中文摘要：

多粒度粗糙集本质上是异构的，但是目前尚未运用于异构数据处理．从绝对约简的角度出发，提出多粒度粗糙集的双层绝对约简——多粒度绝对约简和多粒度绝对粒度约简．分析多粒度双层绝对约简的性质，特别是从异构数据约简的角度探究多粒度双层绝对约简的特性，提出多粒度双层绝对约简算法．理论分析和实例表明多粒度双层绝对约简算法的可行性．

英文摘要：

Multi-granulation rough set is a rough set model for heterogenous data in essence. However, it is still not employed to deal with heterogenous data. From the viewpoints of absolute attribute reduction, double-level absolute reduction for multi-granulation rough sets is proposed, including multi-granulation absolute recducts and multi-granulation absolute granulation reducts, and properties of double-level absolute reduction are analyzed from the perspective of heterogenous data. The algorithms for double-level absolute reduction are presented. Theoretical analysis and example show the validation of multi-granulation absolute reducts, multi-granulation absolute granulation reducts and double-level absolute reducts.