Table 1

Index . | Source . | Equation . | Parameters . |
---|---|---|---|

Partition coefficient | Bezdek (1974a, 1974b) | (8) | V: Partition coefficient _{PC} |

Partition entropy | Bezdek (1974a, 1974b) | (9) | V: Partition entropy _{PE} |

Fukuyama–Sugeno | Fukuyama & Sugeno (1989) | (10) | V: Fukuyama and Sugeno validity measure _{FS} |

V: The extended FCM _{EXB} | |||

Extended Xie–Beni | Xie & Beni (1991) and Pal & Bezdek (1995) | (11) | Xie–Beni index V: Kwon index_{K}N: Number of cells in each layer |

Kwon's index | Kwon (1998) | (12) | c: Number of clusters |

u: Degree of membership_{ij}x: Rescaled feature value for each cell_{j}c and _{i}c : The fuzzy centroids of the _{j}ith cluster |

Index . | Source . | Equation . | Parameters . |
---|---|---|---|

Partition coefficient | Bezdek (1974a, 1974b) | (8) | V: Partition coefficient _{PC} |

Partition entropy | Bezdek (1974a, 1974b) | (9) | V: Partition entropy _{PE} |

Fukuyama–Sugeno | Fukuyama & Sugeno (1989) | (10) | V: Fukuyama and Sugeno validity measure _{FS} |

V: The extended FCM _{EXB} | |||

Extended Xie–Beni | Xie & Beni (1991) and Pal & Bezdek (1995) | (11) | Xie–Beni index V: Kwon index_{K}N: Number of cells in each layer |

Kwon's index | Kwon (1998) | (12) | c: Number of clusters |

u: Degree of membership_{ij}x: Rescaled feature value for each cell_{j}c and _{i}c : The fuzzy centroids of the _{j}ith cluster |

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