ISSN 1002-1027　　CN 11-2952/G2

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

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.