一般二叉树型分层模糊系统的通用逼近性

Universal approximation of general binary tree-type hierarchical fuzzy systems

为解决多变量模糊系统中的“维数灾”问题,该文提出了一般二叉树型分层模糊系统,简化了多输入复杂模糊系统的分析,并研究了它的通用逼近性。利用分片线性函数理论和中值定理,证明了该二叉树型分层模糊系统具有通用逼近性,并得到了该通用逼近性的充分条件。相对于一般模糊系统,分层模糊系统大大减少了系统的规则数。仿真结果表明:在同样的逼近精度下,二叉树型分层模糊系统的规则数比一般模糊系统减少了10倍左右,从而大大简化了系统的设计。

The analysis of the multi-input fuzzy system can become unfunctable as the system size increases. A binary tree-type hierarchical fuzzy system was developed to simplify analysis of large fuzzy systems and the universal approximation of the system is also analyzed. Piecewise linear functions and the Mean Value Theorem are used to prove that the model has the universal approximation property and give the sufficient condition. Contrasting to normal fuzzy systems, hierarchical fuzzy systems have much less fuzzy rules. A simulation example demonstrates that to achieve the same approximation accuracy, hierarchical fuzzy systems use only about one tenth as many as the rules of normal fuzzy systems, greatly simplifying the design.