基于模糊纯度粒球的粗糙集模型  

Rough Set Model Based on Fuzzy Purity Granular Ball

作　　者：王馨 黄兵[1] WANG Xin;HUANG Bing(School of Computer Science,Nanjing Audit University,Nanjing 211815)

机构地区：[1]南京审计大学计算机学院,南京211815

出　　处：《模式识别与人工智能》2025年第3期221-232,共12页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.62276136)资助。

摘　　要：粒球邻域粗糙集(Granular Ball Neighborhood Rough Set,GBNRS)作为一种经典的属性约简方法,要求粒球的纯度严格为1,在类边界处会产生大量样本数为1的粒球.这些粒球通常被误判为离群点并剔除,导致类边界信息的丢失.为了解决此问题.文中首先定义模糊纯度函数,融合隶属度与类别标签,作为粒球质量的评价指标.此函数基于动态质量评估和优化策略,综合考虑数据点的隶属度、数据点的类标签及粒球的类标签三重信息.然后,在粒球分裂过程中,引入分类显著性阈值β,自适应调整M-means的m值,构建模糊纯度粒球生成算法.进一步地,针对粗糙集属性约简问题,设计前向属性约简算法,并提出基于模糊纯度粒球的粗糙集模型(Rough Set Model Based on Fuzzy Purity Granular Ball,FPGBRS).最后,在12个真实数据集上的实验表明,FPGBRS可提升分类精度和效率.As a classical attribute reduction method,granular ball neighborhood rough set(GBNRS)is constrained by the strict requirement that the purity of granular balls must be exactly 1.As a result,a large number of granular balls with a sample size of 1 are generated at the class boundaries.These granular balls are often misjudged as outliers and eliminated,and the loss of boundary information is caused.To address this issue,a fuzzy purity function is first defined.The function integrates membership degree and class labels as an evaluation metric for the quality of granular balls.Based on dynamic quality assessment and optimization strategies,the function takes into account three aspects:the membership degree of data points,the class labels of data points,and the class labels of granular balls.Nextly,during the granular ball splitting process,a classification significance threshold β is introduced,the m value of M-means is adaptively adjusted,and a granular ball generation method based on fuzzy purity is constructed.Furthermore,for the attribute reduction problem in rough set theory,a forward attribute reduction algorithm is designed,and a rough set model based on fuzzy purity granular ball(FPGBRS)is established.Finally,experiments on 12 real datasets demonstrate that FPGBRS can improve classification accuracy and efficiency.

关 键 词：粗糙集 粒球 粒计算 粒球邻域粗糙集(GBNRS) 属性约简 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]