Affiliations: [a] School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, China
| [b] School of Control and Computer Engineering, North China Electric Power University, Beijing, China
| [c] Institute of Automation, Chinese Academy of Sciences, Beijing, China
Correspondence:
[*]
Corresponding author. Chengdong Li, School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China. Tel.: +86 18866410727; E-mail: lichengdong@sdjzu.edu.cn.
Abstract: In many data-driven modeling, prediction or identification applications to unknown systems, linguistic (fuzzy) results described by fuzzy sets are more preferable than the crisp results described by numbers owing to the uncertainties and/or noises existed in the observed data. On the other hand, fuzzy neural network (FNN) provides a powerful tool for providing accurate crisp results, but does not have the ability to achieve linguistic outputs due to its crisp weights. This study extends the crisp weights of FNN to fuzzy ones to obtain linguistic outputs. And, a data-driven design method is proposed to construct this kind of fuzzily weighted FNN (FW-FNN). The proposed data-driven method includes four steps. Firstly, a fully connected FNN is generated. Then, the SVD-QR method based pruning strategy is presented to realize the structure reduction of the initial FW-FNN. Thirdly, the centers of the Gaussian fuzzy weights in the structure reduced FW-FNN are learned by the least square method. Fourthly, the multi-objective algorithm is utilized to optimize the widths of the Gaussian fuzzy weights to achieve the maximum of the average membership grades of the output fuzzy sets and the minimum of the coverage intervals of the linguistic outputs. To evaluate the proposed FW-FNN and the data-driven method, applications to the nonlinear dynamic system identification, the chaotic time series prediction and the traffic flow prediction are given. Simulation results demonstrate that the linguistic outputs can effectively capture the uncertainties and/or noises in the observed data. It provides us a very useful tool for system modeling, prediction and identification especially when uncertainties and/or noises should be taken into account.
