基于最小描述交的覆盖广义粗糙集  

Covering Generalized Rough Sets Based on the Intersection of Minimal Description

作　　者：张晓燕[1] 徐伟华[1] 张文修[2] 

机构地区：[1]重庆理工大学数学与统计学院,重庆400054 [2]西安交通大学理学院,陕西西安710049

出　　处：《模糊系统与数学》2011年第2期146-155,共10页Fuzzy Systems and Mathematics

基　　金：重庆理工大学青年科研项目

摘　　要：针对Bonikowski覆盖广义粗糙集模型的不足,给出了基于最小描述交的覆盖上下近似算子。通过和Pawlak经典粗糙集以及Bonikowski的覆盖广义粗糙集比较,发现给出的覆盖上、下近似算子具有了对偶关系,并得到了相关重要性质;进一步讨论了在新定义下覆盖广义粗糙集的约简和公理化问题,丰富了覆盖广义粗糙集理论,并为覆盖广义粗糙集的应用提供了更确切的理论根据。Bonikowski has got the model of covering generalized rough sets in [4],but there exist some shortcoming.In this paper,we propose new lower and upper approximations based on the intersection of minimal description.And some important properties have been acquired in the generalized rough set induced by a covering.Especially,it shows that the two approximations are dual approximation by comparing with ones of Pawlak＇s rough sets and Bonikowski＇s covering generalized rough sets respectively.Moreover,we investigate the covering reduction based on generalized rough sets with the new approximations and discuss some significant properties of axiomatization.

关 键 词：Pawlak粗糙集 Bonikowski覆盖近似 覆盖约简 公理化方法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]