分级粗糙集和分级知识约简  

Band Rough Set and Band Knowledge Reduction

作　　者：袁修久[1] 高生强[1] 杨宇[1] 

机构地区：[1]空军工程大学理学院,陕西西安710051

出　　处：《空军工程大学学报（自然科学版）》2009年第2期91-94,共4页Journal of Air Force Engineering University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60663003)

摘　　要：Pawlak粗糙集模型认为一个元素要么属于一个集合,要么不属于该集合,要么可能属于该集合,把可能属于该集合的元素的全体称为边界。Pawlak粗糙集模型对边界的研究较少。文章认为对边界的隶属度差别较小的元素以同一个量级属于边界,从而可按一个对象对边界的隶属量级对边界进行划分。基于这一思想提出了分级粗糙集模型和分级最大分布约简、分级分布约简的概念。给出了这两种约简的判定定理及辨识矩阵以及相应的核属性的等价条件。分级粗糙集模型推广了Pawlak粗糙集及变精度粗糙集模型。In Pawlak rough set model, an element is in a set, or not in the set, or possibly in the set. A subset of objects, possibly in the set is called boundary of the set. In the research on Pawlak rough set model, less is paid to the research of the boundary issue. In this paper, two objects with a few minor differences in the degree of membership in a set are viewed in the same level. From this view a partition of the boundary of a rough set is obtained and the concepts of band rough set and band distribution reduction and maximum distribution reduction are presented. The judgment theorems, discernibility matrices, equivalence condition of.core attribute association with band distribution reduction and band maximum distribution reduction are given . Band rough set model is a generalization of the Pawlak rough set and of the variable precision rough set model.

关 键 词：粗糙集 分级粗糙集 分级约简 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]