基于三支决策的差别矩阵属性约简算法  

Attribute Reduction of Discernibility Matrix Based on Three-way Decision

作　　者：宋姝璇 张宇红 万仁霞 苗夺谦[2] SONG Shuxuan;ZHANG Yuhong;WAN Renxia;MIAO Duoqian(College of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China;Department of Computer Science and Technology,Tongji University,Shanghai 201804,China)

机构地区：[1]北方民族大学数学与信息科学学院,银川750021 [2]同济大学计算机科学与技术系,上海201804

出　　处：《计算机科学》2024年第S02期550-555,共6页Computer Science

基　　金：国家自然科学基金(62066001);宁夏自然科学基金(2021AAC03203);宁夏科技领军人才项目(2022GKLRLX08);北方民族大学研究生创新项目(YCX23088)。

摘　　要：属性约简是粗糙集理论研究的核心内容之一,也是粗糙集理论的重要组成部分。该方法旨在减少冗余信息,提取出最具代表性和关键性质的属性集合。在属性约简的过程中,差别矩阵通常用于度量属性之间的关系,通过分析差别矩阵,研究者可以识别那些在描述系统行为方面贡献相似信息的属性,从而进行属性约简。基于三支决策的差别矩阵属性约简算法从差别矩阵的属性出发,首先刻画核以外的属性重要度,并以三支决策理论为基础构建一种新的属性约简方法。算法将传统概率粗糙集的上、下近似划分为三支决策中的正域、负域、边界域,基于不同的区域给出了决策规则,并通过决策损失函数来控制三支决策阈值。与同类算法相比,所提算法可以得到更为简洁的约简集和决策规则,且具有更小的时间复杂度。Attribute reduction is one of the core contents of the study of rough set theory and a crucial component of the theory itself.This approach aims to minimize redundant information and extract a set of attributes that is both representative and pivotal.In the process of attribute reduction,a difference matrix is commonly employed to measure the relationships between attributes.By analyzing the difference matrix,researchers can identify attributes that contribute similar information in describing the system’s behavior,facilitating the process of attribute reduction.The three-decision-based difference matrix attribute reduction algorithm,starting from the attributes of the difference matrix,characterizes the importance of attributes beyond the core.It establishes a novel approach to attribute reduction based on the three-decision theory,dividing the upper and lower approximations of traditional probability rough sets into the positive region,negative region,and boundary region within the framework of three decisions.The proposed algorithm provides decision rules based on different regions and controls the three decision thresholds through a decision loss function.Compared to similar algorithms,it yields more concise reduction sets and decision rules,and has a lower time complexity.

关 键 词：三支决策 阈值 差别矩阵 重要度 属性约简 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]