Abstract: The traditional rough set theory is based on the set theory. It can be found that upper and lower approximation operators have some shortcomings in the description of function. This paper puts forward the definition of upper and lower rough function in view of scale, which can confirm strict partition of a monotone real function defined in the integer, then form rough function model of real domain. It establishes the corresponding Galois concept lattice in light of the analysis of rough function model. It simplifies the property of lattice concept by discernibility matrix.

Key words: scale, Galois lattice, rough function

摘要： 传统粗糙集理论源于集合论平台，其上、下近似算子在描述函数方面存在缺陷。针对该问题，利用定义在整数轴上能严格划分出单调实函数的标度工具，提出上、下粗糙函数概念，形成实数域上的粗糙函数模型。构建与其匹配的Galois格，并通过可辨识矩阵对其概念格进行了知识约简。

关键词: 标度, Galois格, 粗糙函数

CLC Number: 

• TP18