Adaptive neuro-fuzzy inference system for forecasting rubber milk production

Natural Rubber is classified as the top export commodity in Indonesia. Its high production leads to a significant contribution to Indonesia’s foreign exchange. Before natural rubber ready to be exported to another country, the production of rubber milk becomes the primary concern. In this research, we use adaptive neuro-fuzzy inference system (ANFIS) to do rubber milk production forecasting. The data presented here is taken from PT. Anglo Eastern Plantation (AEP), which has high data variance and range for rubber milk production. Our data will span from January 2009 until December 2015. The best forecasting result is 1,182% in term of Mean Absolute Percentage Error (MAPE).


Introduction
Rubber is one of the leading plantation commodities that contribute significantly to non-oil exports. The increase in rubber exports is very significant, of export volume of 1.496 million tons valued at USD 1038 million in 2002 increased to 2.35 million tons valued at USD 7330 million in 2010 or an increase of 57%. The export contribution of plantation sector above is expected to be the driver of national economic development in the future [1]. The increased demand for rubber spurred an increase in the rubber milk production in rubber producing countries in the world, including Indonesia. Rubber is a vital need for human life, and it is associated with the mobility of human and goods that require components made of rubber such as tires, conveyor belt, transmission belt, etc. Rubber industries have to prepare raw materials in accordance with market demand to meet those needs. Rubber milk production is paramount to rubber industries. Rubber companies expect the accurateness of rubber milk production in term of its amount and time. Therefore, state-owned or private plantation companies require a system that can predict the production precisely.
Forecasting is an attempt to predict future circumstances through examination of the past circumstances [2]. One of the quantitative forecasting techniques is time series data forecasting, a set of observations built in sequence within a specified time in which data can be data daily, weekly, monthly, etc. [3]. Time series data forecasting has been developed in soft computing such as fuzzy method, genetic algorithm, neural networks and hybrid method.
ANFIS is a method that uses a neural network to implement fuzzy inference system. In other words, ANFIS is the incorporation of fuzzy inference system mechanisms depicted in artificial neural network architecture. In statistical modeling, ANFIS is applied to classification, clustering, regression, and forecasting in time series data [10].  Several kinds of research have been conducted. In 2013, Agus Harianto did a research on the forecast of rubber milk production using Autoregressive Integrated Moving Average (ARIMA) method [4]. The best ARIMA model for rubber milk production forecasting is ARIMA model (2,1,1) with an estimated R2-squared parameter of 93.20, AIC value (Akaike Information Criterion) of 25.64, SIC value (Schwarz Information Criterion) of 25.84 and significant probability close to zero. With the measurement result of forecasting error with MAPE (Mean Absolute Percentage Error) parameter of 1.37, MAD (Mean Absolute Deviation) value of 380,5, MSE (Mean Squared Error) value of 5.194.584.081 and MPE (Mean percentage Error) value of 0.01. The analysis of production forecasting shows that production of 2012 to 2013 is predicted to be increasing year by year with a small error rate.
In 2015, Hani'ah did adaptive neuro-fuzzy inference system (ANFIS) implementation for water use forecasting at Tirta Moedal Semarang drinking water company [5]. Ria in 2014, did weather forecasting using case-based reasoning and adaptive neuro-fuzzy inference system methods [6]. Gernowo and Yenny in 2013 used ANFIS to predict the variability of Indonesian Rupiah exchange value against US dollar. The result shows that the proposed method is capable in predicting the rise and fall of exchange rate fluctuations [7]. Saputra in 2012 applied ANFIS to analyze time series data [8]. Widyapratiwi in 2012 did short-term power load forecasting in Bali using adaptive approach neuro-fuzzy inference system (ANFIS) [9]. Several other methods to do forecasting also has been analyzed such as exponential smoothing method for palm oil production [11], evolving multilayer perceptron [12] [16], distributed and adaptive neural network [13] [14] [17] and fast learning algorithm [15].
A company needs a precise forecasting of rubber milk production to be used as a reference to compose a business plan. The forecasting of rubber milk production done manually usually experiences a problem in the form of production prediction results that are not in accordance with the actual production results, so it required a proper method that generates a précised forecasting of the production to be used as a reference to compose a business plan of plantation company.

