基于灰关联分析的模糊聚类最优划分判定模型

山东大学学报(工学版)

基于灰关联分析的模糊聚类最优划分判定模型

王耘^1,2，穆勇²，刘庆红²

1. 山东大学数学与系统科学学院，山东济南250100；2. 济南大学理学院，山东济南250022

收稿日期:2004-07-05 修回日期:1900-01-01 出版日期:2006-04-24 发布日期:2006-04-24
通讯作者: 王耘

Judging model of fuzzy cluster optimal dividing based on grey relational grade analysis

WANG Yun1，2，MU Yong2，LIU Qing-hong2

1. School of Mathematics and System Science,Shandong University,Jinan 250100,China; 2. School of Science,Jinan University,Jinan 250022,China

Received:2004-07-05 Revised:1900-01-01 Online:2006-04-24 Published:2006-04-24
Contact: WANG Yun

摘要/Abstract

摘要： 在模糊聚类的模糊模式中，由于只已知样本中的部分样本，以及聚类中心选择的多样性，会得到多个聚类矩阵.如何进行最优划分的判定？针对这一问题，本文提出一个新的判定模型：根据灰色系统理论中灰关联度分析的思想，建立灰关联序模型，根据灰关联算法，判断样本代表性.若样本具有较好的代表性，则由其归纳计算得到最优划分矩阵.示例分析验证了该算法的可行性.本方法为最优划分矩阵的判定问题提供了一种新的研究工具和思路.将相关学科的研究方法与模糊集理论相结合，丰富了模糊集理论的方法体系.

关键词: 模糊聚类分析, 模糊最优划分矩阵, 灰关联度, 样本代表性

Abstract: In the fuzzy pattern of fuzzy cluster, since only parts of samples are known and the various choices of cluster center, several cluster matrices can be obtained. How to judge optimal dividing? The representatives of samples are judged by the thinking of grey relational grade analysis in grey system theory. If the samples have relatively good representative, then the optimal dividing matrix can be induced and computed from them. The feasibility of this algorithm is verified by analyzing the example. A new method and thinking way is provided for judging problem of fuzzy cluster optimal dividing. By combing the studying method of relevant subject with fuzzy sets theory, it riches the methods system of fuzzy sets system.

Key words: fuzzy optimal dividing matrix, grey relational grade, representatives of samples , fuzzy cluster analysis

中图分类号:

O159

王耘,穆勇,刘庆红 . 基于灰关联分析的模糊聚类最优划分判定模型[J]. 山东大学学报(工学版), 2006, 36(2): 86-89 .

WANG Yun,MU Yong,LIU Qing-hong . Judging model of fuzzy cluster optimal dividing based on grey relational grade analysis[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(2): 86-89 .

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[2]	王耘,穆勇,刘庆红 . 基于灰关联分析的模糊聚类最优划分判定模型[J]. 山东大学学报(工学版), 2006, 36(2): 86-89 .