模糊最大集与极大集的关系研究

A Research on the Relationship between the Greatest and the Maximum Fuzzy Set

利用模糊逻辑工具给出模糊最大集与模糊极大集的定义.用截集间的关系证明了模糊集之间的关系,得出自反条件下模糊极大集包含模糊最大集,自反、完全条件下模糊极大集与模糊最大集相等.给出反例指出在S完全或传递条件下模糊最大集与模糊极大集并不相等.

The greatest fuzzy set and the maximum fuzzy set have been defined by using fuzzy logic. By using the relation between cut sets, it is proved that, under reflexive condition, the maximum fuzzy set contains the greatest fuzzy set, and that, under both reflexive and complete conditions, the two sets are equal to each other. In addition, counter examples show that, under S-complete or transitive conditions, the maximum fuzzy set does not equal to the greatest fuzzy set.