The Prediction on the Amount of Fertilizers Ordered Using Mamdani s Method of Fuzzy Inference System

Transcription

1 4 th ICRIEMS Proceedings Published by The Faculty Of Mathematics And Natural Sciences Yogyakarta State University ISBN The Prediction on the Amount of Fertilizers Ordered Using Mamdani s Method of Fuzzy Inference System Fitriani 1 a) Nurafni Retno Kurniasih 1 b) 1 c) Gity Wulang Mandini 2 d) Agus Maman Abadi 1 Graduate Programe of Mathematics Education Yogyakarta State University 2 Department of Mathematics Faculty of Mathematics and Natural Science Yogyakarta State University Jl Kolombo No 1 Karangmalang Depok Sleman Yogyakarta Indonesia a) Corresponding author: fitrianifitri240@gmail.com b) retnoafni@gmail.com c) gitywulangmandini@gmail.com d) agusmaman@uny.ac.id Abstract. The main aim of this research is in order to predict the amount of supplied fertilizer orders based on customers demand and company s supply by using Mamdani method of Fuzzy inference System. The used data is from one distributor of fertilizer sales located in Semarang Jawa Tengah. The data on demand and supply were used as the input and order as the output system. Afterwards the fuzzy set of each input and output variables are defined. From the defined set of fuzzy its fuzzy logic was determined. The specified fuzzy logic is used for the inference process with Mamdani method. After that they were defuzzified with a center of gravity method and therefore the result would be the prediction on supplied fertilizer orders. The result is the prediction by using Mamdani s fuzzy inference system which is well-received with MAPE error rate only reached 15%. INTRODUCTION Any business area that is related to the sale of goods requires further consideration of many aspects in determining the needs of the amount of ordered goods to meet the availability and the demand of / from the supply. Excessive ordered goods or deficiencies can cause various problems one of which is on the financial aspect. Maximum profit comes from maximized sales. Maximum sales means a company has to meet the existing demands. If the amount of products to market by the company is less than the amount of demand then the company will lose the opportunity to reach the maximum profit. Conversely if the amount of products is far more than the amount of demand then the company will lose it. Therefore a plan on the amount of products within the company is very important in order to meet the exact market s demand with the appropriate amount [1]. The result of the rapidly growing development of science and technology is one of the computational methods using the Fuzzy Logic model (blurred logic). Fuzzy models have been applied to various fields such as economics engineering communications medicine climatology and meteorology and so on [2]. One application of fuzzy set theory in economics can be used to predict the amount of produced order of goods from the supply. In predicting with fuzzy logic the two used variables are input and output variables [3]. Fuzzy logic theory was first introduced by Zadeh Lotfi Asker Zadeh a professor at Universitity of California Berkeley USA since Zadeh made a new breakthrough that expanded the concept of the crisp sets in the sense that a firm set is a specific occurrence of fuzzy sets [4]. Fuzzy is defined as something vague obscure and confusing. The three things needed to understand the basics of fuzzy logic are fuzzy set membership function and logic operations [5]. In fuzzy set the existence of one element is no longer about whether it is true or false but it will always be true if it has a degree of membership within the range [6]. Fuzzy systems and controls human knowledge is expressed in the if-then fuzzy rule terms [7]. The calculation of fuzzy logic constitutes several methods including the Mamdani method. In this paper this particular method will be used to assist the business of Toko Distributor Pupuk Umarah in Sidomukti RT.29 RW. 05 Kopeng Getasan Semarang Jawa Tengah. The main problem of this research is determining how to predict the amount of the order by using Mamdani method of fuzzy inference system. Predicting a system is usually done M - 27

