基于多目标演化的模糊认知图学习算法

Learning of fuzzy cognitive maps using multi-objective evolutionary algorithm

针对传统模糊认知图学习算法仅优化概念结点间有向弧的权值误差而造成模型拟合准确程度不高的问题,将多目标演化的思想用于模糊认知图学习算法,设计了以有向弧权值误差与误差权重同时最小化为目标的多目标模糊认知图学习模型,降低了学习算法对权值的依赖。为有效求解该多目标优化模型,提出了一种基于坐标变换的多目标演化算法,分析了算法的参数设置方法与计算复杂度。实验结果表明,基于多目标演化的模糊认知图学习算法可以有效降低结点数据误差与模型误差,能够更准确地得出概念结点间的因果关系。

In learning of fuzzy cognitive maps （FCMs）, traditional learning algorithms only minimize the data error of the directed arcs between every two concepts, which may lead to the low accuracy of the fitting model. The idea of multi-objective optimization is introduced for designing the learning algorithm of FCMs. The multi-obieetive model for learning of FCMs is proposed with the objectives of minimizing the data error of the di- rected arcs and minimizing the proportion of the data error. The proposed multi-objective model can reduce the dependence on the weights of the learning algorithms. A multi-objective evolutionary algorithm based on coordi- nation transformation, termed as multi-objective optimization evolutionary algorithms based on coordinate trans- formation （MOEA/CT）, is used to solve the multi-objective model for learning of FCMs efficiently. The ap- proach of parameter setting for MOEA/CT and computational complexity are studied. Experimental results show that the learning of FCMs by using the proposed MOEA/CT can effectively decrease the data error and the model error and reflect the causal relationship between concepts accurately.