面向缺失数据的多粒度粗糙集模型

Multi-granularity Rough Set Model for Missing Data

经典粗糙集理论关注的是论域上的单个二元等价关系导出的集合的近似。将等价关系弱化为相似关系、相容关系或邻域关系等可得到多种拓展粗糙集模型。但以粒计算的观点来看,这些模型都是单粒度的。本文把单粒度的粗糙集模型推广到不完备信息系统中的多粒度粗糙集模型,用论域上的多个相容关系定义了集合的近似。研究了含有缺失数据的多粒度粗糙集模型的一些数学性质,定义了不完备环境下的多粒度粗糙集模型的近似精度,实例表明多粒度粗糙集模型比单粒度粗糙集模型具有更高的精度。

The classical rough-set model is focused on the approximations of sets described by a single equivalence relation on a given universe. Many scholars have weakened the equivalence relation into similarity relation,compatible relationship or neighborhood,etc.,and have created a variety of rough set models. But with granular computing point of view,these rough-set models are based on a single granulation. This paper first extends the rough-set model based on a tolerance relation to an incomplete rough-set model based on multi-granulations,where set approximations are defined using multiple tolerance relations on the universe. We study some mathematical properties of this model,which contain missing data,and we also define the approximation accuracy of the multi-granularity rough set model which is proved to have a higher accuracy than the single particle rough set model.