2 by learning from the past for which historical data is obtained and analyzed to study the resulting pattern in the markets has boomed in recent years [8]. Predicting any event requires knowledge about past performance. Data from the past is used mainly to learn the patterns that existed. Historical data provides information on the specific pattern of learning the data. Learning from the past provides knowledge about future to some extent [9]. In this research used mamdani method. In terms of use the Mamdani FIS is more widely used mostly because of the reasonable results with a relatively simple structure it provides and the intuitive interpretable nature of the rule base [10]. Fuzzy inference is the process of mapping the given input variables to an output space via fuzzy logic based deducing mechanism which is comprised by If-Then rules membership functions and fuzzy logical operation [11]. The Mamdani method is also known as Min-Max method by finding the minimum value of each rule and the maximum value of the combined consequences of each rule [12]. This study aims to describe the use of fuzzy logic in predicting the amount of orders. For entrepreneurs this research can be the basis of a consideration on the decision of the number of supplied goods orders. For academics the result of this study is expected to be a useful material and to add new finding on the field of entrepreneurship and hopefully it can be a reference for further research. RESEARCH METHODS The determination of the number of orders using Fuzzy Inference System with Mamdani Method in this study went through the six steps there is in each month. These steps are described as follows: 1. To define Input and Output System Inputs that is used in this study consists of two kinds demand and supply. The demand by the set of rules [80 200] and supplies with the set of rules [0 50]. While output used in this research that the amount of order with the set of rules [ ]. 2. To define the Fuzzy Set Membership Function Fuzzification Interface converts the input values into linguistic terms of the input fuzzy variables [13]. Membership function for each input and output consisting Of Three categories category Low Medium and High. 3. To determine the Fuzzy Rules (the rule) This stage is the stage of preparation the rules is using the pair s relationship of data input and output. 4. To perform the Inference and defuzzification Rule that is formed is then used to process the fuzzy inference Mamdani method. The results of this inference is processed using defuzzifier. Defuzzification is the stage where the value obtained from the fuzzy inference process is converted into firm value. The defuzzification using centroid method which takes a central point fuzzy area produced in the process of inference. 5. The determine MAPE and MSE as a large error gauge of a model RESULTS AND DISCUSSION The used data for the system design is the demand supply and orders of fertilizers every month with unit of sack (a sack equals to 50 Kg) from January to December 2016 at Toko Umanah Sidomukti RT.29 RW. 05 Kopeng Getasan Semarang Jawa Tengah. The data mentioned is as follows. TABEL 1. Data the demand supply and orders of fertilizers every month Month Demand Supply Order January February March April May June July August September October M - 28

3 Month Demand Supply Order November December In the process of determining the prediction of the amount of supplied fertilizer orders the steps are presented as follows: 1. To define Input and Output System Based on the data shown in Table 1. two parameters chosen as the inputs are demand as first input supply as second input. Meanwhile the system output is order. 2. To define the Fuzzy Set Membership Function Membership functions used are Triangular Membership Function and Trapezoidal Membership Function. Based on the pre-defined universal set the system membership functions by using the Matlab R2009a application are explained as follows: a. For the membership function with demand variable it consists of (Low Medium High) x x x 100 x 140 low 40 0 x 140 x medium x high 0 x 100 atau x 180 x x x x 40 0 x 140 x x x 180 FIGURE 1. The membership of demand variable b. For the membership function with "supply" variable it consists of (Low Medium High) y y x 10 y 30 low 15 0 x 30 x medium 0 y 10 atau y 40 y y y y 15 M - 29

4 x high 0 y 25 y y y 40 FIGURE 2. The membership of supply variable c. For the membership function with the order variable it consists of (Low Medium High) ( z) z ( z) low 30 low 0 z z 30 z150 ( z) medium z z 150 z 150 z 120 atau z z z 180 z z 180 z 180 FIGURE 3. The membership of order variable M - 30

