基于expectation maximization算法的Mamdani-Larsen模糊系统及其在时间序列预测中的应用

Epanechnikov混合模型和Mamdani-Larsen模糊系统之间的对应关系被建立:任何一个Epanechnikov混合模型都唯一对应着一个Mamdani-Larsen模糊系统，在一定条件下，Epanechnikov混合模型的条件均值和Mamdani-Larsen模糊模型的输出是等价的.一个设计模糊系统的新方法被提出，即利用expectation maximization算法设计模糊系统.将设计的模糊系统应用于时间序列预测，仿真结果表明：利用EM算法设计的模糊系统比其他模糊系统精度更高，抗噪性更强关键词：expectation maximization(EM)算法Mamdani-Larsen模糊系统Epanechnikov混合模型混沌时间序列

Mamdani-Larsen fuzzy system based on expectation maximization algorithm and its applications to time series prediction

This work explores how Epanechnikov mixture model can be translated to Mamdani-Larsen fuzzy model. The mathematical equivalence between the conditional mean of an Epanechnikov mixture model and the defuzzified output of a Mamdani-Larsen fuzzy model is proved. The result provides a new perspective of studying the Mamdani-Larsen fuzzy model by interpreting a fuzzy system from a probabilistic viewpoint. Instead of estimating the parameters of the fuzzy rules directly, the parameters of an Epanechnikov mixture model can be firstly estimated using any popular density estimation algorithm, such as expectation maximization. Mamdani-Larsen fuzzy model trained in the new way has higher accuracy and stronger anti-noise capability. After comparing the simulation results with the ones obtained from other fuzzy system modeling tools, it can be claimed that the results are successful.