Application of Fuzzy Logic for Predicting the Production of Pottery Souvenir

Transcription

1 4 th ICRIEMS Proceedings Published by The Faculty Of Mathematics And Natural Sciences Yogyakarta State University, ISBN Application of Fuzzy Logic for Predicting the Production of Pottery Souvenir Venti Indiani,a), Azmi Yanianti,b), Swasti Diah Widiaswari,c), Agus Maman Abadi ) Postgraduate of Mathematics Education, Yogyakarta State University 4 Department of Mathematics, Faculty of Mathematics and Natural Science, Yogyakarta State University, Jl Kolombo No, Karangmalang, Depok, Sleman, Yogyakarta, Indonesia Corresponding author: a) ventindiani@gmail.com b) azmiyanianti@gmail.com c) swastidiah.5@gmail.com d) agusmaman@uny.ac.id Abstract. In this globalization the industry is faced with increasingly competitive competition. It requires manufacturers to be able to plan or determine the amount of production in order to meet market demand. Thus predicting the amount of production is an important activity in the industrial sector. One of the way to predict the amount of production is using fuzzy logic. This theory is introduced by Lütfi Asker Zadeh in 96. The purpose of this research is to build fuzzy logic by using Mamdani Method application to predict the souvenir production of pottery in Arum Art Craft Centre, Klipoh Borobudur. The steps taken to predict the number of souvenirs of pottery using Mamdani Method are as follows: ) identify input and output variables and the set of the universe; ) define membership function; 3) determine fuzzy rules; 4) inference and defuzzification; 5) determine MAPE as a large error gauge of a model. Implementation of fuzzy logic in the prediction of the number of production looks at the two inputs in the form of demand and supply. The data obtained by interviews with the owner of craft centers. While the output of fuzzy logic in the form of pottery souvenir production quantities. The results of this study can be seen that the application of fuzzy logic using mamdani method can predict the number of souvenir production of pottery with an error rate of or 6.37%. INTRODUCTION In this globalization era, the industry faced an competitive rivalry. It requires manufacturers be able to plan or specify the amount of production in order to fulfil market demand. It can be said that the activity in predicting the amount of production is an essential activity []. In addition, predicted number of production also aimed to reduce the cost production to increase revenue []. A lot of applications of intelligent systems can be used for predicting [3]. One theory that could be used to predict the amount of production of goods that is fuzzy set theory. Fuzzy set theory is a logical structure introduced by Lütfi Asker Zadeh in 96 [4]. This logic theory dealing with the concept of partial truth. If in classical logic claimed that everything can be epressed in terms of binary (0 or ), the fuzzy logic enable membership value between 0 and [4]. Various theories in developing fuzzy logic shows that this fuzzy logic can be used as a model of variety systems. Fuzzy logic is considered able for mapping an input to an output by focusing into eisting factor, as well as working with verbal rules "if... then..." [4]. Based on fuzzy logic, it will produce a model of a system capable to estimate production quantities. There are factors that influence in determining the amount of production with fuzzy logic, the number of demand and the amount of supply. Furthermore, according to some studies said that the use of modern theory can support the management to improve operational efficiency, reduce operating costs and increase revenue[5]. The centre of home industry in Dusun Klipoh District Borobudur Magelang Regency, Central Java is the centre of craft that producing variety of pottery souvenir. This home industry also became tourism place for tourist, not only local but also international for seeking souvenir to be brought to their homes. The strategic location which is located in the center of the Borobudur temple make this home industry has a great opportunity to develop. As in M - 7

