Concept Lattice Attribute Reduction Based on Intersectional Reducible Equivalence Class
LIN Pei-Rong1,ZHANG Qi-Sen2,LI Jin-Jin2
1.Department of Computer Science and Engineering,Zhangzhou Normal University,Zhangzhou 363000 2.Department of Mathematics and Information Science,Zhangzhou Normal University,Zhangzhou,363000
Abstract The concepts of intersectional reducible equivalence class and intersectional reducible element are introduced. The concept lattice attribute reduction and reduction algorithm based on intersectional reducible elements are studied, and attribute characters of different kinds are obtained. The linked list is used to show the logical structure of formal context, and based on the number of extension objects, the index is built to rapidly judge the validity of the intersection operation on attribute reduction. All unnecessary attributes are found out according to the different roles of attributes to intersection operation. Finally, the concept lattice attribute reduction is achieved.
[1] Wille R. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts // Proc of the 7th International Conference on Formal Concept Analysis. Darmstadt, Germany, 2009: 314-339 [2] Yao Yiyu. A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis // Proc of the 4th International Conference on Rough Sets and Current Trends in Computing. Uppsala, Sweden, 2004: 59-68 [3] Maddouri M. Towards a Machine Learning Approach Based on Incremental Concept Formation. Intelligent Data Analysis, 2004, 8(3): 267-280 [4] Burmeister P. Formal Concept Analysis with ConImp: Introduction to the Basic Features [EB/OL]. [2003-01-18]. http://www.mathematik.tu-darmstadt.de/～burmeister/ComImp Intro.pdf [5] Kent R E. Rough Concept Analysis: A Synthesis of Rough Sets and Formal Concept Analysis. Foundation Information, 1996, 27(2/3): 169-181 [6] Ganter B, Wille R. Formal Concept Analysis: Mathematical Foundations. Berlin, Germany: Springer, 1999 [7]Zhang Wenxiu, Wei Ling, Qi Jianjun. Attribute Reduction Theory and Approach to Concept Lattice. Science in China: Series E, 2005, 35(6): 628-639 (in Chinese) (张文修,魏 玲,祁建军.概念格的属性约简理论与方法.中国科学E辑, 2005, 35(6): 628-639) [8]Shao Mingwen. The Reduction for Two Kind of Generalized Concept Lattice // Proc of the 4th International Conference on Machine Learning and Cybernetics. Guangzhou, China, 2005, Ⅳ: 2217-2222 [9]Yao Yiyu, Chen Yaohua. Rough Set Approximations in Formal Concept Analysis // Deters J F, Skowron A, eds. Trans on Rough Set V. Berlin, Germany: Springer, 2006: 285-305 [10]Li Hongru, Zhang Wenxiu, Wang Hong. Classification and Reduction of Attributes in Concept Lattices // Proc of the IEEE International Conference on Granular Computing. Los Alamitos, USA, 2006: 142-147 [11]Li Lifeng, Wang Guojun. A Method to Explore the Reduction of Concept Lattice. Computer Engineering and Applications, 2006, 42(20): 147-149,216 (in Chinese) (李立峰,王国俊.一种求概念格属性约简的方法.计算机工程与应用, 2006, 42(20): 147-149,216) [12] Qiu Guofang, Chen Jin. Rule Reductions and Characters of Attributes in Concept Lattices. Journal of Zhejiang University: Science Edition, 2007, 34(2): 158-162 (in Chinese) (仇国芳,陈 劲.概念格的规则约简与属性特征.浙江大学学报:理学版, 2007, 34(2): 158-162) [13] Wang Xia, Zhang Wenxiu. Attribute Reduction in Concept Lattices and Attribute Characteristics. Computer Engineering and Applications, 2008, 44(12): 1- 4 (in Chinese) (王 霞,张文修.概念格的属性约简与属性特征.计算机工程与应用, 2008, 44(12): 1- 4) [14]Yang Bin, Xu Baowen. Distributive Reduction of Attributes in Concept Lattice. Journal of Computer Research and Development, 2008, 45(7): 1169-1176 (in Chinese) (杨 彬,徐宝文.分布式概念格的属性约简研究.计算机研究与发展, 2008, 45(7): 1169-1176) [15] Xie Baiqing, She Xiaoge. Algorithms and Data Structures. Beijing, China: Higher Education Press, 2001 (in Chinese) (谢柏青,佘晓歌.算法与数据结构.北京:高等教育出版社, 2001)
2010, Vol. 23 
