Acta Scientiarum Naturalium Universitatis Pekinensis

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A New Definition of Fuzzy Partition and Its Application

YU Jian, CHENG Qiansheng   

  1. School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:1999-12-18 Online:2000-09-20 Published:2000-09-20


于剑, 程乾生   

  1. 北京大学数学科学学院信息科学系,北京,100871

Abstract: In this paper, we pointed out that the Ruspini's definition of fuzzy partition has a shortcoming, which does not always coincide with our intuition. So we proposed a new definition for fuzzy partition and proved the new definition of fuzzy partition has a desired property consistent with our intuition and applications of fuzzy partition (e.g., fuzzy decision making, fuzzy clustering, fuzzy control, etc.). It can follow Ruspini's definition of fuzzy partition, which are cited frequently in current papers. According to the new definition of fuzzy partition, we defined the relative clearness of fuzzy sets and the mean clearness of fuzzy partition. The latter is proved effective for evaluating the performance of FCM algorithm by the experiments.

Key words: fuzzy sets, fuzzy partition, FCM algorithm

摘要: 提出了模糊划分的一个新定义。可以证明它蕴含了Ruspini的定义,并且具有与直观及其实际应用相符的性质。而且根据此定义,可以定义模糊集合的相对清晰度及模糊划分的平均清晰度。实验证明,模糊划分的平均清晰度可以衡量FCM算法的聚类效果。

关键词: 模糊集合, 模糊划分, FCM算法

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