基于边界域的变精度粗糙集  

Variable precision rough sets based on boundary region

作　　者：马周明 王育齐 林依婷 MA Zhouming;WANG Yuqi;LIN Yiting(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,P.R.China;School of Computer Science,Minnan Normal University,Zhangzhou 363000,P.R.China;Digital Fujian Meteorological Big Data Research Institute,ZhangZhou 363000,P.R.China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]闽南师范大学计算机学院,福建漳州363000 [3]数字福建气象大数据研究所,福建漳州363000

出　　处：《重庆邮电大学学报（自然科学版）》2021年第5期751-758,共8页Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition)

基　　金：国家自然科学基金(11871259,61672272);福建省自然科学基金(2017J01507,2019J01748,2020J01812,2020J01792,2020J02043,2021J01979)。

摘　　要：粗糙集理论作为分类学习的一种工具,借助一对极值映射的一元算子,利用已知的知识结构表示未知的研究对象。具体主要体现在已知知识包含于未知对象集或与对象集相交不空。随着数据规模的不断增长以及数据形式的日趋复杂,严格意义的包含常常不能满足现实的需要。因此,经典粗糙集忽略了非常接近于严格包含的情况。变精度粗糙集放宽了严格包含关系。弥补了经典粗糙集理论的这一不足。然而,和经典粗糙集相比,变精度粗糙集不可避免地失去了一些基本性质。为了进一步探讨这些性质的本质内涵,在研究已有变精度粗糙集结构和性质的基础上,提出了3类基于边界域的变精度粗糙集模型,比较研究了这些模型之间的联系和区别。结果表明,第Ⅰ类变精度模型是已有变精度粗糙集模型的推广,第Ⅱ类变精度模型则是经典粗糙集的直接拓展形式之一。这2类变精度模型都侧重于从局部多数包含的角度刻画对象集。第Ⅲ类变精度模型侧重从对象集的整体边界域,即整体多数包含的角度描述了未知知识。Rough set theory,as a tool for classification learning,uses the known knowledge structure to represent the unknown research objects by means of a pair of unary operators of extremal mappings.It is mainly embodied in the fact that the known knowledge is contained in the unknown object set or intersects with the object set.With the continuous growing of data scale and the increasing complexity of data form,the strict inclusion relations often cannot meet the practical needs.So the classical rough sets ignore the cases that are very close to the strict inclusion relations.The variable precision rough set relaxes the strict inclusion relation.It makes up for the deficiency of the classical rough set theory.However,compared with the classical rough sets,the variable precision rough sets inevitably lose some basic properties.In order to further explore the essence of these properties,three types of models of variable precision rough sets based on boundary region are proposed on the basis of studying the structure and properties of the existing variable precision rough sets.And the connections and differences among these models are compared.The results show that the modelⅠof variable precision is a generalization of the existing variable precision rough set model.The modelⅡof variable precision is one of the direct developments of the classical rough set.The two types of variable precision models focus on describing object sets from the perspective of local majority inclusion relation.The variable precision modelⅢdescribes the unknown knowledge from the point of view of the whole boundary region of an object set,that is,the whole majority inclusion relation.

关 键 词：粗糙集 变精度 边界域 边界算子 近似算子 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]