Yen J, Wang L
Dept. of Comput. Sci., Texas A&M Univ., College Station, TX.
IEEE Trans Syst Man Cybern B Cybern. 1999;29(1):13-24. doi: 10.1109/3477.740162.
An important issue in fuzzy-rule-based modeling is how to select a set of important fuzzy rules from a given rule base. Even though it is conceivable that removal of redundant or less important fuzzy rules from the rule base can result in a compact fuzzy model with better generalizing ability, the decision as to which rules are redundant or less important is not an easy exercise. In this paper, we introduce several orthogonal transformation-based methods that provide new or alternative tools for rule selection. These methods include an orthogonal least squares (OLS) method, an eigenvalue decomposition (ED) method, a singular value decomposition and QR with column pivoting (SVD-QR) method, a total least squares (TLS) method, and a direct singular value decomposition (D-SVD) method. A common attribute of these methods is that they all work on a firing strength matrix and employ some measure index to detect the rules that should be retained and eliminated. We show the performance of these methods by applying them to solving a nonlinear plant modeling problem. Our conclusions based on analysis and simulation can be used as a guideline for choosing a proper rule selection method for a specific application.
基于模糊规则的建模中的一个重要问题是如何从给定的规则库中选择一组重要的模糊规则。尽管可以想象从规则库中删除冗余或不太重要的模糊规则会得到一个具有更好泛化能力的紧凑模糊模型，但确定哪些规则是冗余或不太重要的并非易事。在本文中，我们介绍了几种基于正交变换的方法，这些方法为规则选择提供了新的或替代的工具。这些方法包括正交最小二乘法（OLS）、特征值分解（ED）法、带列主元的奇异值分解和QR分解（SVD-QR）法、总体最小二乘法（TLS）和直接奇异值分解（D-SVD）法。这些方法的一个共同特点是它们都作用于一个激发强度矩阵，并采用某种度量指标来检测应保留和消除的规则。我们通过将这些方法应用于解决非线性对象建模问题来展示它们的性能。基于分析和仿真得出的结论可作为为特定应用选择合适规则选择方法的指导。
