中文摘要：

本文研究了模糊粗糙集中属性约简问题.利用模糊粗糙集和多粒度粗糙集各自优点的结合,提出了两类多粒度模糊粗糙集模型,使得两类粗糙集中的上下近似算子关于负算子对偶.同时研究了多粒度模糊粗糙集的性质及与单粒度模糊粗糙集的关系.并通过构造区分函数的方法提出了一类多粒度模糊粗糙集模型的近似约简方法.最后用一个实例核对了该类多粒度模糊粗糙决策系统近似约简方法的有效性.

英文摘要：

In this paper,attribute reduction in fuzzy rough sets is studied.By the combination of advantage of rough set and multi-granulation fuzzy rough set,two type multi-granulation fuzzy rough set models are proposed,which make the upper and lower approximate sets be dual.Meanwhile,the properties of multi-granulation fuzzy rough set and their relations with single granulation fuzzy rough set are discussed.Furthermore,approximation reduction approach of a type of multi-granulation fuzzy rough set model is put forward by constructing discernibility functions.Finally,we examine the effectiveness of the approximation reduction approaches of multi-granulation fuzzy rough decision systems with a detailed example.