区间值序信息系统中差别信息树的属性约简
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摘要
属性约简是粗糙集领域的一个热门研究课题,而差别矩阵是获得属性约简的有效方法。然而,差别矩阵含有重复元素,增加了获得约简所需要的时间。差别信息树的提出解决了差别矩阵含有重复元素的问题,实现了对差别矩阵中非空元素的压缩存储。但是差别信息树是在等价关系下的差别矩阵的基础上提出的,并没有考虑序决策信息系统的情况。在区间值序信息系统的背景下提出了基于可分辨矩阵的差别信息树,解决了可分辨矩阵中存在冗余元素的问题,实现了对可分辨矩阵中非空元素的压缩存储。得到了该树的相关性质定理并对其进行了验证,并在此基础上给出区间值序信息系统的基于差别信息树的完备的属性约简方法。最后给出了实证分析,验证了该方法的可行性以及有效性。
Attribute reduction is a hot topic in rough set, and discernibility matrix is an effective method to get attribute reduction. However, the discernibility matrix contains duplicate elements, which increases the time needed to get the reduction. The discernibility information tree solves the issue, and realizes the compression storage of the non-empty elements in the discernibility matrix. Unfortunately, the discernibility information tree is based on the discernibility matrix under the equivalence relation, and does not consider the situation of the ordered decision information system. In this paper, a discernibility information tree is proposed based on distinguishable matrix in interval-valued ordered information systems, which solves the problem of redundant elements in the distinguishable matrix and realizes the compression storage of non-empty elements in the distinguishable matrix. Furthermore, the related theorem of the tree is obtained and verified carefully. And, a complete attribute reduction method is given based on the discernibility information tree of the interval-valued ordered information system. Finally, an empirical analysis is addressed, which verifies the feasibility and effectiveness of the method.
Attribute reduction is a hot topic in rough set, and discernibility matrix is an effective method to get attribute reduction. However, the discernibility matrix contains duplicate elements, which increases the time needed to get the reduction. The discernibility information tree solves the issue, and realizes the compression storage of the non-empty elements in the discernibility matrix. Unfortunately, the discernibility information tree is based on the discernibility matrix under the equivalence relation, and does not consider the situation of the ordered decision information system. In this paper, a discernibility information tree is proposed based on distinguishable matrix in interval-valued ordered information systems, which solves the problem of redundant elements in the distinguishable matrix and realizes the compression storage of non-empty elements in the distinguishable matrix. Furthermore, the related theorem of the tree is obtained and verified carefully. And, a complete attribute reduction method is given based on the discernibility information tree of the interval-valued ordered information system. Finally, an empirical analysis is addressed, which verifies the feasibility and effectiveness of the method.
引文
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[8]Sang B B,Xu W H.Distribution reduction of intuitionistic fuzzy decision making information system[J].Computer Science,2017,44(S1):164-170.
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[13]Wang B,Chen S B.A complete algorithm for attribute reduction based on discernibility matrix[J].Journal of Shanghai Jiao Tong University,2004,38(1):43-46.
[14]Yang M,Yang P.A novel condensing tree structure for rough set feature selection[J].Neurocomputing,2008,71(4):1092-1100.
[15]Jiang Y.Rough set attribute reduction algorithm based on differential information tree[J].Control and Decision,2015,30(8):1531-1536.
[16]Xu W H.Preface information system and rough set[M].Beijing:Science Press,2013.
[2]张小红,裴道武,代建华.模糊数学与Rough集理论[M].北京:清华大学出版社,2013.
[3]徐伟华,张文修.基于优势关系下不协调目标信息系统的分布约简[J].模糊系统与数学,2007,21(4):124-131.
[4]米据生,吴伟志,张文修.不协调目标信息系统知识约简的比较研究[J].模糊系统与数学,2003,17(3):54-60.
[5]桑彬彬,徐伟华.直觉模糊序决策信息系统的分布约简[J].模糊系统与数学,2017,31(2):164-170.
[6]张文修,米据生,吴伟志.不协调目标信息系统的知识约简[J].计算机学报,2003,26(1):12-18.
[7]徐伟华,张文修.基于优势关系下不协调目标信息系统的知识约简[J].计算机科学,2006,33(2):182-184.
[8]桑彬彬,徐伟华.直觉模糊序决策信息系统的分配约简[J].计算机科学,2017,44(S1):164-170.
[11]蒋瑜,王燮,叶振.基于差别矩阵的Rough集属性约简算法[J].系统仿真学报,2008,20(14):3717-3720.
