# Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review
## 3 Neural Network-Based Forecasting Approaches
### Fuzzy with ANN-Based Forecasting Approaches  
FNN is a hybrid network developed using ANN's learning ability and fuzzy logic's noise handling capability. The architecture of the FNN is also shown in Figure 4. The figure shows that the network has four layers: the input layer, fuzzification layer, inference layer, and defuzzification layer (refer to the yellow dotted lines in Figure 4). FNN uses two approaches, namely (i) Mamdani and (ii) Takagi and Sugeno. Fuzzy logic is represented using the neural network's structure and trained using either a BP or an optimization algorithm. The FNN is implemented in the following three ways:  
* Fuzzy inputs with real weights;
* Fuzzy inputs and fuzzy weights. In [50], the authors developed the self-organizing Takagi and Sugeno-type FNN model for predicting the short-term traffic flow. The experimental results of the developed model showed to be feasible and more effective than RBFNN. In [54], the researchers developed the distributed chaotic fuzzy RBFNN method applied to fault section estimation in the distribution network. The simulation results of the developed strategy achieved better efficiency, learning ability, fault-tolerance, and low convergence rates than the BPNN model. On the other hand, in [66], the work presented a subtractive clustering-based FNN for forecasting the traffic flow and used the GA for deciding the clustering radius. [PERSON] and [PERSON] introduced an adaptive neural network-based fuzzy inference system for predicting the monthly average flow in a hydrological station, which showed better results than the AR model [67]. The authors of [69] developed the fuzzy descriptor model integrated with singular spectrum analysis for predicting the various time series, including Mackey-Glass, Lorenz, Darwin sea level pressure, and the disturbance storm time index. The presented model results showed to be better than the MLP and RBFNN models. Another forecasting method known as the FNN model based on chaos theory for predicting the hydraulic pumps' vibration signal was proposed in [75]. It is to be noted that this model can also be used to improve prediction accuracy by readjusting the minimal embedding dimension optimally. The dynamic recurrent FNN model used to predict the power systems' short-term load was developed in [76]. It was proved that the developed model's convergence rate and forecasting accuracy are enhanced compared to the conventional FNN model. In [97], the researchers presented the interval type-2 fuzzy cerebellar model articulation controller for forecasting the Henon system of chaotic time series and the chaos synchronization of the Duffing-Holmes system. The proposed model of simulation results showed to be better than the FNN and interval type-2 FNN. In [104], the researchers proposed the saliency back-emf-based wavelet FNN model for a torque observer, using a new maximum torque per ampere control for forecasting the speed of a sensorless interior permanent magnet synchronous motor. In [110], the authors presented the embedding theorem-repetitive fuzzy method for predicting the time series data of Mackey-Glass, Lorenz, and sunspot numbers. The proposed model's experimental results provided better forecasting than the simple fuzzy, adaptive neuro-fuzzy inference and other models in terms of error indices. [PERSON] and [PERSON] presented the self-constructing recurrent FNN model for forecasting the logistic and Henon time series [112]. The proposed model had a worthier performance in convergence rate and forecasting accuracy than the self-constructing FNN. The authors of [117] presented the interactively recurrent fuzzy functions model for predicting the time series data of Lorenz, Mackey-Glass, and real-time lung sound signal modeling. The benchmark and real-time models' results showed to be better than the recurrent networks, such as fuzzy WNN, self-evolving FNN, ESN, and LS. [PERSON] and [PERSON] presented the application of  
* Generalized zonary time-variant fuzzy information granule;
* LSTM mechanism with FNN model.