1.Department of Computer Science and Technology, Tongji University, Shanghai 201804 2.College of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004
Abstract:A quantitative representation for the classification ability of knowledge is described, and a representation for knowledge is given. Firstly, the algebraic representation of main concepts in rough sets is presented. Next, the concept of partition granularity is defined, and its properties are analyzed. Finally, the equivalence between the algebraic representation of knowledge and partition granularity representation is proved.
[1] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Dordrecht, Netherlands: Kluwer Academic Publishers, 1991 [2] Zhang Weixiu, Wu Weizhi, Liang Jiye, et al. Rough Set Theory and Methods. Beijing, China: Science Press, 2003 (in Chinese) (张文修,吴伟志,梁吉业,等.粗糙集理论与方法.北京:科学出版社, 2003) [3] Wang Jue, Yuan Xiaohong, Shi Chunyi, et al. Discussions on Knowledge Representation. Chinese Journal of Computers, 1995, 18(3): 212-224 (in Chinese) (王 珏,袁小红,石纯一,等.关于知识表示的理论.计算机学报, 1995, 18(3): 212-224) [4] Miao Duoqian, Wang Jue. An Information Representation of the Concepts and Operations in Rough Set Theory. Journal of Software, 1999, 10(2): 113-116 (in Chinese) (苗夺谦,王 珏.粗糙集理论中概念与运算的信息表示.软件学报, 1999, 10(2): 113-116) [5] Miao Duoqian, Wang Jue. Information-Based Algorithm for Reduction of Knowledge // Proc of the IEEE International Conference on Intelligent Processing Systems.Beijing, China, 1997, Ⅱ: 1155-1158 [6] Miao Duoqian, Hu Guirong. A Heuristic Algorithm for Reduction of Knowledge. Journal of Computer Research and Development, 1999, 36(6): 681-684 (in Chinese) (苗夺谦,胡桂荣.知识约简的一种启发式算法.计算机研究与发展, 1999, 36(6): 681-684) [7] Liang Jiye, Shi Zhongzhi. The Information Entropy, Rough Entropy and Knowledge Granulation in Rough Set Theory. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 2004, 12(1): 37-46 [8] Xu Yan, Huai Jinpeng, Wang Zhaoqi. Reduction Algorithm Based on Discernibility and Its Applications. Chinese Journal of Computers, 2003, 26(1): 97-103 (in Chinese) (徐 燕,怀进鹏,王兆其.基于区分能力大小的启发式约简算法及其应用.计算机学报, 2003, 26(1): 97-103) [9] Chen Tangmin. Research of the Heuristic Reduced Algorithm Based on the Separating Capacity. Chinese Journal of Computers, 2006, 29(3): 480-487 (in Chinese) (陈堂敏.基于区分能力大小的启发式约简算法的研究.计算机学报, 2006, 29(3): 480-487) [10] Nguyen S H, Nguyen H S. Some Efficient Algorithms for Rough Set Methods // Proc of the 6th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Granada, Spain, 1996, Ⅱ: 1451-1456 [11] Wang Yu, Hu Yunfa, Zhang Kai. Research on Knowledge Capacity Measurement of Knowledge Base Based on Rough Set. Journal of Computer Research and Development, 2004, 41(9): 1500-1506 (in Chinese) (王 瑜,胡运发,张 凯,基于粗集理论的知识含量度量研究.计算机研究与发展, 2004, 41(9): 1500-1506)