Metric-based L-fuzzy rough sets: Approximation operators and definable sets
Metric-based L-fuzzy rough sets: Approximation operators and definable sets
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DOI：
10.1016/j.knosys.2018.08.023
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
W. Yao;Yanhong She;Ling-Xia Lu
中科院分区：
文献类型：
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作者：
W. Yao;Yanhong She;Ling-Xia Lu
二元关系、覆盖和邻域系统/算子是研究粗糙集理论的有用工具。本文利用拓扑与分析中标准度量的弱版本——⊕-半度量的概念，作为研究L-模糊粗糙集理论的基本结构，其中L是一个完全剩馀格。定义了一对l -模糊上下逼近算子，研究了它们的性质和关系。对于L-fuzzy子集间的模糊包含关系的L-fuzzy阶，这两个算子都是单调的。L-模糊上逼近算子比下逼近算子有更好的性质，如果L是正则的，半对称的，则它们是对偶的。然后研究了该模型的上下可定义集。上可定义集合族构成Alexandrov分层l拓扑，而下可定义集合族则不一定。如果L是正则的（即使半对称不是对称的），则上可定义性与下可定义性重合。最后给出了基于度量的l -模糊集理论在加权图模糊聚类中的应用。
Binary relations, coverings and neighborhood systems/operators are useful tools to study rough set theory. In this paper, we use the notion of⊕-hemimetric, a weak version of the standard metric in topology and analysis, as the basic structure to study L-fuzzy rough set theory, where L is a complete residuated lattice. We define a pair of L-fuzzy upper and lower approximation operators and then investigate their properties and relations. It is shown that both operators are monotone with respect to the L-fuzzy order of fuzzy inclusion relation between L-fuzzy subsets. The L-fuzzy upper approximation operator has more nice properties than the lower one, and if L is regular and the hemimetric is symmetric, then they are dual to each other. We then study the upper and lower definable sets in this model. The family of upper definable sets forms an Alexandrov stratified L-topology while that of lower definable ones does not necessarily. If L is regular (even if the hemimetric is not symmetric), the upper definability coincides with the lower definability. We finally present an application of metric-based L-fuzzy set theory to fuzzy clustering for weighted graphs.