### Abstract

In this paper, the fuzzy classification functions of the entropy regularized 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 entropy regularized 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 | 2008 IEEE International Conference on Granular Computing, GRC 2008 |

Pages | 350-355 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2008 Dec 30 |

Event | 2008 IEEE International Conference on Granular Computing, GRC 2008 - Hangzhou, China Duration: 2008 Aug 26 → 2008 Aug 28 |

### Publication series

Name | 2008 IEEE International Conference on Granular Computing, GRC 2008 |
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### Conference

Conference | 2008 IEEE International Conference on Granular Computing, GRC 2008 |
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Country | China |

City | Hangzhou |

Period | 08/8/26 → 08/8/28 |

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### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Software

### Cite this

*2008 IEEE International Conference on Granular Computing, GRC 2008*(pp. 350-355). [4664765] (2008 IEEE International Conference on Granular Computing, GRC 2008). https://doi.org/10.1109/GRC.2008.4664765