矩阵方法计算加权变精度广义粗糙集
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摘要
文章通过矩阵理论计算加权变精度广义粗糙集的上、下近似。首先,根据加权经典粗糙集模型,提出加权变精度广义粗糙集的概念;然后,用矩阵方法计算加权变精度广义粗糙集的上、下近似;最后,给出矩阵计算加权变精度广义粗糙集的上、下近似的算法。
In this paper,the lower and upper approximation operators in weighted variable precision generalized rough sets are computed through matrices.Firstly,the concepts of weighted variable precision generalized rough sets are proposed based on weighted classical rough sets.Secondly,the lower and upper approximation operators in weighted variable precision generalized rough sets are computed from the viewpoint of weighted matrices.Finally,an algorithm to compute the lower and upper approximations is established.
In this paper,the lower and upper approximation operators in weighted variable precision generalized rough sets are computed through matrices.Firstly,the concepts of weighted variable precision generalized rough sets are proposed based on weighted classical rough sets.Secondly,the lower and upper approximation operators in weighted variable precision generalized rough sets are computed from the viewpoint of weighted matrices.Finally,an algorithm to compute the lower and upper approximations is established.
引文
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[13]巩增泰,孙秉珍,邵亚斌,等.一般关系下的变精度粗糙集模型[J].兰州大学学报:自然科学版,2006,41(6):110-114.
[14]张明,程科,杨习贝,等.基于加权粒度的多粒度粗糙集[J].控制与决策,2015,30(2):222-228.
[15]Skowron A,Swiniarski R,Synak P.Approximation spaces and information granulation[C].Rough Sets and Current Trends in Computing.Springer Berlin Heidelberg,2004:116-126.
[16]孙峰,王敬前.覆盖粗糙集的图表示和2-部矩阵[J].计算机科学,2014,41(3):85-87.
[17]Liu G L.The axiomatization of the rough set upper approximation operations[J].Fundamenta Informaticae,2006,69(3):331-342.
[18]Wang S P,Zhu W,Zhu Q X,et al.Characteristic matrix of covering and its application to Boolean matrix decomposition[J].Information Sciences,2014,263:186-197.
[19]林姿琼,王敬前,祝峰.矩阵方法计算覆盖粗糙集中最小,最大描述[J].山东大学学报(理学版),2014,49(08):97-101.
[20]Wang J Q,Zhu W.Applications of matrices to a matroidal structure of rough sets[J].Journal of Applied Mathematics,2013,2013.
[2]Ziarko W.Variable precision rough set model[J].Journal of computer and system sciences,1993,46(1):39-59.
[3]余鹰,苗夺谦,刘财辉,等.基于变精度粗糙集的KNN分类改进算法[J].模式识别与人工智能,2012,25(4):617-623.
[4]Mi J S,Wu W Z,Zhang W X.Approaches to knowledge reduction based on variable precision rough set model[J].Information sciences,2004,159(3):255-272.
[5]马廷淮,唐美丽,潘锦基.加权粗糙集模型[J].计算机应用,2007,7:1744-1747.
[6]杨勇,鲁小云,李廉.加权粗糙集的矩阵表示[J].计算机工程与应用,2009,44(18):34-35.
[7]吴正江,张静敏,高岩.遗传算法与区分矩阵的属性约简算法[J].计算机工程与应用,2014,50(2):120-123.
[8]Hu Q H,An S,Yu D R.Soft fuzzy rough sets for robust feature evaluation and selection[J].Information Sciences,2010,180(22):4384-4400.
[9]Yang X B,Xie J,Song X N,et al.Credible rules in incomplete decision system based on descriptors[J].Knowledge-Based Systems,2009,22(1):8-17.
[10]Zhong N.Rough sets in knowledge discovery and data mining[J].Journal of Japan Society for Fuzzy Theory and Systems,2001,13:581-591.
[11]Zhu W.Generalized rough sets based on relations[J].Information Sciences,2007,177(22):4997-5011.
[12]孙士保,普杰信,秦克云.广义变精度粗糙集模型中近似算子研究[J].计算机科学,2007,34(9):194-197.
[13]巩增泰,孙秉珍,邵亚斌,等.一般关系下的变精度粗糙集模型[J].兰州大学学报:自然科学版,2006,41(6):110-114.
[14]张明,程科,杨习贝,等.基于加权粒度的多粒度粗糙集[J].控制与决策,2015,30(2):222-228.
[15]Skowron A,Swiniarski R,Synak P.Approximation spaces and information granulation[C].Rough Sets and Current Trends in Computing.Springer Berlin Heidelberg,2004:116-126.
[16]孙峰,王敬前.覆盖粗糙集的图表示和2-部矩阵[J].计算机科学,2014,41(3):85-87.
[17]Liu G L.The axiomatization of the rough set upper approximation operations[J].Fundamenta Informaticae,2006,69(3):331-342.
[18]Wang S P,Zhu W,Zhu Q X,et al.Characteristic matrix of covering and its application to Boolean matrix decomposition[J].Information Sciences,2014,263:186-197.
[19]林姿琼,王敬前,祝峰.矩阵方法计算覆盖粗糙集中最小,最大描述[J].山东大学学报(理学版),2014,49(08):97-101.
[20]Wang J Q,Zhu W.Applications of matrices to a matroidal structure of rough sets[J].Journal of Applied Mathematics,2013,2013.