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论文类型：会议论文

发表时间：2009-01-01

收录刊物：SCIE、CPCI-S

卷号：62

页面范围：501-510

关键字：Fuzzy sets; cut sets; interval-valued level cut sets; decomposition theorems; representation theorems

摘要：In this paper, the concepts of interval-valued level cut sets on Zadeh fuzzy sets are presented axed new decomposition theorems of Zadeh fuzzy sets based on new cut sets are established. Firstly, four interval-valued level cut sets on Zadeh fuzzy sets are introduced, which are generalizations of the normal cut sets on Zadeh fuzzy sets and have the same properties as that of the normal cut sets on Zadeh frizzy sets. Secondly, based on these new cut sets, the new decomposition theorems of Zadeh fuzzy sets are established. It is pointed that each kind of interval-valued level cut sets corresponds to two decomposition theorems. Thus eight decomposition theorems are obtained. Finally, the definitions of L-inverse order nested sets and L-order nested sets are introduced and we established eight new representation theorems on Zadeh fuzzy sets by using the concept of new nested sets.