基于SVD 方法的简约型区间二型模糊模型构建

针对奇异值-QR分解方法存在有效奇异值难以确定的问题，采用奇异值分解方法分析从区间二型模糊模型抽取的两个激活强度矩阵，提出了奇异值归一化差值的概念以描述相邻奇异值的变化情况，从而反映了重要规则和冗余规则在奇异值变化上的本质差异；进而根据其临界点确定有效奇异值个数，并利用QR分解得到有效奇异值所对应的重要规则构建简约型区间二型模糊结构。仿真实例验证了所提出方法的有效性和可行性。

Construction of parsimonious interval type-2 fuzzy model based on SVD

As the determination of number for effective singular value is a problem for the simplification of interval type-2
fuzzy model structure by using the singular value decomposition-QR method, two firing strength matrixes are got though
the analysis of interval type-2 fuzzy model structure and then analyzed by using the singular value decomposition method.
The concept of normalized difference of singular value is proposed to describe the change of adjacent singular value so as
to reflect the essential differences between important rules and redundant rules in aspect of singular value. Then the number
of effective singular can be determined according to its critical point, and the parsimonious interval type-2 fuzzy model is
constructed with rules located by QR decomposition. Finally, simulation results show the effectiveness and feasibility of the
proposed method.