Fuzzy Support Vector Classification Based on Possibility Theory
YANG ZhiMin1, DENG NaiYang2
1.Department of Science, Zhijiang College of Zhejiang University of Technology, Hangzhou 310024 2.College of Science, China Agriculture University, Beijing 100083
Abstract：The fuzzy support vector classification is discussed, in which both the output of the training point and the value of the final fuzzy classification function are triangle fuzzy number. First, the fuzzy classification problem is formulated as a fuzzy chance constrained programming. Then, this programming is transformed into its equivalence quadratic programming. As a result, fuzzy support vector classification algorithm is proposed. An example is presented to show the rationality of the algorithm.
杨志民，邓乃扬. 基于可能性理论的模糊支持向量分类机*[J]. 模式识别与人工智能, 2007, 20(1): 7-14.
YANG ZhiMin , DENG NaiYang. Fuzzy Support Vector Classification Based on Possibility Theory. , 2007, 20(1): 7-14.
[1] Vapnik V N. The Nature of Statistical Learning Theory. New York, USA: SpringerVerlag,1995 [2] Cristianini N, ShaweTaylor J. Introduction to Support Vector Machines. Cambridge, UK: Cambridge University Press, 2000 [3]Deng Naiyang, Tian Yingjie. The New Method in Data Mining-Support Vector Machines. Beijing, China: Science Press, 2004 (in Chinese) (邓乃扬,田英杰.数据挖掘中的新方法——支持向量机.北京:科学出版社,2004) [4]Lin Chunfu, Wang Shengde. Fuzzy Support Vector Machines. IEEE Trans on Neural Networks, 2002, 13(2): 464471 [5]Tao Qing, Wang Jue. A New Fuzzy Support Vector Machine Based on the Weighted Margin. Neural Procession Letters, 2004, 20(3): 139150 [6] Lee K Y, Kim D W, Lee K H, et al. Possibilistic Support Vector Machines. Pattern Recognition, 2005, 38(3): 13251327 [7] Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338353 [8] Zadeh L A. Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1978, 1(1): 328 [9] Liu B, Iwamura K. Chance Constrained Programming with Fuzzy Parameters. Fuzzy Sets and Systems, 1998, 94(2): 227237 [10]Liu Baoding, Zhao Ruiqing. Random Programming and Fuzzy Programming. Beijing, China: Tsinghua University Press, 1998 (in Chinese) (刘宝碇,赵瑞清.随机规划与模糊规划.北京:清华大学出版社, 1998) [11]Deng Naiyang, Zhu Meifang. Optimal Methods. Shenyang, China: Liaoning Education Press, 1987 (in Chinese) (邓乃扬,诸梅芳.最优化方法.沈阳:辽宁教育出版社, 1987) [12]Yuan Yaxiang, Sun Wenyu. Optimal Theories and Methods. Beijing, China: Science Press, 1997 (in Chinese) (袁亚湘,孙文瑜.最优化理论与方法.北京:科学出版社, 1997) [13]Zhang Wenxiu. Foundation of Fuzzy Mathematics. Xi’an, China: Xi’an Jiaotong University Press, 1995 (in Chinese) (张文修.模糊数学基础.西安:西安交通大出版社, 1995)
2007, Vol. 20 
