Abstract：The theory of quotient space is one of the three main methods of granular computing. The research of its combination is to find the relationship between the quotient space and the original space and to reduce the computational complexity by simplifying complex problems. The combination of domains is intended to implement granularity transform, fine or coarse, according to the different needs. The topological structure is the unique structure in the quotient space theory, and its combination has a variety of forms. In addition to the fine combination and the semi-order structure combination, the coarse combination and the converse quotient combination based on the converse-quotient topology are presented. The combination reflects the relationship between different topological structures. The combination of attribute functions lies in the formation of different equivalence relation of domain. These studies extend the basic theory of quotient space combination and make it better.
[1] Yao Y Y. Granular Computing: Basic Issues and Possible Solutions // Proc of the 5th Joint Conference on Information Sciences. Atlantic City, USA, 2000: 186-189 [2] Xie Gang, Liu Jing. A Review of the Present Studying State and Prospect of Granular Computing. Software, 2011, 32(3): 5-10 (in Chinese) (谢 刚,刘 静.粒计算研究现状及展望.软件, 2011, 32(3): 5-10) [3] Zhang Ling, Zhang Bo. Theory and Applications of Problem Solving: Theory and Applications of Quotient Space. Beijing, China: Tsinghua University Press, 2007 (in Chinese) (张 铃,张 钹.问题求解理论及应用:商空间粒度计算理论及应用.北京:清华大学出版社, 2007) [4] Xu Feng, Zhang Ling, Wang Lunwen. The Approach of the Fuzzy Granular Computing Based on the Theory of Quotient Space. Pattern Recognition and Artificial Intelligence, 2004, 17(4): 124-129 (in Chinese) (徐 峰,张 铃,王伦文.基于商空间理论的模糊粒度计算方法.模式识别与人工智能, 2004, 17(4): 124-129) [5] Xu Yun. The Join and Intersection Operations of Equivalence Relation in Rough. Journal of Xinjiang University: Natural Science, 2001, 18(1): 16-21 (in Chinese) (徐 云.粗集理论中等价关系的交与并运算.新疆大学学报:自然科学版, 2001, 18(1): 16-21) [6] Cheng Jishu, Chen Shuili. Point Set Topology. Beijing, China: Science Press, 2008 (in Chinese) (程吉树,陈水利.点集拓扑学.北京:科学出版社, 2008) [7] Munkres J R. Topology. 2nd Edition. Upper Saddle River, USA: Prentice Hall, 2000 [8] Xiong Jincheng. Lecture Notes on Point Set Topology. 3rd Edition. Beijing, China: Higher Education Press, 2003 (in Chinese) (熊金成.点集拓扑讲义.第3版.北京:高等教育出版社, 2003) [9] Zhang Yanping, Zhang Ling, Xia Ying. To Compare the Theory of Quotient Space with Rough Set. Microcomputer Development, 2004, 14(10): 21-24 (in Chinese) (张燕平,张 铃,夏 莹.商空间理论与粗糙集的比较.微机发展,2004, 14(10): 21-24) [10] Huang Jiantao. Vector-Space-Model Text Categorization Method Based on Quotient Space Theory. Journal of Computer Applications, 2011, 31(z2): 67-69 (in Chinese) (黄剑韬.基于商空间的向量空间模型文本分类方法.计算机应用, 2011, 31(z2): 67-69) [11] Shi Xiaojing, Han Xie. 3D Mesh Segmentation Based on Granula-rity of Quotient Space Theory. Application Research of Computers, 2010, 27(4): 1598-1600 (in Chinese) (石晓敬,韩 燮.基于商空间粒度理论的三维网格分割方法.计算机应用研究, 2010, 27(4): 1598-1600) [12] Wang Lifang, Han Xie. Anomaly Intrusion Detection Based on Quotient Space Granularity Clustering. Computer Applications and Software, 2010, 27(5): 1911-1913 (in Chinese) (王丽芳,韩 燮.基于商空间粒度聚类的异常入侵检测.计算机应用与软件, 2010, 27(5): 1911-1913) [13] Zhang Jian, Fang Hongbin, Sun Qilin, et al. Classification Algorithm for Imbalance Dataset Based on Quotient Space Theory. Journal of Computer Applications, 2012, 32(1): 210-212 (in Chinese) (张 健,方宏彬,孙启林,等.基于商空间理论的非平衡数据集分类算法.计算机应用, 2012, 32(1): 210-212)
2013, Vol. 26 
