基于覆盖粗糙集友元的粒约简研究

Research on the Granular Reduction of Friend Elements of Covering Rough Sets

随着粗糙集的发展,覆盖粗糙集在大数据方面有着较为广泛的应用,是粗糙集的重要组成部分.文章首先通过覆盖粗糙集友元的定义,给出基于友元的覆盖粗糙集上下近似的定义,研究上下近似的性质.其次,在给出上下近似的基础上,提出覆盖粗糙集的F约简和交约简,举例说明两者的不同之处.最后,证明任一覆盖粗糙集在F约简和交约简前后保持上下近似一致,同时证明用这两种约简方法约简前后粒度F是保持不变的.

Along with the development of rough sets,covering rough sets has been widely applied in large data and the major part of rough sets. Firstly,this paper,based on the friends of covering rough sets given theupper and lower approximations of friends,studies the properties of the upper and lower approximations. Then the paper based on the upper and lower approximations are givenFreduction and meet reduction of the covering rough sets,to prove the difference about them by the illustrate. Lastly the paper proves any covering rough sets before and after which are consistent by bothFreduction and meet reduction. At the same time, it proves both before and after of those reductions the granularFremain unchanged.