变精度粗糙集推广模型及其性质研究

数据挖掘的主要目标之一是进行有效分类，粗糙集的上下近似空间正是为了对信息系统进行分类。变精度粗糙集作为经典粗糙集的推广模型，目前研究仅局限于有限集。针对变精度粗糙集模型无法处理无限集合的问题，在变精度粗糙集和测度的理论基础上，提出了基于Lebesgue测度的变精度粗糙集模型。首先，引入Lebesgue测度的概念，构造了一种基于Lebesgue测度的变精度粗糙集模型，将变精度粗糙集理论推广到无限集；其次，定义了该模型的上、下近似空间；最后，证明了其相关性质。通过理论研究表明，该模型能有效处理无限集合问题，对变精度粗糙集的理论研究形成突破，也将极大的扩充其应用范围。

Study on the extensions of the variable precision rough set and its proposition

One of the main goals of data mining is to make an effective classification, and the upper and lower approximation space of rough set is to classify the information system. The variable precision rough set is an extended model of rough set, however the research of the variable precision rough set has been limited to the finite set so far. To address the problem the variable precision rough set could not deal with the infinite set, this paper proposed the variable precision rough set model based on Lebesgue measure on the basis of the variable precision rough set and measure theory. Firstly, this paper introduced the Lebesgue measure, and it constructed the variable precision rough set model based on Lebesgue measure which extended the variable precision rough set to the infinite set; secondly, it defined the upper and lower approximation space of the new model; finally, it provided the properties. The theoretical study show that the new model can deal with the infinite set effectively. It will make a breakthrough in the theory of the variable precision rough sets, and greatly expand its scope of application.