近似空间上粗糙路径的研究及应用

以Pawlak粗糙集理论中近似空间M=(U,R)为基础展开讨论,不采用粗糙集理论通常以上、下近似开始的做法,而是从M上二元关系S粗糙化后所得到的粗糙关系S觹出发,给出关于S粗糙路径的概念。同时,通过对跨度的定义与讨论,又建立起粗糙路径与上近似之间的联系,这是对粗糙路径研究所得到的重要性质。为了应用目的,构建了判定粗糙路径是否存在的路径矩阵。这为其系统化的应用奠定了基础。

Studies of Rough Paths in Approximate Space and Their Applications

Beginning with discussions based on Pawlak approximate space M=(U,R),and not adopting the method of upper and lower approximation which are in common use in rough set theory,this paper proceeds from a rough relation S that is produced by roughing a relation S on M,and defines the conception of rough path.At same time,through defining and discussing the span of a rough path,the connections between rough paths and upper approximation are found,and this is an important property for studying rough paths in this paper.For the aim of applications,a matrix which is used to determine whether there exists a rough path is constructed.It lays a foundation for the systematic applications of rough paths.