1109/FUZZY.2008.4630504

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Kanzawa, Y, Endo, Y & Miyamoto, S 2008, Fuzzy classification function of fuzzy c-means algorithms for data with tolerance. in 2008 IEEE International Conference on Fuzzy Systems, FUZZ 2008., 4630504, IEEE International Conference on Fuzzy Systems, pp. 1081-1088, 2008 IEEE International Conference on Fuzzy Systems, FUZZ 2008, Hong Kong, China, 08/6/1. https://doi.org/10.1109/FUZZY.2008.4630504

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N2 - In this paper, two fuzzy classification functions of fuzzy c-means for data with tolerance are proposed. First, two clustering algorithms for data with tolerance are introduced. One is based on the standard method and the other is on the entropy-based one. Second, the fuzzy classification function for fuzzy c-means without tolerance is discussed as the solution of a certain optimization problem. Third, two optimization problems are shown so that the solutions are the fuzzy classification function values for fuzzy c-means algorithms with respect to data with tolerance, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, and two iterative algorithms are proposed for the optimization problems, respectively. Through some numerical examples, the proposed algorithms are discussed.

AB - In this paper, two fuzzy classification functions of fuzzy c-means for data with tolerance are proposed. First, two clustering algorithms for data with tolerance are introduced. One is based on the standard method and the other is on the entropy-based one. Second, the fuzzy classification function for fuzzy c-means without tolerance is discussed as the solution of a certain optimization problem. Third, two optimization problems are shown so that the solutions are the fuzzy classification function values for fuzzy c-means algorithms with respect to data with tolerance, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, and two iterative algorithms are proposed for the optimization problems, respectively. Through some numerical examples, the proposed algorithms are discussed.

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Fuzzy classification function of fuzzy c-means algorithms for data with tolerance

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