中文摘要：

文中深入研究了变精度粗糙集的属性约简问题,给出了3种属性约简的概念,针对不同概念的属性约简,分别提出了两种不同的求解变精度粗糙集最小属性约简算法：基于容差矩阵和属性核的最小约简.提出了变精度粗糙集的属性核思想,对其进行了形式化描述,说明了变精度粗糙集的属性核真正具备了核的本质特征,从而更深层地提出了基于属性核的启发式约简以求解最小约简.理论分析和实例表明,所提出的两种最小约简算法可以减小属性约简的搜索空间,提高约简的效率,使得变精度粗糙集的属性约简具有了实用性.

英文摘要：

The attributes reduction in Variable Precision Rough Set（VPRS） is researched by this paper thoroughly.We define different attributes reduction and propose two methods of calculating minimal reduction based on tolerance matrix and core of attributes.The core attributes concept is presented.We discuss some properties of core attributes,which means that attributes core has the essential character about feature of core and makes the attributes reduction in VPRS practical.The theoretical analysis and example demonstrate two methods of calculating minimal reduction proposed in this paper can reduce space of attributes reduction to improve the efficiency of calculating it.