A Non-boolean Lattice Derived by Double Indiscernibility
A Non-boolean Lattice Derived by Double Indiscernibility
复制标题
DOI：
10.1007/978-3-642-14467-7_11
复制
发表时间：
2010-01-01
期刊：
影响因子：
--
通讯作者：
Haruna, Taichi
中科院分区：
文献类型：
--
作者：
Gunji, Yukio-Pegio;Haruna, Taichi
粗糙集的中心概念是基于等价关系的不可约性。由于等价关系在等价类中表现出强束缚，它形成了伽罗瓦连接，并且失去了上下近似之间的差异。在这里，我们引入了两个不同的等价关系，一个用于上近似，一个用于下近似，并构造了一个复合近似算子组成的不同的等价关系。我们证明了一个关于算子的不动点的集合是一个格，并且存在一个表示定理。
The central notion of a rough set is the indiscernibility that is based on an equivalence relation. Because an equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between the upper and lower approximations is lost. Here, we introduce two different equivalence relations, one for the upper approximation and one for the lower approximation, and construct a composite approximation operator consisting of different equivalence relations. We show that a collection of fixed points with respect to the operator is a lattice and there exists a representation theorem for that construction.