模糊树模型对有限样本集的逼近

Approximate Limit Sampling Data Using Fuzzy Tree Model

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 .

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.