不完备系统中的多粒度粗糙集及其对比分析

Multigranulation rough set models and their comparisons in incomplete systems

多粒度方法是粗糙集理论中的一种新的数据处理模式.为了使得多粒度方法能够用于处理不完备信息系统,分别采用容差关系、相似关系和限制容差关系构建乐观和悲观多粒度粗糙集模型.不仅分析了这些多粒度粗糙集的基本性质,还对他们之间的关系进行了讨论,得出的结论是,基于限制容差关系的多粒度下近似介于基于容差关系和相似关系的多粒度下近似之间,基于限制容差关系的多粒度上近似介于基于容差关系和相似关系的多粒度下近似之间,这与单粒度框架下得到的结论一致.

Muhigranulation approach is a new data analyzing model in rough set theory. To deal with the incomplete information system through the multigranulation approach, the tolerance relations, similarity relations and limited tolerance relations are employed to construct optimistic and pessimistic multigtanulation rough sets, respectively. Not only are the basic properties about these multigranulation rough sets analyzed, but also the relationships among them discussed. It is shown that by the muhigranulation approach, the limited tolerance relations based multigranulation lower approximations fall between the tolerance and the similarity relations based multigranulation lower approximations, the limited tolerance relations based muhigranulation upper approximations fall between the similarity and the tolerance relations based muhigranulation upper approximations. Such results are consistent with those in single-granulation based rough sets models.