关键词: 模糊集合, 模糊划分, FCM算法

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