### Abstract

In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 122-133 |

Number of pages | 12 |

Volume | 5285 LNAI |

DOIs | |

Publication status | Published - 2008 |

Event | 5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008 - Sabadell Duration: 2008 Oct 30 → 2008 Oct 31 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5285 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008 |
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City | Sabadell |

Period | 08/10/30 → 08/10/31 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 5285 LNAI, pp. 122-133). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5285 LNAI). https://doi.org/10.1007/978-3-540-88269-5-12

**Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function.** / Kanzawa, Yuchi; Endo, Yasunori; Miyamoto, Sadaaki.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 5285 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5285 LNAI, pp. 122-133, 5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008, Sabadell, 08/10/30. https://doi.org/10.1007/978-3-540-88269-5-12

}

TY - GEN

T1 - Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function

AU - Kanzawa, Yuchi

AU - Endo, Yasunori

AU - Miyamoto, Sadaaki

PY - 2008

Y1 - 2008

N2 - In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

AB - In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

UR - http://www.scopus.com/inward/record.url?scp=58049085676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049085676&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-88269-5-12

DO - 10.1007/978-3-540-88269-5-12

M3 - Conference contribution

AN - SCOPUS:58049085676

SN - 3540882685

SN - 9783540882688

VL - 5285 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 122

EP - 133

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -