**Fuzzy Time Series and Artificial Neural Network: Forecasting Exportation of Natural Rubber in Malaysia**
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**HIGHLIGHTS**
- There are seven algorithms chosen in this study which are Quick Propagation, Conjugate Gradient Descent, Quasi-Newton, Limited Memory Quasi-Newton, Levenberg-Marquardt, Online Back Propagation and Batch Back Propagation.
- The smallest absolute error which is 6054.3744 by Limited Memory Quasi-Newton algorithm.
- The lowest value of MSE, RMSE and MAPE by using Fuzzy Time Series compared to Artificial Neural Network (ANN) Model.
ABSTRACT
*Natural rubber is one of the most important crops in Malaysia alongside palm oil, cocoa, paddy, and pineapple. Being a tropical country, Malaysia is one of the top five exporters and producers of rubber in the world. The purpose of this study is to find the forecasted value of the actual data of the number of exportations of natural rubber by using Fuzzy Time Series and Artificial Neural Network. This study is also conducted to determine the best model by making comparison between Fuzzy Time Series and Artificial Neural Network. Fuzzy Time Series has allowed to overcome a downside where the classical time series method cannot deal with forecasting problem in which values of time series are linguistic terms represented by fuzzy sets. Artificial Neural Network was introduced as one of the systematic tools of modelling which has been forecasting for about 20 years ago. The error measure that was used in this study to make comparisons were Mean Square Error, Root Mean Square Error and Mean Absolute Percentage Error. The results of this study showed that the fuzzy time series method has the smallest error value compared to artificial neural network which means it was more accurate compared to artificial neural network.*
*Keywords: Fuzzy Time Series, Artificial Neural Network, exportations of natural rubber, Mean Square Error, Root Mean Square Error, Mean Absolute Percentage Error*
# INTRODUCTION
Natural rubber is one of the most important crops in Malaysia alongside the palm oil, cocoa, paddy, and pineapple. Being a tropical country, Malaysia is one of the top five exporters and producers of rubber in the world. According to Cornish (2017), tropical countries that were currently natural rubber supplies were vulnerable because global demand is increasing rapidly that led by the industrialization of developing countries, labour shortages and fungal crop diseases.
According to MdLudin, Applanaidu, and Abdullah (2016), one of the main contributors in Malaysia is the agricultural sector and it is also considered as one of the main contributors in Malaysia Gross Domestic Product (GDP) in 1980 with contribution around 22.9 percent. They also stated that the rubber has contributed around 39.8 percent in the agricultural sector in 1984. This shows that rubber is important to the agricultural sector as it is one of the biggest contributors in that sector. However, according to Department of Statistics Malaysia, the implementation of the Movement Control Order in this year has an impact to the establishment that carries out rubber processing activities. The production of natural rubber for this year is decreases compared to the last year. The techniques used in this study were Fuzzy Time Series and Artificial Neural Network. According to Cai, Zhang, Zheng and Leung (2015), fuzzy time series were first introduced by Song and Chissom in 1993. They also stated that the fuzzy time series have been proven that it can be appropriately applied to datasets of linguistic values to generate forecasting rules with high accuracy. Next, artificial neural networks are one type of network that see the node as artificial neurons and it is a software implementation that resembles the biological term central nervous system that is the human brain (Narvekar & Fargose, 2015).
When the exportation of natural rubber increases, the rubber industry export earnings increase, the foreign exchange earnings increase, and income of Malaysia also increase as natural rubber is one of the contributors to income in Malaysia. However, there is a variation in the monthly exportation of natural rubber statistics. This will lead to vagueness in the level of export earnings, foreign exchange earnings and it will affect the income of Malaysia too. Therefore, a precise forecasting model is needed in order to aid the government to predict the future value of the exportation of the natural rubber. The forecasting model also helps the government to make a felicitous plan to avoid losing the income, losing in export earnings and also losing in the foreign exchange earnings.