Methodology
Forecasting system of rubber milk production using adaptive neuro-fuzzy inference system (ANFIS) is a system that delivers results in rubber milk production forecasting based on time series data in the past. The system will receive input in the form of monthly production data. Afterwards, the data will be processed using adaptive neuro-fuzzy inference system method to generate the forecast result. The general flowchart of the proposed method can be seen in Figure 1. The principal work of the forecasting system of rubber milk production to be built is designed as follows: 1. Input CSV file data containing rubber milk production data through input form. 2. Set the input parameters in the form of with maximum epoch and maximum error. 3. Form network structure of ANFIS. 4. Classify rubber milk production data inputted into two clusters using fuzzy c-means algorithm and determine the type of membership function to be used. The system will use generalized bell membership function, as follows: Where: ( ) = membership degree Z = the amount of production c = premise parameter, the initial value is determined using mean cluster = premise parameter, the initial value is determined using the standard deviation of the cluster b = premises parameter value 1 3

1234567890''""
10th The output value of generalized bell membership function is layer 1 output of ANFIS. 5. Compute layer 2 output by multiplying weight values in the corresponding layer 1. 6. Compute layer 3 output by dividing the weight of each w1 or w2 by the amount of weights w1 + w2 in the second layer. 7. Compute output layer 4 by multiplying the output weights of layer 3 3 w1f1 and w2f2 also set the consequent parameter values using LSE Recursive. 8. Compute layer 5 output, in the form of output prediction which error value can be calculated by subtracting the actual output value with the value of output prediction. If the error is smaller than the maximum error specified in the input form, the system will stop and generate an output prediction. 9. The system will store the production data into a database along with all premise and consequent parameters.

ANFIS Simulation
The implementation of ANFIS calculation in the prediction of rubber milk production can be simulated as follows. Supposed the given time series data of 8 rubber milk production data are shown in Table 1 4 1234567890''"" Given ANFIS input in the form of −1 and −2 while the output is in the form of as shown in Table 2. Since the number of clusters is 2, then Sugeno model of ANFIS rule is as follows: 2 ℎ = 2 −2 + 2 −1 + 2 Afterwards, clustering process will be performed using fuzzy c-means clustering. Clustering result can be seen in Table 3 Since the membership function used is generalized bell: Determined the value of b=1 also as the initial value of a and c, mean value and standard deviation were used can be seen in Table 4. The result of layer 1 output in the form of membership degree of each data can be seen in Table 5. w 1 = μ A1 (x). μ B1 (X); w 2 = μ A2 (x). μ B2 (X); The calculation result of layer 2 output can be seen in Table 6.
The calculation result of layer 2 output can be seen in Table 7.
The calculation result of layer 4 output can be seen in Table 8. The estimation of consequent parameters (p1, p2, r1, p2, q2, and r2) can be computed using LSE recursive method as follows:
Layer 5: layer 5 output can be computed by multiplying the obtained consequent parameters with layer 4 output (A matrix), layer 5 output can be seen in Table 9. The estimation of premise parameters (a,c) is using error gradient descent propagation model.

Experimental Results
Data used for the testing in this research is monthly rubber milk production data of private company period January 2009 -December 2015. Production data consists of 696 data. The composition of training data amounted to 588 data and data testing amounted to 108 data.
The training result of ANFIS method can be tested using mean absolute percentage error (MAPE) as follows: Where y is the actual data, p is the prediction data, and n is the amount of data. From the result, obtained MAPE value of 1.182%.  After training result was obtained, continued by performing a test on 108 data testing of rubber milk production data period January 2015 -December 2015. Based on training data, produced the smallest error value during training process which is 1.198%. The testing aims to test the accuracy of ANFIS architecture in identifying time series data patterns. From the testing results, obtained the smallest MAPE error value of 1.182%. The testing result of rubber milk production prediction that generates MAPE error value of 1.182% can be seen in Table 10, Figure 2 and Figure 4.

Figure 4. Graphic of testing result
The prediction testing is conducted to find out the result of rubber milk production for the next 12 periods. The testing result will show the predictive production data and prediction testing graphic. In Figure 4.5. Can be seen the results of production predictions and the graphs for production period January 2016 -December 2016. Based on the results of data training and data testing that have been conducted, it can be seen that the ANFIS prediction of rubber milk production generated MAPE error of 1.182%. When compared to Harianto's research in 2013 which researched rubber milk production using ARIMA method that produces MAPE error of 1.370%, the prediction of rubber milk production using ANFIS generates relatively smaller error compared to ARIMA method.

Conclusion
Based on the result, ANFIS is successfully implemented in a system to predict the production of rubber milk. The error rate of prediction result using ANFIS is relatively smaller, which is MAPE error value of 1,182%, if compared to previous research done by Harianto using ARIMA with MAPE error value of 1,370%.
For further research, we can apply other fuzzy determination methods to determine the value of fuzzy in the early stage of adaptive neuro-fuzzy inference system method. It is expected that adaptive neuro-fuzzy inference system method can be analyzed and compared to other methods in similar research data, to get more accurate prediction results by comparing the mean error between those methods.