摘要
首先指出一个直觉模糊集是L-模糊集且X上所有直觉模糊集的集合是一个完备格.其次,分别给出了直觉模糊集截集、直觉集合套的定义;讨论了有关直觉模糊集截集的性质.在此基础上,给出了直觉模糊集的分解定理和表现定理.最后,讨论了直觉模糊集截集与直觉模糊子群的关系,证明了A是群G的一个直觉模糊子群的充分必要条件是A的截集是G的一个子群.
In this paper, firstly, it is stated that,an intuitionistic fuzzy sets is a L-fuzzy set, and a set of all intuitionistic fuzzy sets over X is a complete lattice. Secondly, the definitions of cut set on intuitionistic fuzzy sets and an intuitionistic nested set are given. Properties of cut sets, decomposition theorem, representation theorem of intuitionistic fuzzy sets are discussed. Finally, the relation between cut sets on intuitionistic fuzzy sets and an intuitionistic fuzzy subset of a group is discussed. It is proved that A is an intuitionistic fuzzy subset of a group G if and only if cut sets of A are subgroup of G.
出处
《辽宁师范大学学报（自然科学版）》
CAS
北大核心
2007年第2期152-154,共3页
Journal of Liaoning Normal University:Natural Science Edition
关键词
直觉模糊集
截集
分解定理
表现定理
intuitionistic fuzzy sets
cut sets
decomposition theorem
representation theorem
