北京航空航天大学学报 ›› 2000, Vol. 26 ›› Issue (2): 231-234.

• 论文 • 上一篇    下一篇

模糊树模型对有限样本集的逼近

毛剑琴1, 张建刚1, 代冀阳1, 魏可惠2   

  1. 1. 北京航空航天大学 理学院;
    2. 中国工程物理研究院 电子工程研究所
  • 收稿日期:1998-10-14 出版日期:2000-02-29 发布日期:2010-09-27
  • 作者简介:毛剑琴(1940-),女,上海人,教授,100083,北京.
  • 基金资助:

    国家自然科学基金资助项目(69874002)

Approximate Limit Sampling Data Using Fuzzy-Tree Model

MAO Jian-qin1, ZHANG Jian-gang1, DAI Ji-yang1, WEI Ke-hui2   

  1. 1. Beijing University of Aeronautics and Astronautics,School of Science;
    2. Academe of Engineering Physics
  • Received:1998-10-14 Online:2000-02-29 Published:2010-09-27

摘要: 对含高度非线性的复杂系统的辨识与建模提出了一种二叉线性模糊树方法.证明了对n维空间中任一闭集上的有限样本集或连续函数,总存在模糊树模型以任一精度逼近之.仿真结果表明,与已有的其它方法比较,模糊树模型不仅具有计算量小,精度高,对于输入空间维数不敏感等优点,同时它的逼近误差是单调下降的.模糊树模型在一定程度上模拟了对复杂问题进行分层、分段简化决策的思维过程.仿真结果描述了这种方法的性能.

Abstract: A linear binary fuzzy tree structure approach, i.e. Fuzzy-Tree model, is proposed for complex nonlinear system modeling. In comparison with some other modeling approaches, such as ANFIS and Neural Network model, the proposed model is of less computation, higher accuracy, especially insensitivity to high dimension. It is proved that for any square integrated continuous function, there always exists a Fuzzy-Tree model to approximate it arbitrarily. Fuzzy-Tree model simulates the layered decision-making and piece-wise linearized processing procedure for solving complex problems. A numerical solution was given to show the approach.

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