Hedge-Embedded Linguistic Fuzzy Neural Networks for Systems Identification and Control

In the realm of natural language processing, hedge-embedded structures have contributed considerably by appreciating linguistic variables and distinguishing overlapped classes. This aspect of natural languages considerably affects the building of linguistically interpretable architectures for fuzzy neural networks (FNNs). Here, we propose extending the idea of hedge-embedded linguistic fuzzy neural networks (LiFNNs) to the systems identification and control paradigm. This perspective leads us to the universal approximation property for this mathematical construct using the Stone–Weierstrass theorem and the proof of stability for the resulting nonlinear system identification process using the Lyapunov function. Furthermore, the power activation functions in the membership degrees of the proposed network enable linguistic hedge interpretation and more precise learning. Finally, the proposed LiFNN, optimized using a backpropagation learning algorithm, is evaluated on several problems in function approximation (periodic functions and quadratic Hermite function), system identification (a nonlinear system), and direct adaptive control fields. Results show that memberships are more distinguishable in the proposed LiFNN, leading to $\sim$50% less error on the average and higher granulation and interpretability.