2 this study, researchers took samples of data on craft center "Arum Art", one home industry is located in the Dusun Klipoh District of Borobudur Magelang, Central Java. Based on the above, it can be drawn the research problem that is how to predict the number of souvenir pottery production based on fuzzy logic by focusing the number of demand and supply. This study aimed to design a fuzzy system applications that can estimate the number of souvenir pottery production by focusing the number of demand and supply. Some of the benefits that epected of this study are: () as a useful input for producers to consider the amount of production, () epected to be able as a measurement of the production planning process, and (3) increase knowledge in the application of the concept of fuzzy logic, especially for industry. METHODOLOGY This study is conducted Fuzzy Inference System using Mamdani method. Mamdani is the basic and easy [6]. So this paper Mamdani method is selected. Standard fuzzy logic controller is using membership function to define the input variable or variables as well as the output variable[7]. Membership function is a curve showing the mapping of points in the data input to a values or degree of membership in a fuzzy set with an interval 0 and which is different from membership value in crips set which has possibilities only, namely 0 and [8]. The fuzzy controller can be different type but the most frequently used is the triangular membership function [7]. Here are the steps to predict the number of pottery souvenir production using Mamdani method as follows.. Identify the input and output variables as well as the set of rules Inputs that is used in this study consists of two kinds, demand and supply. The demand by the set of rules [ ] and supplies with the set of rules [0 50]. While output used in this research that the amount of production with the set of rules [ ].. Define the function of membership (Fuzzification) Fuzzification Interface converts the input values into linguistic terms of the input fuzzy variables [9]. Membership function for each input and output consisting Of Three categories, category Slight, Fair, and Much. 3. Determine Fuzzy Rule The Rule base is defined by the rules for the desired relationship between the input and output [9]. This stage is the stage of preparation, the rules is using the pair s relationship of data input and output. 4. Interference and Defuzification Rule that is formed is then used to process the fuzzy inference Mamdani method. The results of this inference is processed using defuzzifier. The output of the fuzzy logic controller depends on the membership grades of the rules [0]. 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. The output of inference stage of Mamdani method is a fuzzy set. Defozzyificatin refers to evaluating a crisp output from a set of singleton, asset of center of gravities, or a fuzzy set []. 5. Determine MAPE as a measuring errors of a model. RESULTS AND DISCUSSION Based on several studies show that fuzzy logic can be used as a predictive item that is quite accurate. In the study there are two inputs, namely the demand and supply of the Month in October 05 to October 06 were obtained directly from the manufacturer Craft Center "Arum Art" which is located in the Dusun Klipoh, Borobudur, Magelang, Central Java. For the demand data, supply, and production quantities of souvenir pottery at Crafts Center "Arum Art" which is located in the Dusun Klipoh, Borobudur as follows. M - 8

3 TABLE. Demand, supply and total production data of pottery souvenir Period Demand (Unit) Supply (Unit) Total of Production (Unit) October November Desember January February March April May June July August September October The data listed in the column above is the rest of souvenir pottery production from the previous month. For eample, inventory listed in October 05 is the remnant souvenir pottery in the previous month in September 05. Here is the steps to predict amount of pottery souvenir as follow.. Identify the input and output variables with the set of rules talks Based on the data in Table, determined inputs they are inputs demand and supply. While the output of the system is production. TABEL. Determine variabel input and output and set of rule talks Function Name of Set of Talks Notes Variable Input Demand [ ] total demand in a month (unit) Supply [0 50] total supply in a month (unit) Output Total Production [ ] total production in a month (unit). Define the Function of Membership TABLE 3. Fuzzy sets Function Name of Name of Fuzzy Set of Talks Domain (unit) Variable Sets Input Demand Slight [ ] [ ] Fair [ ] Much [ ] Supply Slight [0 50] [0 30] Fair [70 470] Banyak [40 50] Output Total Slight [ ] [ ] Production Sedang [ ] Much [ ] The function of membership that is used is Triangular Membership Function and Trapeziodal Membership Function. a. The function of membership demand input Eplanation: s = slight f = fair m = much M - 9

4 f m ( ( ) ) and and A membership function of demand graph is obtained as follows. FIGURE. Graph of a membership function b. The function of membership supply input Eplanation: s = slight f = fair m = much ( f s ( 0 ) ) and and M - 0

5 m ( ) and A membership function of supply graph is obtained as follows. FIGURE. Graph of a membership supply function c. The function of membership production output Eplanation: s = slight f = fair m = much s f m 0 ( y) 4050 y y 3600 ( y) y y 450 ( y) 480 y 300 and y y y 4050 y 3600 and y y y 5000 y 450 and y y y 5500 A membership function of production graph is obtained as follows. M -

6 FIGURE 3. Graph a membership function of production 3. Determine Fuzzy Rule Before determining fuzzy rule, then we are looking for a degree of each membership of input and output based on the chart above. TABLE 4. Degree of each membership of input and output No Demnd C DM Supply C DM Prodct C DM Output 4850 Fr 0, Fr 0, Fr 0,357 0, Mc 40 Fr 0, Mc 0, Mc 0, Mc 4850 Mc 0,688 0, Fr 0, Fr 4300 Fr 0, Sl 0, Sl 0, Sl 0,667 0, Fr 0, Fr 0, Sl 0,49 0, Sl 30 Sl 300 Sl Sl 0, Fr 0, Sl 0, Mc 0,6 490 Mc 5000 Mc 0, Fr 0, Sl 0, Fr 0,43 0, Sl 0,5 0 Sl 3900 Sl 0,333 0, Fr 0, Fr 0,9 400 Fr 0,74 0, Sl 70 Sl 3600 Sl Eplanation Demnd = Demand C = Category Sl = Slight Fr = Fair Mc = Much DM = Degree of Membership Suppl = Supply Prodct = Production M -

