统计粗糙集

发布时间：2018-04-22 17:20

本文选题：随机抽样 + 近似算子　；参考：《软件学报》2016年07期

【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.
[Abstract]:Due to the complexity of the basic theory, the existing fuzzy rough set method can not be applied to large-scale data sets. Considering that random sampling is a statistical method which can greatly reduce the computational complexity, a statistical rough set model is established by introducing random sampling into the classical fuzzy rough set theory. Firstly, the concept of statistical lower approximation is proposed, which is superior to the classical fuzzy rough set model in that the large scale complete set is replaced by the small volume samples obtained by random sampling, thus the computational complexity is reduced significantly. Moreover, as the number of samples increases, the number of samples does not increase significantly. In addition, the properties of statistical upper approximation and lower approximation are discussed, and the relationship between statistical upper, lower approximation and classical upper approximation is revealed. Furthermore, a theorem is proposed, which ensures that the statistical errors of statistical lower approximation and classical lower approximation are within the allowable range. Finally, the numerical experiments show that the statistical approximation has a significant advantage in computing time.
【作者单位】：数据工程与知识工程教育部重点实验室(中国人民大学);中国人民大学信息学院计算机系;
【基金】：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)~~
【分类号】：TP18

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