On intuitionistic fuzzy rough sets and their topological structures
On intuitionistic fuzzy rough sets and their topological structures
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论直觉模糊粗糙集及其拓扑结构
DOI：
10.1080/03081070802187723
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发表时间：
2009-07
影响因子：
2
通讯作者：
Zhang, Wen-Xiu
中科院分区：
文献类型：
--
作者：
Wu, Wei-Zhi;Zhou, Lei;Zhang, Wen-Xiu
本文首先定义了直觉模糊集关于直觉模糊逼近空间的上、下逼近。研究了直觉模糊逼近算子的性质。然后讨论了直觉模糊粗糙集近似与直觉模糊拓扑之间的关系。证明了基于直觉模糊自反传递逼近空间的所有下近似集构成直觉模糊拓扑；反之，对于直觉模糊粗糙拓扑空间，存在直觉模糊自反传递逼近空间，使得直觉模糊粗糙拓扑空间中的拓扑恰好是直觉模糊自反传递逼近空间中所有下近似集的集合。也就是说，所有直觉模糊自反和传递逼近空间的集合与所有直觉模糊粗糙拓扑空间的集合之间存在一一对应关系。最后，研究了直觉模糊粗糙近似框架下的直觉模糊伪闭包算子。
In this paper, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of intuitionistic fuzzy approximation operators are examined. Relationships between intuitionistic fuzzy rough set approximations and intuitionistic fuzzy topologies are then discussed. It is proved that the set of all lower approximation sets based on an intuitionistic fuzzy reflexive and transitive approximation space forms an intuitionistic fuzzy topology; and conversely, for an intuitionistic fuzzy rough topological space, there exists an intuitionistic fuzzy reflexive and transitive approximation space such that the topology in the intuitionistic fuzzy rough topological space is just the set of all lower approximation sets in the intuitionistic fuzzy reflexive and transitive approximation space. That is to say, there exists an one-to-one correspondence between the set of all intuitionistic fuzzy reflexive and transitive approximation spaces and the set of all intuitionistic fuzzy rough topological spaces. Finally, intuitionistic fuzzy pseudo-closure operators in the framework of intuitionistic fuzzy rough approximations are investigated.
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DOI：
10.1007/978-3-319-99368-3
发表时间：
2018-10
期刊：
--
影响因子：
--
作者：
R. Efendi;Voni Apriana Dewi;Rahmadeni;Sri Basriati;Dadang Syarif
通讯作者：
R. Efendi;Voni Apriana Dewi;Rahmadeni;Sri Basriati;Dadang Syarif
影响因子：
--
作者：
ZADEH, LA
通讯作者：
ZADEH, LA
DOI：
10.1016/s0020-0255(02)00180-9
发表时间：
2002-07
期刊：
Inf. Sci.
影响因子：
--
作者：
Weizhi Wu;Wenxiu Zhang
通讯作者：
Weizhi Wu;Wenxiu Zhang
影响因子：
2
作者：
D. Pei
通讯作者：
D. Pei
DOI：
10.1007/978-1-4471-3238-7_31
发表时间：
1993-10
期刊：
--
影响因子：
--
作者：
T. Lin;Qing Liu
通讯作者：
T. Lin;Qing Liu