基于粒计算的Rough集模型

GrC-based Rough Set Model

上近似、下近似是Rough集的基本定义,它使我们能够用精确的集合讨论不精确的概念,Rough集利用可计算的边界域实现了G.Frege的边界思想。然而,Rough集本身的代数定义和其他各种扩展模型并没有提供简单直观的计算边界元素数目的算法。在二进制粒计算的基础上,通过定义粒矩阵和粒矩阵运算,建立了基于粒计算的知识表示方法和基于粒计算的Rough集模型,据此可以获得Rough集基本概念的粒矩阵表示和粒矩阵快速计算方法,为建立基于粒计算的知识发现算法提供了理论基础。举例证明了Rough包含与Rough相等的隶属度函数定义并非充要条件。同时给出了基于粒计算的Rough包含与Rough相等的充要条件。

Upper approximation and lower approximation are the basic definitions in Rough Set Theory （RST）, it makes vague boundary computable, however, none of existing definition of RST brings efficient way to compute boundary. Based on Bit Granular Computing, Granular Matrix and its operation were defined and GrC-based RST model was established to complete the basic definition and computation of RST. The new model builds theoretic foundations for GrCbased knowledge discovery algorithms. Furthermore, modified sufficient and necessary conditions for rough inclusion and rough equivalent was proposed, some examples were given to illustrate the efficiency of the proposed model.