奇异值分解在重构模糊决策系统规则库中的应用

中国管理科学 ›› 2005, Vol. ›› Issue (3): 103-107.

奇异值分解在重构模糊决策系统规则库中的应用

刘斌, 何建敏, 曹卉宇

东南大学经济管理学院, 江苏, 南京, 210096

收稿日期:2003-11-17 修回日期:2005-05-08 出版日期:2005-06-28 发布日期:2012-03-07

Rebuilding PSG Fuzzy Decision-making System Using SVD Method

LIU Bin, HE Jian-min, CAO Hui-yu

College of Economic Management, Southeast University, Nanjing 210096, China

Received:2003-11-17 Revised:2005-05-08 Online:2005-06-28 Published:2012-03-07

摘要/Abstract

摘要： 利用SVD技术重构PSG模糊规则库,降低规则的数量。根据矩阵奇异值的性质,适当取舍模糊规则库后件矩阵Ω的奇异值,得到Ω的近似表示Ω,利用Ω重新构建规则库,新规则库的输入变量域的维数比原规则库的维数小,从而有效地降低了模糊规则数。仿真结果证明了该方法是有效的。

关键词: PSG模糊模型, 规则库, 奇异值分解(SVD), 约简

Abstract: The method using SVD to rebuilding PSG fuzzy model is presented in this paper,in new model,the number of fuzzy rules is reduced.In terms of the property of singular values,an approximation of matrix Ω,which is conducted by consequents of fuzzy rules,is obtained by selecting proper singular values of Ω.Using the approximation of Ω,a new rule base is constructed.Generally,the dimension of imput variables in new rule base is smaller than in original one,thus,the size of rule base is reduced effectively.Finally,a numerical example with simulations is given to demonstrate the method discussed throughout this paper.

Key words: PSG fuzzy model, rule base, SVD(singular value decomposition), reduction

中图分类号:

TP273.4
C931

刘斌, 何建敏, 曹卉宇. 奇异值分解在重构模糊决策系统规则库中的应用[J]. 中国管理科学, 2005, (3): 103-107.

LIU Bin, HE Jian-min, CAO Hui-yu. Rebuilding PSG Fuzzy Decision-making System Using SVD Method[J]. Chinese Journal of Management Science, 2005, (3): 103-107.

[1]	骆公志, 杨晓江. 变精度优势粗糙集属性约简择优算法[J]. 中国管理科学, 2009, 17(2): 169-175.
[2]	戴毓, 周德群. 基于粗糙集理论的格序选择方法[J]. 中国管理科学, 2007, 15(6): 105-110.