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广义粗糙集是经典粗糙集的延伸,而拟阵论是线性代数和图论的推广.将拟阵与广义粗糙集结合,有利于充分利用拟阵的理论体系来发展粗糙集.本文建立了三种任意关系下粗糙集的拟阵结构,并利用拟阵的特征来研究粗糙集.首先,构造了基于任意关系下左邻域为空和右邻域为空的两个集族,并证明其满足拟阵的独立集公理,从而形成了两种拟阵结构.其次,研究了这两个拟阵的关系,继而利用这两个拟阵的特征来研究粗糙集中上下近似的关系.最后,研究了孤立集对于可定义集族的影响.构造了一个去掉孤立集后满足拟阵闭集公理的集族,进而形成一个拟阵.同时讨论了这个拟阵的特性,如独立集、极小圈、秩函数等.
The generalized rough set is an extension of the classical rough set, and the pseudo-matrix theory is a generalization of linear algebra and graph theory. Combining the quasi-matrix with the generalized rough set helps to make full use of the theoretical system of the pseudo-matrix to develop the rough set.In this paper, This paper studies the rough set based on the properties of the quasi-matrices.Firstly, we construct two sets that are based on the empty space in the left neighborhood and the empty space in the right neighborhood under arbitrary relations, and prove that Which satisfies the independent set of axioms of the quasi-matrices and forms two types of quasi-matrix structures.Secondly, the relationship between these two quasi-matrices is studied and the characteristics of the two quasi-matrices are used to study the relationship between the top and bottom approximations of the rough set.Finally, The influence of isolated set on the definable set is also studied. A set of clashes that satisfy the axiomatic set of closed set after removing the isolated set is constructed to form a quasi-matrix. The properties of the quasi-matrix, such as independent set, , Rank function and so on.