Forecasting Motorcycle Sales Using Nearest Symmetric Trapezoidal Fuzzy Number

—A business activity aimed at obtaining forecasting as an initial step in planning activities helps provide an overview of sales in a business for the coming period based on data available. This research aims to design and develop a motorcycle sales forecasting application using Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Number approach to predict the next period sales of PT Mutiara Motor. To test the accuracy of the method used in application, we used the MSE and MAPE criteria. Based on the results of three experiments taken: (1) monthly ‘All Category’-’All Type’ with MSE = 54.42 and MAPE = 4.28%, (2) monthly ‘Beat CW Fuel Injection’ with MSE = 3.67 and MAPE = 4.04%, and (3) daily ‘All Category’-’All Type’ with MSE = 1.42 and MAPE = 27.36% we indicate that Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Number approach could give higher accuracy than the Single Exponential Smoothing method as comparison in forecasting motorcycle sales.


Introduction
relies on the sales of existing products.However, companies often have problems in determining what inventory should be held for get maximum sales, achieve targets, and in accordance with market needs.Inventory that are not well planned can result in the accumulation of goods in the warehouse which then reduces the company's procurement of goods exceeds the results obtained from the sales [1]. of plans that can be performed by a company.PT Mutiara Motor is a business that is engaged in the sales of Honda motorcycles.Companies the appropriate inventory planning and sales that according to market needs, which resulting in the accumulation or shortages of stock that the company, in this case the managers require a computerized application that can help to see and predict the level of sales that exist in the company Forecasting method chosen to develop applications in this research is the fuzzy time series with Nearest Symmetric Trapezoidal Fuzzy Numbers (NSTFN) approach which is part of the modern time series methods [2,3].
Fuzzy time series in implementation as method of forecasting has been proven that the prediction results are very accurate indicated by the small value of the forecasting error measurement [4 -6].There are even some derivative works on fuzzy time series which had been done [7 -10].The use of fuzzy number can overcome the problems of conventional fuzzy time series related to give the results in the form of trapezoidal fuzzy value [11] The use of fuzzy number can overcome the problems of conventional fuzzy time series related to give the results in the form of trapezoidal fuzzy number instead of a single value, so that the decision maker gets wider picture when making a forecast or a plan.Furthermore, with the Nearest Symmetric Trapezoidal Fuzzy Number, we can fuzziness of the original value.5.If the value of the historical data is located in the range of v j , then it belongs to the fuzzy number A j the corresponding fuzzy numbers.

Derive the fuzzy logical relationships based on
Suppose F(t-1) = A i and F(t) = A j, a fuzzy logical relationship can be derived as A i A j where A i and A j are called the left hand side and the right hand side of the fuzzy logical relationship respectively.8.The forecasted value at time t, Fv t, is determined by the following three heuristic rules.Assume the fuzzy number Av t at time t-1 is A j.
Rule 1: If the fuzzy logical relationship group of A j is empty, Aj or A j A j, then the forecasted value Fv t is R[NSTFN(A j )].
Rule 2: If the fuzzy logical relationship group of A j is one to one, i.e., A j A k, then the forecasted value Fv t is R[NSTFN(A k )].
Rule 3: If the fuzzy logical relationship group of A j is one to many, i.e., A j A k1, Aj A k2, ... , A j A kp, then the forecasted value Fv t is calculated as.
For that rules, this following formulas are applied: a.For the trapezoidal fuzzy number A = (t 1 , t  By utilizing the trapezoidal fuzzy number and Interval forecast [F L , F U ] which is lower limit and upper limit of interval respectively, is obtained by [14], (5) and Forecast Error Measurement After doing the forecasting, it is necessary to measure the accuracy of forecasting methods because errors may occur.Forecasting error is the difference between the forecasted data with the actual data.There are several methods to measure forecast error, such as Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE).

Implementation and Results
Fuzzy Time Series Method with Nearest Symmetric Trapezoidal Fuzzy Number approach is used on Forecasting page at the application and used to perform sales forecasting of motorcycles.Fig. 2 and Fig. 3 show the forecasting process consecutively.In the forecasting page, managers are asked forecasting, which is the product that will be predicted by category and by product name.If no change of selection, sales forecasting will include all categories and all products, by default.
There are two sales forecasting period, i.e., daily and monthly that can be chosen.Default mode is monthly.Daily mode is an additional feature to make sales forecasting more frequently and only for 'All Category'-'All Type'.Managers will enter a period of historical data that will be used in the form of start month and year, as well as end month and year in monthly mode.The start date and end date is used if it is in the daily mode.b.Divide U into seven intervals, U i, i = 1 to 7 with equal length is described in Table 1.
divide the intervals U 1 to U 7 as described in Table 3. From the frequency distribution of the U 6 , the frequency obtained is 0, so it will not be included to determine v j .A 3 [80,100,107,113] A 4 [100,107,113,120] A 5 [107,113,120,124] A 6 [113,120,124,128] A 7 [120,124,128,132] A 8 [124,128,132,136] A 9 [128,132,136,140] A 10 [132,136,140,160] A 11 [136,140,160,200] A 12 [140,160,200,240] b.The next step is to fuzzify the historical data as shown in Table 5.

Period Actual Data
April According to manager of this company, the given by, 122,130] or can be expressed sales forecast for the month of April 2014 was between 122 units and 130 units.
Forecasted data and the MSE and MAPE generated by Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Numbers approach is described in Table 6.After three experiments, (1) ' Category' -' monthly (2) ' -' CW Fuel Injection' monthly (3) ' Category' -' daily, each using 12 historical sales data test the accuracy of the method of Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Numbers approach compare with the conventional method which in this study were compared with the Single Exponential Smoothing method.From the experiments taken the results are as follows.

Fig. 1 .
Fig. 1.Trapezoidal Fuzzy Number (x 0, y 0, [12] Fuzzy Time Series with Nearest Symmetric Trapezoidal Fuzzy Number approach consists of the following steps [12]:1.Collect the historical data Av t .2. Find the maximum D max and the minimum D min among all Av t.To form the universe of discourse, two small numbers D 1 and D 2 are

7.
Arrange the fuzzy logical relationships into the fuzzy logical relationship groups based on the same fuzzy number on the left hand sides of the fuzzy logical relationships.If the transition happens to the same fuzzy set, make a separate logical relationship group.

Fig. 4 .
Fig. 4. The Interface of Forecasting Page

Table 3 .
Partition of V