Abstract: The traditional Takagi-Sugeno (T-S) fuzzy systems always have a poor interpretability because they use all the attributes of the samples in the rules. The existence of redundant features inevitably leads to the over fitting problem and further reduces the generalization performance of the fuzzy model. To this end, this paper proposes a novel joint sparse modeling method for Takagi-Sugeno fuzzy system called L2-common feature selection fuzzy inference systems (L2-CFS-FIS), which aims to improve the generalization performance and interpretability of the T-S fuzzy systems simultaneously. Taking advantage of the common feature information among different rules, and introducing the over fitting mechanism, this paper formulates a joint sparse optimization problem based on double regularization terms and further develops an alternating direction method of multipliers (ADMM) procedure to find the optimal solution. The experimental results demonstrate that the proposed method can not only obtain a satisfactory generalization performance of the fuzzy model, but also effectively mine the discriminant attributes from original data to ensure better interpretability of the model.

Key words: T-S fuzzy system modeling, common feature selection, joint optimization, alternating direction method of multipliers (ADMM) procedure

摘要： 传统Takagi-Sugeno（T-S）模糊系统模型因模糊规则使用样本全部特征，导致模型的可解释性较差，冗余特征的存在还会导致模型的过拟合，降低模型的泛化性能。针对该问题，提出了一种模糊系统联合稀疏建模新方法L2-CFS-FIS（L2-common feature selection fuzzy inference systems），从而提高模型的泛化性能和可解释性。该方法充分考虑存在于模糊规则间的公共特征信息，同时引入模型过拟合处理机制，将模糊系统建模问题转化为一个基于双正则的联合优化问题，并使用交替方向乘子（alternating direction method of multipliers，ADMM）算法来进行求解。实验结果表明，该方法所构造的模糊系统不仅能够获得较为满意的泛化性能，而且通过有效地挖掘规则间重要的公共特征，可以确保模型具有较高的可解释性。

关键词: T-S模糊系统建模, 公共特征选择, 联合优化, ADMM算法