Rough Approximate Operators: Axiomatic Rough Set Theory
Rough Approximate Operators: Axiomatic Rough Set Theory
复制标题
DOI：
10.1007/978-1-4471-3238-7_31
复制
发表时间：
1993-10
期刊：
影响因子：
--
通讯作者：
T. Lin;Qing Liu
中科院分区：
文献类型：
--
作者：
T. Lin;Qing Liu
在粗糙集理论中，上下近似是根据等价关系定义的。在本文中，反向问题被认为是。设H和L是作用在论域U的幂集上的两个抽象算子。如果这两个算子满足六个公理，则存在定义在U上的等价关系，使得H（X）和L（X）恰好是上近似和下近似。这六个公理是从Kuratowski闭包算子的公理中得到的。证明是点集拓扑的一个简单应用。对于基于Frechet（V）空间的邻域系统（广义粗糙集理论）也得到了类似的结果（5个公理）。这些结果可以看作是公理化粗糙集理论的一个开端。
In rough set theory, the upper and lower approximations are defined in terms of equivalence relation. In this paper, the reverse problem is considered. Let H and L are two abstract operators acting on the power set of U, the universe of discourse. If the two operators satisfy six axioms, then there is an equivalence relation defined on U such that H(X) and L(X) are precisely the upper and lower approximations. The six axioms are adopted from the axioms of Kuratowski’s closure operator. The proof is an easy application of point set topology. Similar results (five axioms) are also obtained for neighborhood systems (a generalized rough set theory) which are based on Frechet (V)spaces. The results can be viewed as a beginning of an axiomatic rough set theory.