南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (2): 300.
马对霞*,祝 峰,林姿琼
Ma Duixia*,Zhu Feng,Lin Ziqiong
摘要: 粗糙拟阵是同时推广了粗糙集和拟阵的数学工具,它既可以被理解为是借助拟阵研究粗糙集,也可以被当作是通过粗糙集来研究拟阵.粗糙拟阵能够利用粗糙集和拟阵各自的优势处理和分析数据.通过等价关系上可定义集的性质,研究了基于等价关系的上粗糙拟阵和下粗糙拟阵.事实上,基于等价关系的上粗糙拟阵同时也是基于这个等价关系的下粗糙拟阵.因此给出了基于等价关系的粗糙拟阵的概念.类比拟阵中基的概念,定义了基于等价关系的粗糙拟阵的基,并且研究了这些基的性质.根据基的性质得到一个论域上所有的粗糙拟阵.特别地,讨论了论域的任何一个子集与该论域上的粗糙拟阵之间的某种对应关系.
[1] Zadeh L A.Fuzzy sets.Information and Control,1965,8(3):338-353. [2] Lin T Y.Granular computing on binary relations analysis of conflict and Chinese wall security policy.In:Rough Sets and Current Trends in Computing Springer Berlin Heidelberg.Malvern:Spring Press,2002,296-299. [3] Pawlak Z.Rough sets.International Journal of Computer and Information Science,1982,11(5):341-356. [4] Min F,He H,Qian Y,et al.Testcostsensitive attribute reduction.Information Sciences,2011,181(22):4928-4942. [5] Skowron A.Extracting laws from decision tables:A rough set approach.Computational Intelligence,1995,11(2):371-388. [6] Hu Q,Pan W,An S,et al.An efficient gene selection technique for cancer recognition based on neighborhood mutual information.International Journal of Machine Learning and Cybernetics,2010,1(1-4):63-74. [7] Dai J,Xu Q.Approximations and uncertainty measures in incomplete information systems.Information Sciences,2012,198:62-80. [8] Lawler E L.Combinatorial optimization:Networks and matroids.Courier Corporation,1976,76-391. [9] Dougherty R,Freiling C,Zeger K.Networks,matroids,and nonShannon information inequalities.IEEE Transactions on Information Theory,2007,53(6):1949-1969. [10] Huang A,Zhao H,Zhu W.Nullitybased matroid of rough sets and its application to attribute reduction.Information Sciences,2014,263:153-165. [11] Wang S,Zhu W.Matroidal structure of coveringbased rough sets through the upper approximation number.International Journal of Granular Computing,Rough Sets and Intelligent Systems,2011,2(2):141-148. [12] Wang S,Zhu Q,Zhu W,et al.Matroidal structure of rough sets and its characterization to attribute reduction.KnowledgeBased Systems,2012,36:155-161. [13] Yang B,Zhu W.Matroidal structure of generalized rough sets based on symmetric and transitive relations.In:The 26th Annual IEEE Canadian Conference on Electrical and Computer Engineering(CCECE2013).Regina:IEEE Press,2013,1-5. [14] 王石平,祝 峰,朱培勇等.基于抽象相关关系的粗糙集研究.南京大学学报(自然科学),2010,46(5):507-510.(Wang S P,Zhu F,Zhu P Y,et al.Abstract interdependency in rough sets.Journal of Nanjing University(Natural Sciences),2010,46(5):507-510.) [15] 苏礼润,林姿琼,祝 峰.一种覆盖粗糙集的拟阵结构.南京大学学报(自然科学),2013,49(5):561-566.(Su L R,Lin Z Q,Zhu F.A type of matroidal structure of covering-based rough sets.Journal of Nanjing University(Natural Sciences),2013,49(5):561-566.) [16] Zhu W,Wang S.Rough matroids based on relations.Information Sciences,2013,232(2013):241-252. [17] Yao Y Y.Constructive and algebraic methods of the theory of rough sets.Information Sciences,1998,109(1):21-47. [18] Zhu W.Relationship between generalized rough sets based on binary relation and covering.Information Sciences,2009,179(3):210-225. [19] 赖虹建.拟阵论.北京:高等教育出版社,2001,7-29. |
No related articles found! |
|