IMPLEMENTATION OF THE ADAFTIVE NEURO FUZZY INFERENCE SYSTEM (ANFIS) METHOD FOR PREDICTING TIME SERIES DATA

1. INTRODUCTION

Prediction is one very important element in decision making, effective or not because a decision usually depends on several factors that we can not see at the present and the past (Setyaningsih, 2010). Prediction of time series data are widely used for various fields, such as economics, tourism, marketing, manufacturing, corporate administration and population. In the economic field, including time series data is used to represent the amount of the Gross Domestic Regional Product (GDRP).

Gross Domestic Regional Product (GDRP) is the total value of final goods and services produced by all business units on a regional / area within a certain time period (BPS, 2009). One tool that is used as a measuring tool that can describe the success rate of development is Gross Domestic Regional Product (GDRP). That information is in addition to showing the development is also a result of development problems and challenges that must be faced.

Along with the development of prediction methods, soft computing methods to alternative methods that make the emergence of new discoveries to help make humans in solving problems in various fields. Soft computing methods are commonly used are fuzzy logic,  neural networks, genetic algorithms and hybrid methods for the incorporation of several methods such as methods of Adaptive Neuro-Fuzzy Inference System (ANFIS) that utilizes forte of neural network methods and fuzzy systems. ANFIS is a method that uses neural networks to implement the fuzzy inference system.

Using a fuzzy system will be found difficulty in determining the rules that will be incorporated into the rule base system is vague and the difficulties encountered in designing how many layers in neural networks, can be overcome by combining the two systems into a system of neuro-fuzzy structure of ANFIS. In ANFIS number of hidden nodes in neural network is in accordance with the cryptic system (Fariza, et al., 2007). So that the ANFIS model can provide a solution of the prediction system that is able to adapt well to deal with complex systems, nonlinear and change with time through a learning algorithm for the numerical data of the system.

2. RESEARCH METHODS

Adaptive Neuro Fuzzy Inference System (ANFIS)

Neuro-fuzzy system structure ANFIS (Adaptive Neuro Fuzzy Inference System) belongs to a class of neural networks, but by the same function with fuzzy inference system. In the neuro-fuzzy, neural network learning process on the number of pairs of data useful for updating the parameters of a fuzzy inference system.

ANFIS structure for the same function shown in Figure 1, where the nodes in the same layer have the same function. The output of each node in the display written O_{l, i} (Jang, Sun, and Mizutani, 2004).

Figure 1. Equivalent ANFIS architecture

3.   RESULTS AND DISCUSSION

3.1 ANFIS Modelling of testing

Tests carried out by a combination of modeling ANFIS training parameters which include: the amount of data, the number of membership functions, type of membership function, the value of epochs and Error Goal. Several stages of testing carried out for combinations of parameter values .

Tests conducted on the combination of parameters for which will be used in the training process, the training data and checking data and number of epochs, the number of fuzzy membership functions, and error tolerance.

- Number of Membership Functions = 3

- Error Tolerance = 1E-07

For more details first test ANFIS training results can be seen in Table 1.

Table 1 Testing results of ANFIS training I

From the test results by using a combination of parameters I mentioned in the previous section, it is found that the best available training data RMSE of the parameters are: number of data = 25, type MF is trimf with RMSE value = 1.82E-07.

Table 2 Testing results of ANFIS training VI

From VI of the test results using the parameters mentioned in the previous bagin it is found that the smallest RMSE training data derived from parameters, namely: the number of data = 16, type MF is trapmf with RMSE value = 1.35E-07. More detail can be seen in Figure 6.8 for the amount of training data as much as 16 data.

Figure 2. Graph the results of ANFIS training with the maximum number of training epochs 5000 with a total of 27 data. (a) Type Generalized bell mf, (b) Triangular mf type, (c) trapezoidal mf type.

Based on Figure 2, can be seen that the comparison charts ANFIS training process by using a combination of testing parameters. The maximum number of epoch 5000 and the third type a different set of vague membership, showed ANFIS training process has been demonstrated convergent graphs.

3.2 The test results to changes in the training parameters

By looking at the ratio of RMSE values ​​in Table 2 can be seen that ANFIS model has a good result to make the training process with indicators of GDRP growth data, where the results of this training produces the best RMSE value of the RMSE on the test as a whole is 1.35E-07 .

The best RMSE obtained from the parameters: number of training data = 16 data, the number of Membership Functions = 3, the membership function type = trimf (Triangular), number of epochs = 5000, Error Tolerance = 1.00E-07 and RMSE = 1.35E-07.

Figure 3 Results Training GDRP data

In Figure 3 which shows the menu ANFIS training data and graph the results of GDRP. In the next process if the coach has been completed, rather than to a plot before and after the training process.

3.3 Model Validation Test

Test the validity of the model carried by the F test (Fisher), which measures the closeness between the predicted GDRP growth generated by ANFIS modeling with actual data GDRP growth. Validation test is divided into two parts, namely based on the input training data and testing data.

Test Model With Input Data Validation Testing

ANFIS system output in the form of the predictive value of GDRP growth from the period 1995 to 2010 period using the input data and results of testing are tested F.

                 3.695> 3.478

Therefore F_Value> F_Table, then the model is made ​​valid.

3.4 Prediction of the next period of data

GDRP growth forecast process for the next period the previous data used as input system. Suppose, for predicting GDRP growth in the period in 2011, then used the data indicator of growth in 2010. If the prediction is done by entering the 5 indicators of GDRP data, to obtain the value of GDRP growth in subsequent periods of the year 2011 for the period that is equal to 5.7614%.

4. CONCLUSIONS

Based on research that was conducted and based on the results of testing of GDRP Growth Prediction System with ANFIS, it can be concluded as follows:

1.   GDRP growth forecast simulation using ANFIS with hybrid training algorithm,  yielding the best error of 1.35E-07 using 16 training data and the type of membership function of triangular.

2.   Model validation test using the F test, obtained F calculated is smaller than the F table. So it can be concluded that there is a closeness between the results of ANFIS model predictions with actual data (Model is Valid).

3.   The simulation results predicted GDRP growth for the next period, using five indicators of GDRP in 2010 as input data, generate the GDRP growth in 2011 for a period of 5.7614%.

4.   Membership function type and amount of data will affect the faint end of the inference system is obtained which also affects the prediction accuracy, as evidenced by variations in the RMSE of the overall test results.