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| 统计粗糙集 |
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陈俞1,2, 赵素云1, 陈红1,2, 李翠平1,2, 孙辉1,2
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1.数据工程与知识工程教育部重点实验室(中国人民大学), 北京 100872;2.中国人民大学 信息学院 计算机系, 北京 100872
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| 摘要: |
| 现有的模糊粗糙集方法,由于其基础理论复杂度的桎梏,无法应用到大规模数据集上.考虑到随机抽样是一种可以极大地减少运算量的统计学方法,将随机抽样引入到经典的模糊粗糙集理论中,建立了一种统计粗糙集模型.首先,提出了统计上、下近似的概念,它相比经典模糊粗糙集模型的优势在于,以随机抽样得到的小容量样本代替了大规模全集,从而显著降低了计算量.而且,随着全集数量的增大,抽样样本数量并不会显著增大.此外,还讨论了统计上、下近似的性质,揭示统计上、下近似和经典上、下近似之间的关系.并且,提出了一个定理,该定理保证了统计下近似与经典下近似的取值统计误差在允许的范围内.最后,通过数值实验验证了统计下近似在计算时间上的显著优势. |
| 关键词: 随机抽样 近似算子 统计粗糙集 模糊粗糙集 |
| DOI：10.13328/j.cnki.jos.005036 |
| 分类号: |
| 基金项目:国家重点基础研究发展计划(973)(2012CB316205);国家高技术研究发展计划(863)(2014AA015204);国家自然科学基金(61532021,61202114,61272137);中国人民大学科学研究基金(15XNLQ06) |
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| Statistical Rough Sets |
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CHEN Yu1,2, ZHAO Su-Yun1, CHEN Hong1,2, LI Cui-Ping1,2, SUN Hui1,2
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1.Key Laboratory of Data Engineering and Knowledge Engineering, MOE(Renmin University of China), Beijing 100872, China;2.Department of Computer Science, School of Information, Renmin University of China, Beijing 100872, China
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| Abstract: |
| This paper introduces random sampling into traditional fuzzy rough methods and proposes a random sampling based statistical rough set model. The work focuses on how to bring random sampling into traditional rough set. First, random sampling is used to propose a concept of k-limit, which can dramatically reduce the amount of computation during the computing of lower approximation value. Then, statistical upper and lower approximation is formulated. By mathematical reasoning, sufficient theorem and proof are used to valid the reliability of new model. Finally, numerical experiments illustrate the efficiency of the proposed statistical rough sets. |
| Key words: random sampling approximate operator statistical rough set fuzzy rough set |
