JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (08): 97-101.doi: 10.6040/j.issn.1671-9352.1.2014.034

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Computing minimal description and maximal description in covering-based rough sets through matrices

LIN Zi-qiong, WANG Jing-qian, ZHU William   

  1. Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, Fujian, China
  • Received:2014-06-02 Revised:2014-07-08 Published:2014-09-24

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Abstract: The minimal description and maximal description in covering-based rough sets are computed through matrices. Firstly, some significant matrices about coverings are presented through the matrix representation of a covering. Secondly, according to these proposed matrices and a new matrix operation, the minimal description and maximal description in covering-based rough sets are computed from the viewpoint of matrices.

Key words: minimal description, maximal description, matrix, covering-based rough set

CLC Number: 

  • TP18
[1] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5):341-356.
[2] 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. WU Zhengjiang, ZHANG Jingmin, GAO Yan. Attribute reduction algorithm based on genetic algorithms and discernable matrixes[J]. Computer Engineering and Applications, 2014, 50(2):120-123.
[3] HU Qinghua, AN Shuang, YU Daren. Soft fuzzy rough sets for robust feature evaluation and selection[J]. Information Sciences, 2010, 180(22):4384-4400.
[4] YANG Xibei, XIE Jun, SONG Xiaoning, et al. Credible rules in incomplete decision system based on descriptors[J]. Knowledge-Based Systems, 2009, 22(1):8-17.
[5] ZHONG Ning. Rough sets in knowledge discovery and data mining[J]. Journal of Japan Society for Fuzzy Theory and Systems, 2001, 13:581-591.
[6] ZAKOWSKI W. Approximations in the space (U,Ⅱ)[J]. Demonstration Mathematical, 1983, 16:761-769.
[7] BONILOWSKI Z, BRYNIARSKI E, WYBRANIEC-SKARDOWSKA U. Extensions and intentions in the rough set theory[J]. Information Sciences, 1998, 107(1):149-167.
[8] ZHU William, WANG Feiyue. A new type of covering rough sets[C]//Proc of the 3rd IEEE International Conf on Intelligent Systems. London: IEEE Computer Society, 2006:444-449.
[9] ZHU William, WANG Feiyue. On three types of covering-based rough sets[J]. Knowledge and Data Engineering, IEEE Transactions on, 2007, 19(8):1131-1144.
[10] FU Li. The minimal description of formal concept analysis[J]. Journal of Mathematics Research, 2010, 2(1):69-73.
[11] 张晓燕, 徐伟华, 张文修. 基于最小描述交的覆盖广义粗糙集[J]. 模糊系统与数学, 2011, 25(2):146-155. ZHANG Xiaoyan, XU Weihua, ZHANG Wenxiu. Covering generalized rough sets based on the intersection of minimal description[J]. Fuzzy Systems and Mathematics, 2011, 25(2):146-155.
[12] 黄婧, 李进金. 最小描述的多粒度覆盖粗糙集模型[J]. 计算机工程与应用, 2013, 49(9):134-149. HUANG Jing, LI Jinjin. Covering rough sets model based on multi-granulation of minimal description[J]. Computer Engineering and Applications, 2013, 49(9):134-139.
[13] WANG Zhaohao, SHU Lan, DING Xiuyong. Minimal description and maximal description in covering-based rough sets[J]. Fundamenta Informaticae, 2013, 128(4):503-526.
[14] SKOWRON A, SWINIARSKI R, SYNAK P. Approximation spaces and information granulation[C]. Rough Sets and Current Trends in Computing. Berlin: Springer, 2004: 116-126.
[15] 苗夺谦, 李道国. 粗糙集理论, 算法与应用[M].北京:清华大学出版社, 2008. MIAO Duoqian, LI Daoguo. Rough set theory, algorithm and its application[M]. Beijing: Qinghua University press, 2008.
[16] 刘贵龙. 基于两个集合上粗集模型的算法实现[J]. 计算机科学, 2006, 33(3):181-184. LIU Guilong. The algorithms of rough sets based on two universes[J]. Computer Science, 2006, 33(3):181-184.
[17] LIU Guilong. The axiomatization of the rough set upper approximation operations[J]. Fundamenta Informaticae, 2006, 69(3):331-342.
[18] WANG Jingqian, ZHU William, WANG Feiyue, et al. Conditions for coverings to induce matroids[J]. International Journal of Machine Learning and Cybernetics, 2014: 1-8.
[19] 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. SUN Feng, WANG Jingqian. Graph representation and 2-part matrix of covering-based rough sets[J]. Computer Science, 2014, 41(3):85-87.
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