基于正交变换的区间Ⅱ型模糊模型结构精简

Interval TypeⅡ Fuzzy Model Simplification Based on Orthogonal Transformation Methods

针对奇异值-QR(SVD-QR)分解方法存在有效奇异值难以确定的问题,提出采用列选主QR分解方法对模糊模型结构进行分析.运用该方法分析从模糊模型抽取的2个激活强度矩阵,利用矩阵R主对角元素作为判断规则重要性的依据,根据矩阵Π中每列值为1的元素位置确定所对应的规则,从而选取重要的规则,构建简约的区间Ⅱ型模糊模型.将本文方法和奇异值-QR分解方法应用于混沌时间序列预测,同时还对比了两种方法选取的重要规则在不同样本条件下的适应能力.结果表明,两种方法选取的重要规则存在明显差异,并且采用本文方法可以获得更小的误差,平均误差为0.108 6;在不同样本条件下采用本文方法所得误差基本一致,具有更强的泛化能力.

As the effective singular value is hard to determine in the singular value decomposition-QR （SVD-QR）, QR decomposition with column pivoting （pivoted-QR） was proposed to analyze the fuzzy model structure. By applying it to the two firing strength matrices of the fuzzy model, the absolute values of R-diagonal elements were used as a rule ranking index, and specific rule was located according to the position of element with the value of each column of H equaling one. Finally, a chaos time series was predicted with the SVD-QR and pivoted-QR, and adaptability of important rules selected by both methods were compared with different samples. The simulation results indicate that the two methods are clearly distinct in the selection of a set of important fuzzy rules. The error of pivoted- QR is 0. 108 6 in average, much less than that of the QR. The errors of pivoted-QR with different input samoles are close, demonstratinz that it has better generalization nerformance.