两类广义粗糙集的拟阵结构

Two types of matroidal structure of generalized rough sets

基于邻域粗糙集模型和覆盖粗糙集模型,分别构造了两类拟阵结构,即邻域上近似数诱导的拟阵和覆盖上近似数诱导的拟阵。一方面,通过广义粗糙集定义了两类上近似数,并证明了它们满足拟阵理论中的秩公理,从而由秩函数的观点出发得到了两类拟阵;另一方面,利用粗糙集方法研究了这两类拟阵的独立集、极小圈、闭包、闭集等的表达形式,说明了粗糙集中的上近似算子与拟阵中的闭包算子的关系,进一步通过探讨覆盖和拟阵的关系,得到了覆盖中的元素及其任意并是由覆盖上近似数诱导的拟阵的闭集。

Based on neighborhood-based rough set model and covering-based rough set model,two matroidal structures which were matroid induced by neighborhood upper approximation number and matroid induced by covering upper approximation number were constructed. On one hand,two types of upper approximation number were defined through generalized rough set,and they were proven to satisfy rank function axiom in matroid theory,thus two types of matroids were obtained from the viewpoint of the rank function. On the other hand,some properties,such as independent sets,circuits,closures,closed sets,were proposed through rough set approach. Moreover,the concentions between upper approximation operators and closure operators were investigated. Futhuremore,the relationship between the covering and the matroid was studied. Result shows that elements and any union of them in covering are the closed sets of matroid induced by covering upper approximation number.