# RESEARCH METHODOLOGY
**Fuzzy Time Series**
**Step 1:** All of the data were analyzed and then they were changed into percentage form. The formula is as shown below:
(1)
where;
\(y_{n}\)= number of exportations of the natural rubber
\(y_{n - 1}\)=number of exportations of the natural rubber before
**Step 2:** There were two values that needed to be identified from the percentage of changes which were the minimum value and the maximum value. The universe of discourse (*U*) needed to be identified by using *U*= \[\(D_{\min} - D_{1},D_{\max} + D_{2}\rbrack\) after identifying the two values. \(D_{1}\) and \(D_{2}\) represent two positive numbers that need to be assigned in *U*.
**Step 3:** The fuzzy sets \(U_{i}\) needed to be constructed within the same length of intervals where *i* equal to 1 until 7. The fuzzification of interval and the frequency distribution of each interval needed to be identified in this step. The length of interval for fuzzification is calculate as:
Length of interval = \(\frac{\left( D_{\max} + D_{2} \right) - \left( D_{\min} - D_{1} \right)}{7}\) (2)
**Step 4:** The interval of \(v_{1}\), \(v_{2}\),…,\(\ v_{n}\) needed to be generated based on step 2. The interval needed to be done in the form of trapezoidal number. It can be represented as shown below:
\(A_{1}\)= \[\(b_{o},b_{1},b_{2},b_{3}\)\],
\(A_{2}\)= \[\(b_{1},b_{2},b_{3},b_{4}\)\],
\(A_{3}\)= \[\(b_{2},b_{3},b_{4},b_{5}\)\],
.
.
.
\(A_{n}\)= \[\(b_{n - 1},b_{n},b_{n + 1},b_{n + 2}\)\]
**Step 5:** All of the data were listed in terms of percentage and each data was classified based on the interval that has been generated in step 4. The fuzzy set \(A_{i}\) showed a linguistic value and if the data were founded in the range of \(v_{j}\), then it would be a fuzzy number that was \(A_{j}\). Then, fuzzy logical relationship needed to be generated based on the data that have been classified. Fuzzy logical relation is symbolized as shown below:
\(A_{i}\) → \(A_{j}\) ,
where \(A_{i}\) is presented in form and \(A_{j}\ \)is the future form.
**Step 6:** Based on the fuzzy logical relations in step 5, fuzzy logical relationship rule needed to be created. The fuzzy logical relationship rule needed to be arranged in groups.
**Step 7:** Each fuzzy relationship rule group should be classified into one of three different types of rule. The forecasted production for each group was different according to the rules set. The rules are as shown below:
Rule 1: The fuzzy group of \(A_{j}\) is empty which means \(A_{j}\) has no relationship rule others. It can be symbolized as \(A_{j}\) →∅ or it can also be represented as \(A_{j}\)→\(A_{j}\). The forecasted value formula for this rule is:
\(F_{\text{vt}}\)= *R* \[*NSTFN (*\(A_{j})\)\]. (3)
Rule 2: The fuzzy group of \(A_{j}\) is one to one which means there is only one relationship rule that is related to \(A_{j}\) and can be written as \(A_{j}\)→\(A_{m}\). The forecasted value is calculated as formula shown below:
\(F_{\text{vt}}\)= *R* \[*NSTFN* (\(A_{m})\)\]. (4)
Rule 3: The fuzzy group of \(A_{j}\) is one to many. The forecasted value is calculated as shown below:
\(F_{\text{vt}}\) = *R* \(\left\lbrack \frac{\text{NSTFN}\left( A_{m1} \right) + NSTFN\left( A_{m2} \right) + NSFTN\left( A_{m2} \right)}{n}\ \right\rbrack\) (5)
where n is the number of \(A_{i}\) *in this group.*
**Figure 1:** Step of Fuzzy Time Series
**Artificial Neural Network**
**Figure 2:** Steps of using Alyuda NeuroIntelligence Software
**FINDINGS AND DISCUSSION**
**Fuzzy Time Series**
**The figure below shows the actual value versus forecasted value.**
\[CHART\]
> **Figure 3:** Actual value versus forecasted value of exportations of natural rubber
**Artificial Neural Network**
**There are seven algorithms that were compared by the absolute error. The table below shows the absolute error of the training network output of the 7 algorithms.**
***Table 1:** Absolute error of the algorithms of the training network output*
| **Type of algorithms** | **Absolute error** |
| ------------------------------- | ------------------ |
| **Quick Propagation** | **6054.3862** |
| **Conjugate Gradient Descent** | **6116.9826** |
| **Quasi-Newton** | **6114.5047** |
| **Limited Memory Quasi-Newton** | **6054.3744** |
| **Levenberg-Marquardt** | **15104.3879** |
| **Online Back Propagation** | **6580.4901** |
| **Batch Back Propagation** | **9881.7004** |
From Table 1 above, Limited Memory Quasi-Newton algorithm has the smallest absolute error which is 6054.3744. Figure below shows the result of the network training.
