Hierarchical Structure Analysis of Fuzzy Quotient Space
ZHANG Qing-Hua, WANG Guo-Yin, LIU Xian-Quan
School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031 Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065
Abstract In this paper, the fuzzy quotient space theory for the cut-relation of fuzzy equivalence relation with any threshold is discussed. A method is proposed for hierarchically constructing normalized isosceles distance function between different quotient spaces. And a hierarchical structure of fuzzy quotient space is constructed. The relation between the operations(intersection and combination)of fuzzy equivalence relation and the synthesis of quotient spaces is discussed.
[1] Zhang Ling, Zhang Bo. Theory of Fuzzy Quotient Space (Methods of Fuzzy Granular Computing). Journal of Software, 2003, 14(4): 770-776 (in Chinese) (张 铃,张 钹.模糊商空间理论(模糊粒度计算方法).软件学报, 2003, 14(4): 770-776) [2] Zhang Bo, Zhang Ling. Theory and Applications of Problem Solving. Beijing, China: Tsinghua University Press, 1990 (in Chinese) (张 钹,张 铃.问题求解理论及应用.北京:清华大学出版社, 1990) [3] Zhang Bo, Zhang Ling. Theory and Applications of Problem Solving. New York, USA: Elsevier Science, 1992 [4] Liu Renjin, Huang Xianwu. The Granular Theorem of Quotient Space in Image Segmentation. Chinese Journal of Computers, 2005, 28(10): 1680-1685 (in Chinese) (刘仁金,黄贤武.图像分割的商空间粒度原理.计算机学报, 2005, 28(10): 1680-1685) [5] Zhang Ling, Zhang Bo. A Quotient Space Approximation Model of Multi-Resolution Signal Analysis. Journal of Computer Science and Technology, 2005, 20(1): 90-94 [6] Zhang Yanping, Zhang Ling, Wu Tao. The Representation of Different Granular Worlds: A Quotient Space. Chinese Journal of Computers, 2004, 27(3): 328-333 (in Chinese) (张燕平,张 铃,吴 涛.不同粒度世界的描述法——商空间法.计算机学报, 2004, 27(3): 328-333) [7] Liu Yan, Li Youyi, Chen Zhanjun, et al. Application of Fuzzy Controller Based on Quotient Space Theory to Aerial Camera. Journal of Nanjing University of Aeronautics & Astronautics, 2006, 38(Z1): 88-90 (in Chinese) (刘 岩,李友一,陈占军,等.基于商空间理论的模糊控制在航空相机中的应用.南京航空航天大学学报, 2006, 38(Z1): 88-90) [8] Zhang Ling, Zhang Bo. Theory and Applications of Problem Solving-Quotient Space Based Granular Computing. 2nd Edition. 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其应用.第2版.北京:清华大学出版社, 2007) [9] Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5), 341-356 [10] Zadeh L A. Fuzzy Logic=Computing with Words. IEEE Trans on Fuzzy Systems.1996, 4(2): 103-111 [11] Zadeh L A. Towards a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic. Fuzzy Sets and Systems, 1997, 90(2): 111-127 [12] 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): 424-429 (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): 424-429) [13] Mao Junjun, Zhang Ling, Xu Yisheng. Fuzzy Clustering Analysis Based on Quotient Space and Information Granularity. Operations Research and Management Science, 2004, 13(4): 25-29 (in Chinese) (毛军军,张 铃,许义生.基于商空间和信息粒度的Fuzzy聚类分析.运筹与管理, 2004, 13(4): 25-29) [14] Xu Feng, Zhang Ling. An Analysis of Uneven Granules Clustering Based on Quotient Space. Computer Engineering, 2005, 31(3): 26-28,53 (in Chinese) (徐 峰,张 铃.基于商空间的非均匀粒度聚类分析.计算机工程, 2005, 31(3): 26-28,53) [15] Zhang Chijian, Li Yang, Zhang Ling. Realizing the High-Precision Fuzzy Control Based on the Theory of Quotient Space(Methods of Granular Computing). Computer Engineering and Applications, 2004, 40(11): 37-39,45 (in Chinese) (张持健,李 旸, 张 铃.商空间理论(粒度计算方法)实现高精度模糊控制.计算机工程与应用, 2004, 40(11): 37-39,45) [16] Zhang Ling, Zhang Bo. Quotient Space Model Based Hierarchical Machine Learning // Proc of the International Conference on Neural Networks and Brain. Beijing, China, 2005: 81-83 [17] Yang Lunbiao, Gao Yingyi. Fuzzy Mathematics: Theory and Application. Guangzhou, China: South China University of Technology Press, 2004 (in Chinese) (杨纶标,高英仪.模糊数学原理及应用.广州:华南理工大学出版社, 2004) [18] Zhang Ling, Zhang Bo. The Quotient Space Theory of Problem Solving. Fundamenta Informaticae, 2004, 59(2/3): 287-298
2008, Vol. 21 
