| 直觉模糊集的截集 |
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| 引用本文： | 李敏.直觉模糊集的截集[J].辽宁师范大学学报(自然科学版),2007,30(2):152-154. |
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| 作者姓名： | 李敏 |
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| 作者单位： | 东北财经大学数学与数量经济学院,辽宁大连116025 |
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| 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．
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| 关 键 词： | 直觉模糊集 截集 分解定理 表现定理 |
| 文章编号： | 1000-1735（2007）02-0152-03 |
| 修稿时间： | 2006-03-10 |
Cut sets of intuitionistic fuzzy sets |
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| LI Min.Cut sets of intuitionistic fuzzy sets[J].Journal of Liaoning Normal University(Natural Science Edition),2007,30(2):152-154. |
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| Authors: | LI Min |
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| Institution: | School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China |
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| Abstract: | 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. |
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| Keywords: | intuitionistic fuzzy sets cut sets decomposition theorem representation theorem |
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