邻域系统粗糙集和覆盖粗糙集

邻域系统粗糙集和覆盖粗糙集是经典粗糙集的两种重要扩展。通过分别比较各模型中下(上)近似集之间的包含关系和近似精度之间的大小关系,深入探讨邻域系统粗糙集和6种覆盖粗糙集模型之间的关系,得出了邻域系统粗糙集和6种覆盖粗糙集模型的下(或上)近似集之间的关系是明确的,其要么是可以比较的,要么是不可以比较的,证明了可比较的具有包含甚至等价关系,不可比较的通过反例进行了佐证。对不同扩展粗糙集的对比研究加深了对这些模型的理解,同时也为宏观上学习和认识粗糙集提供了帮助。

Neighborhood System Based Rough Set and Covering Based Rough Set

Neighborhood system based rough set and covering based rough set arc two important expansions of the clas- sical rough set, I3y means of comparing the lower approximation sets, the upper approximation sets and accuracy meas- ures,thc relationships of neighborhood system based rough set and six covering based rough set models were systemati- cally studied. The conclusion is that the relationships between the lower or upper approximations of neighborhood sys- tem based rough set and six covering based rough set models are clear, either can be compared, or not. Under the compa- ruble situation, it was proved that there arc inclusion even equivalence relations. Under the incomparable situation, it was proved by counter-examples. The comparative study on different expansions of rough set not only provides a better un- derstanding of these models, but also gives a hand on learning rough set in the macroscopic level.