基于最小二乘支持向量回归机的Mamdani模糊系统结构

为了提高模糊系统处理高维问题的推广能力,基于最小二乘支持向量回归机(LSSVR)的思想提出了一个设计Mamdani模糊系统的新算法。传统算法都存在过学习问题,该算法在目标函数中考虑了结构风险避免了过学习现象,并将模糊系统的参数寻优问题转化为一个二次规划问题进行求解。在此算法中,构造了一种新的具有语言意义的数据依赖型模糊核函数,它是一种Mercer核。实验结果证明，该算法提高了Mamdani模糊系统的逼近能力和推广能力。

Mamdani fuzzy system structure identification based on LSSVR

To design a Mamdani fuzzy system with good generalization ability in high dimensional feature space, a novel learning algorithm based on Least Squares Support Vector Regression (LSSVR) was presented in this paper. The structural risk was considered in the goal function to avoid overfitting in traditional algorithms and then the parameter estimation of a Mamdani fuzzy system was converted to a quadratic optimization problem. In the proposed algorithm, the fuzzy kernel generated by premise membership functions is proved to be a mercer kernel. Numerical experiments show that the presented algorithm improves the approximation ability and the generalization ability of Mamdani fuzzy systems.