An axiomatic approach of fuzzy rough sets based on residuated lattices
An axiomatic approach of fuzzy rough sets based on residuated lattices
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DOI：
10.1016/j.camwa.2009.03.100
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发表时间：
2009-07
期刊：
影响因子：
--
通讯作者：
Yan She;Guo-Jun Wang
中科院分区：
文献类型：
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作者：
Yan She;Guo-Jun Wang
粗糙集理论是由Pawlak发展起来的一种对数据进行近似推理的形式化工具。在文献中已经提出了各种粗糙近似的模糊推广。作为粗糙集概念的进一步推广，Radzikowska和Kerre提出了L-fuzzy粗糙集。本文给出了L-fuzzy粗糙集的一个面向算子的刻画，即用公理定义L-fuzzy近似算子。L-fuzzy上、下集合论算子的公理化方法保证了产生这些算子的相应L-fuzzy关系的存在性。此外，还得到了L-模糊粗糙集与L-拓扑空间之间的关系。研究了由L-fuzzy拓扑空间导出的L-fuzzy内（闭包）算子可以与L-fuzzy自反传递关系相联系，使得相应的L-fuzzy下（上）近似算子是L-fuzzy内（闭包）算子的猜想的充要条件.
Rough set theory was developed by Pawlak as a formal tool for approximate reasoning about data. Various fuzzy generalizations of rough approximations have been proposed in the literature. As a further generalization of the notion of rough sets, L-fuzzy rough sets were proposed by Radzikowska and Kerre. In this paper, we present an operator-oriented characterization of L-fuzzy rough sets, that is, L-fuzzy approximation operators are defined by axioms. The methods of axiomatization of L-fuzzy upper and L-fuzzy lower set-theoretic operators guarantee the existence of corresponding L-fuzzy relations which produce the operators. Moreover, the relationship between L-fuzzy rough sets and L-topological spaces is obtained. The sufficient and necessary condition for the conjecture that an L-fuzzy interior (closure) operator derived from an L-fuzzy topological space can associate with an L-fuzzy reflexive and transitive relation such that the corresponding L-fuzzy lower (upper) approximation operator is the L-fuzzy interior (closure) operator is examined.