7 TABLE 5. Selection of fuzzy rule Input Demand Fr Mc Mc Fr Sl Fr Sl Sl Mc Fr Sl Fr Sl Supply Fr Fr Mc Fr Sl Fr Sl Fr Mc Sl Sl Fr Sl Output Product Fr Mc Mc Fr Sl Fr Sl Sl Mc Fr Sl Fr Sl Result of Multipl 0,7 0,5 0,443 0,947 0,33 0,39 0,675 0,6 0,047 0,70 0,37 Rule R R R3 R4 R5 R6 Based on the information from the table above, obtained 6 rule or rule as follows. TABLE 6. daftar fuzzy rule Rule Mc Fr Mc If demand much and supply fair then production lot Rule Fr Fr Fr If demand is fair and supply is fair then production is fair Rule 3 Sl Sl Sl If demand is slight and supply is slight then production is slight Rule 4 Sl Fr Sl If demand is slight and supply is fair then production is slight Rule 5 Mc Mc Mc If demand is much and supply is much then production is much Rule 6 Fr Sl Fr If demand is fair and supply slight then production is fair 4. Inference and Defuzzication Using Mamdani Fuzzy Inference System (FIS) and centroid defuzzification, obtained data of predictive of souvenir pottery production as Table 7. TABLE 7. The number of souvenir pottery production Period Predictive Production of (Unit) Production October November Desember January February March April May June July August September October Determine MAPE as a measuring errors of a model After obtaining the predicted value of the amount of production (G ^ *), continuing to calculate the MAPE. MAPE is the mid value in absolute percentage error of prediction. MAPE indicates how big a mistake in predicting that compared to the real value in the series. Here is the formula [] for calculating the MAPE. MAPE n n Y t G t Y t Calculation G and MAPE in this study as shown in TABLE 8. * t M - 3

8 TABLE 8. Calculation of MAPE on prediction No MAPE Y t * Gt Y t G Y t , , , , , , , , , , , ,036 Average 0,06374 * t Based on the table above it can be seen that the MAPE on the predicted number of pottery souvenir production using fuzzy system application that is or 6.37%. CONCLUSION Based on the above it can be concluded that the application of fuzzy system designed to predict the number of souvenir pottery production by focusing on account input of demand and supply has accuracy with an error rate of or 6.39% that obtained based on MAPE. Furthermore, researchers felt the need to do further research to improve the accuracy of prediction of the number of souvenir pottery production, for eample by adding more data and add another input that affects the number of souvenir pottery production. REFERENCES. R. Ramlan, A. P. Chen, S. W. Chan, & Y. Ngadiman, Proceedings of the 06 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, 5-58, (06).. H.Taghizadeh, A. Bazrkar, & M. Abedzadeh, Modern Applied Science, 9, 68-77, (05). 3. Aryanti and M. Ikhtison, Advanced Science Letters, 3, 8-30, (07). 4. M. Poongodi, L. Manjula, S. Pradeepkumar, & M. Umadevi, International Journal of Current Research, 4, 06-0, (0). 5. F. Zhao, & J. Yu, International Conference on Control, Automation and System Engineering, CASE, 4, - 4, (0). 6. Awanit Kumar et al, International Journal of Computer Science and Mobile Computing, 4, 44-56, (05). 7. K. Mousavi, Mashadi, M. Shokohinis,The Journal of Mathematics and Computer Science, 4, , (0). 8. S. M. Mazloumzadeh, M. Shamsi, and H. Nezamabadi, Precision Agric , (00). 9. NamithaSona, ShantharamaRai.c, International Journal of Recent Technology and Engineering,, , (03). 0. EltahirHussan, Ali Hamouda, International Journal of Advanced Research in Electronics and Instrumentation Engineering, 3, 89-84, (04).. G. S. Nhivekar, S. S. Nirmale, R. R. Mudholker, International Journal of Engineering Science and Technology, 3, 76-83, (0).. Wang, Li Xin, A course in fuzzy systems and control, (Prentice-Hall International: New Jersey,997). (reference) M - 4