TY - GEN
T1 - Fuzzy classification function of fuzzy c-means algorithms for data with tolerance
AU - Kanzawa, Yuchi
AU - Endo, Yasunori
AU - Miyamoto, Sadaaki
PY - 2008/11/7
Y1 - 2008/11/7
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.
UR - http://www.scopus.com/inward/record.url?scp=55249086974&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=55249086974&partnerID=8YFLogxK
U2 - 10.1109/FUZZY.2008.4630504
DO - 10.1109/FUZZY.2008.4630504
M3 - Conference contribution
AN - SCOPUS:55249086974
SN - 9781424418190
T3 - IEEE International Conference on Fuzzy Systems
SP - 1081
EP - 1088
BT - 2008 IEEE International Conference on Fuzzy Systems, FUZZ 2008
T2 - 2008 IEEE International Conference on Fuzzy Systems, FUZZ 2008
Y2 - 1 June 2008 through 6 June 2008
ER -