MULTIPLE ENSEMBLE NEURAL NETWORK MODELS WITHFUZZY RESPONSE AGGREGATION FOR PREDICTING COVID19 TIME SERIES THE CASE OF MEXICO

1. MULTIPLE ENSEMBLE NEURAL NETWORK MODELS WITH
FUZZY RESPONSE AGGREGATION FOR PREDICTING
COVID-19 TIME SERIES: THE CASE OF MEXICO

2. INTRODUCTION
In this paper, a multiple ensemble neural network model with fuzzy
response aggregation for the COVID-19 time series is presented.
Ensemble neural networks are composed of a set of modules, which
are used to produce several predictions under different conditions.
The modules are simple neural networks. Fuzzy logic is then used to
aggregate the responses of several predictor modules, in this way,
improving the final prediction by combining the outputs of the
modules in an intelligent way.

3. METHODOLOGY
Nonlinear Autoregressive Neural Networks (NAR):
The NAR (nonlinear autoregressive) neural network uses past values
of the time series to estimate predicted future values.
where y(t) is the value of the considered time series y at time t, and d
is the time delay and F denotes the transfer function

4. CONTINUED……
Function Fitting Neural Network (FITNET):
Most commonly used Multi-Layer Perceptron
uses the process of training a neural network on
a set of inputs in order to produce an associate
set of target outputs.
The FITNET is used for curve-fitting and
regression.
Fig.2. The general architecture of an artificial neural
network of FITNET type.

5. THE MAIN ARCHITECTURE OF THE
SYSTEM

6. CONTINUED……
In the main architecture of the ensemble neural network model, NAR
is used in modules 1 and 2 of the ensemble, and in module 3 we use
the FITNET neural network to train and learn from the given
information.
The mean square error (MSE) of the training and actual data is
normalized using Equation (2):

7. CONTINUED……
Then the normalized mean square errors are used in the fuzzy
integrator to produce the weights w1, w2, w3 and then by using the
expression in Equation (5) we combine the predictions to obtain the
total prediction PT:
Where w1 =weight of module1,w2 = the weight of module 2, w3 =
the weight of module 3, p1 = the predicted value of module 1, p2 = the
predicted value of module 2, and p3 = the predicted value of module 3.

8. CONTINUED……
Here each ensemble has its own fuzzy aggregator to produce the final
prediction of the ensemble.
The structure of the fuzzy integrator system is shown in Figure 4,
which is formed by the inputs before fuzzification, the fuzzy inference
system (integrator), and the fuzzy outputs after defuzzification.
The inputs e1, e2, and e3 consist of the normalized mean square errors
of the three neural networks that have been used to predict. In this
case, e1 is the MSE of module 1, e2 is the NMSE of module 2, and e3
is the NMSE of module 3. The fuzzy inference system consists of
three fuzzy rules, and the three outputs are w1, w2, and w3, which are
obtained with the weighted mean in the defuzzification process.

9. THE FUZZY INPUT MEMBERSHIP
FUNCTIONS OF e1,e2, e3

10. THE FUZZY INPUT MEMBERSHIP FUNCTIONS OF
w1,w2, w3

11. SIMULATION RESULTS

12. SIMULATION RESULTS

13. CONCLUSION
Ensemble neural networks were used to produce several predictions
under different conditions.
 Fuzzy logic was then used to aggregate the responses of several
predictor modules, in this way, improving the final prediction by
combining, in a proper way, the outputs of the modules.
Fuzzy logic helps in handling the uncertainty in the process of making
a final decision about the prediction.

14. REFERENCES
1. Chen, Y.W.; Yiu, C.P.B.; Wong, K.Y. Prediction of the SARS-CoV-2
(2019-nCoV) 3C-like protease (3CLpro) structure: Virtual screening
reveals velpatasvir, ledipasvir, and other drug repurposing
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