[12]蒋瑜,王鹏,王燮,等.基于差别矩阵的属性约简完备算法[J].计算机工程与应用,2007,43(19):185-187.
[13]王兵,陈善本.一种基于差别矩阵的属性约简完备算法[J].上海交通大学学报,2004,38(1):43-46.
[15]蒋瑜.基于差别信息树的Rough Set属性约简算法[J].控制与决策,2015,30(8):1531-1536.
[16]徐伟华.序信息系统与粗糙集[M].北京:科学出版社,2013.
[2]Zhang X H,Pei D W,Dai J H.Fuzzy mathematics and rough set theory[M].Beijing:Tsinghua University Press,2013.
[3]Xu W H,Zhang W X.Distribution reduction of information systems with inconsistent objectives based on dominance relations[J].Fuzzy Systems and Mathematics,2007,21(4):124-131.
[4]Mi J S,Wu W Z,Zhang W X.A comparative study of knowledge reduction in inconsistent objective information systems[J].Fuzzy Systems and Mathematics,2003,17(3):54-60.
[5]Sang B B,Xu W H.Distribution reduction of intuitionistic fuzzy ordered decision information systems[J].Fuzzy Systems and Mathematics,2017,31(2):164-170.
[6]Zhang W X,Mi J S,Wu W Z.Inconsistent knowledge reduction of target information system[J].Journal of Computer Science,2003,26(1):12-18.
[7]Xu W H,Zhang W X.Knowledge reduction in inconsistent information systems based on dominance relations[J].Computer Science,2006,33(2):182-184.
[8]Sang B B,Xu W H.Distribution reduction of intuitionistic fuzzy decision making information system[J].Computer Science,2017,44(S1):164-170.
[9]Thangavel K,Pethalakshmi A.Dimensionality reduction based on rough set theory:a review[J].Applied Soft Computing Journal,2009,9(1):1-12.
[10]Skowron A,Rauszer C.The discernibility matrices and functions in information systems[J].Intelligent Decision Support,1992,11:331-362.
[11]Jiang Y,Wang X,Ye Z.Attribute reduction algorithm of rough sets based on discernibility matrix[J].Journal of System Simulation,2008,20(14):3717-3720.
[12]Jiang Y,Wang P,Wang X,et al.Complete algorithm of attribute reduction based on discernibility matrix[J].Computer Engineering and Applications,2007,43(19):185-187.
[13]Wang B,Chen S B.A complete algorithm for attribute reduction based on discernibility matrix[J].Journal of Shanghai Jiao Tong University,2004,38(1):43-46.
[14]Yang M,Yang P.A novel condensing tree structure for rough set feature selection[J].Neurocomputing,2008,71(4):1092-1100.
[15]Jiang Y.Rough set attribute reduction algorithm based on differential information tree[J].Control and Decision,2015,30(8):1531-1536.
[16]Xu W H.Preface information system and rough set[M].Beijing:Science Press,2013.
[2]张小红,裴道武,代建华.模糊数学与Rough集理论[M].北京:清华大学出版社,2013.
[3]徐伟华,张文修.基于优势关系下不协调目标信息系统的分布约简[J].模糊系统与数学,2007,21(4):124-131.
[4]米据生,吴伟志,张文修.不协调目标信息系统知识约简的比较研究[J].模糊系统与数学,2003,17(3):54-60.
[5]桑彬彬,徐伟华.直觉模糊序决策信息系统的分布约简[J].模糊系统与数学,2017,31(2):164-170.
[6]张文修,米据生,吴伟志.不协调目标信息系统的知识约简[J].计算机学报,2003,26(1):12-18.
[7]徐伟华,张文修.基于优势关系下不协调目标信息系统的知识约简[J].计算机科学,2006,33(2):182-184.
[8]桑彬彬,徐伟华.直觉模糊序决策信息系统的分配约简[J].计算机科学,2017,44(S1):164-170.
[11]蒋瑜,王燮,叶振.基于差别矩阵的Rough集属性约简算法[J].系统仿真学报,2008,20(14):3717-3720.
[12]蒋瑜,王鹏,王燮,等.基于差别矩阵的属性约简完备算法[J].计算机工程与应用,2007,43(19):185-187.
[13]王兵,陈善本.一种基于差别矩阵的属性约简完备算法[J].上海交通大学学报,2004,38(1):43-46.
[15]蒋瑜.基于差别信息树的Rough Set属性约简算法[J].控制与决策,2015,30(8):1531-1536.
[16]徐伟华.序信息系统与粗糙集[M].北京:科学出版社,2013.