Figure 4 below showed the graph of actual data versus output data based on Limited Memory Quasi-Newton and the Table 3 below shows the summary table that contains the value of the target, output, absolute error (AE), absolute relative error (ARE), mean, standard deviation, minimum and maximum value based on Limited Memory Quasi-Newton.
> **Figure 4:** Graph of Actual versus Output based on Limited Memory Quasi-Newton
***Table 2:** Summary table based on Limited Memory Quasi-Newton*
| | **Target** | **Output** | **AE** | **ARE** |
| ------------------ | -------------- | ---------------- | -------------- | ---------- |
| **Mean** | **63502.4815** | **63680.0424** | **6326.9094** | **0.0985** |
| **Std. Deviation** | **12448.3609** | **9944.8572** | **5720.0362** | **0.0749** |
| **Min** | **40512** | **51278.9074** | **198.5680** | **0.0038** |
| **Max** | **111020** | **95580.606728** | **39666.0426** | **0.3573** |
**The correlation value and r-squared value of the target and output are 0.7316 and 0.2644 respectively.**
**Comparison of Models and Selection of The Best Model**
Table below shows the comparison between the two models by using model evaluations which are MSE, RMSE and MAPE for Fuzzy Time Series and Artificial Neural Network techniques.
**Table 3:** Comparison of model evaluation
| **Error** | **Techniques** | |
| --------- | --------------------- | ----------------------------- |
| | **Fuzzy Time Series** | **Artificial Neural Network** |
| MSE | 57120876.6463 | 72748596.88677 |
| RMSE | 7557.8354 | 8529.2788 |
| MAPE | 7.1457 | 9.8528 |
Table above shows that the fuzzy time series techniques have the lowest value of MSE, RMSE and MAPE than the artificial neural network techniques. Therefore, the best model to forecast the monthly export of natural rubber is by using fuzzy time series model because it has the lowest value of MSE, RMSE and MAPE.
**CONCLUSION AND RECOMMENDATION**
In conclusion, fuzzy time series method and artificial neural network method have been used in this study to make comparisons. The data used was the number of exportations of natural rubber. Both methods also have been used to determine which method was the best method by comparing the error measures. The method that has the smallest error value was the best method because it was more accurate. The results obtained show that the fuzzy time series method has the smallest error value compared to artificial neural network. The value of MSE, RMSE and MAPE of fuzzy time series are 57120876.6463, 7557.8354 and 7.1457 respectively. Since, fuzzy time series method has the smallest error measure, fuzzy time series is the best method compared to artificial neural network method.
There are several recommendations that are suggested for future study. First, researchers can also use another data to make comparison by using the same techniques. Next, other methods can be used to make comparisons and with this, it can help to see the variation of the techniques used. Lastly, another error measure can also be applied in order to choose the best method such as Geometric Root Mean Squared Error (GRMSE).
**FINDINGS AND DISCUSSIONS**
The purpose of the discussion is to interpret and describe the significance of your findings considering what was already known about the research problem being investigated, and to explain any new understanding or insights about the problem after you've taken the findings into consideration. The discussion will always connect to the introduction by way of the research questions or hypotheses you posed and the literature you reviewed, but it does not simply repeat or rearrange the introduction; the discussion should always explain how your study has moved the reader's understanding of the research problem forward from where you left them at the end of the introduction. (Annesley, 2010).
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