5 3. To determine the Fuzzy Rules The determination process of the rule used the membership function of the pre-defined fertilizer demand supply and production. With these functions the research continues to seek the highest degree of membership of multiplication between the fuzzy numbers on each input. TABLE 2. The calculation of the Membership Degree (Dk) Category Membership Degree (MD) MD No. Demand Supply Order Multiplication Demand Supply Order Demand Supply Order High Medium Low Medium Medium Medium Medium Medium Medium Low Medium Medium Medium Medium Medium Medium High Medium High High Low Medium Medium Medium Medium High Medium Medium Low Tinggi High Low Low Medium Low High TABEL 3. Fuzzy rule selection Input Demand T S S R S S T S S S T S Supply S S S S S T T S T R R R Outpu t Order R S S S S S R S S T R T The multiplication result Rule R1 R2 R3 R4 R5 R6 R7 Additional Information: S: Medium R: Low T: High Therefore the formed rules are 7 with the translation as follows: TABEL 4. Resulted fuzzy rules Role Rule 1 T-S-R If the demand is HIGH and the supply is MEDIUM the order will be LOW Rule 2 S-S-S If the demand is MEDIUM and the supply is MEDIUM the order will be MEDIUM Rule 3 R-S-S If the demand is LOW and the supply is MEDIUM the order will be MEDIUM Rule 4 T-T-R If the demand is HIGH and the supply is HIGH the order will be MEDIUM Rule 5 S-T-S If the demand is MEDIUM and the supply is HIGH the order will be MEDIUM Rule 6 S-R-T If the demand is LOW and the supply is MEDIUM the order will be HIGH Rule 7 T-R-R If the demand is HIGH and the supply is LOW the order will be LOW 4. Inference and defuzzification Using Mamdani Fuzzy Inference System (FIS) and centroid defuzzification obtained data of predictive of souvenir pottery production as Table 5. M - 31

6 TABLE 5. The prediction on the fertilizer orders Month Demand Supply Order Prediction Order January February March April May June July August September October November December To determine MAPE and MSE of a model After finding out the predicted value of orders amount (P*) the research proceeds to count the MSE (Mean Squared Error) and MAPE (Mean Absolute Percentage Error). MSE is the average error in predicting the squared. This method calculates a large error prediction because these errors are squared. Here's the formula for in calculating the MSE. MSE n 1 n ( Yt P) 2 t1 Meanwhile MAPE is the middle value of the absolute percentage error of the prediction. MAPE indicates how much error occurs in predicting the order compared to the actual value in the series. Here's the formula for calculating the MAPE. MAPE n 1 n t1 Yt P* t Y The calculation of P* MSE and MAPE in this research data are shown in the table below TABLE 6. Data MSE and MAPE MSE No. Yt G*t ( t t Y P* ) t 2 MAPE Y t P* t Yt Median M - 32

7 Based on the table 6 it is known that the prediction on the error rate of fertilizer orders by using the Mamdani method of vague inference system is or 15%. CONCLUSION Based on the description above it can be concluded that the prediction of the amount of fertilizer orders by using the Fuzzy Inference System with input in the form of fertilizers demand and supply the result shows a good accuracy with error rate of or 15%. REFERENCES 1. M. Abrori and A. H Prihamayu Kaunia Journal of UGM (2015). 2. H. Tatli and Z. Sen Journal of Engineering and Environmental Science (1999). 3. S. Sandhopi IEEE Journal (2004). 4. F.S. J Susilo Himpunan dan Logika Kabur serta Aplikasinya (Graha Ilmu: Yogyakarta 2006). 5. R. T. Wang Title of Chapter in Classic Physiques (Publisher Name Publisher City 1999). 6. Fitriah Aidatul and A. M. Abadi AIP Conference Proceedings 620 (American Institute of Physics: New York 2002). 7. G. J. Klir dan B. Yuan Fuzzy Sets & Fuzzy Logic Theory & Applications (Prentice Hall International: New Jersey 1997). 8. L. X. Wang A Course in Fuzzy System and Control (Prentice Hall International: New Jersey 1997). 9. J. Wolfers E. Zitzewitz IZZA Discussion Paper (2006). 10. V. Vaidehi S. Monica M. S. Safeer D. M. Sangeetha A Prediction System Based on Fuzzy Logic (WCECS:San Fransisco 2008). 11. J. J. Jassbi P. J. A. Serra R. A. Ribeiro and A. Donati A International Journal of Computer Applications (2015). 12. C. Wang A study of membership functions on mamdani-type fuzzy inference system for industrial decisionmaking Candidacy for the Degree of Masters of Science Lehigh University (2015). 13. NamithaSona ShantharamaRai.c International Journal of Recent Technology and Engineering (2013). M - 33

8 M - 34