近似空间的笛卡尔积粗集模型及其可分解性

Cartesian Product Rough Model of Approximation Spaces and Decomposability

为处理人工智能中不精确和不确定的数据和知识,Pawlak提出了粗集理论。之后粗集理论得到拓广,人们提出了许多新的粗集模型。拓展的方法主要有两种,一种是减弱对等价关系的依赖,另一种是把讨论问题的论域从一个拓展到两个。Y.Y.Yao提出了一种基于两个论域的粗集模型。现研究基于两个近似空间的笛卡尔积粗集模型,给出了积近似空间的概念,刻画了可分解集合的上(下)近似、近似精度和粗糙度。最后研究了笛卡尔积粗集模型的可分解问题,给出了一个近似空间积可分解的充分必要条件。

Pawlak proposed the rough set model,in order to processing data and knowledge which are imprecise or uncertainty in artificial intelligence.Then,the rough set model has been extended and many new rough set models have been put forward.There are two main methods of extension,one method is to weaken the dependence of equivalence relation,the other is to expand the domain from one to two,and Y.Y.Yao ever proposed a rough set model of two-domain.In this paper,we made some research for cartesian product rough models based on two（finite） approximation spaces,and gave the concept of product approximation space.Afterwards,we described the upper（lower） approximation of decomposable subsets of a cartesian product,and the approximate precision and roughness of decomposable subsets.Finally,we studied the decomposable problem of cartesian product rough models,and obtained the sufficient and necessary conditions of decomposition of a product approximation space.