## 3 A Case Study  
A real case is used to validate the effectiveness of the agent-based fuzzy collaborative intelligence approach. To this end, the price data of a DDR2 1G DRAM product have been collected for 256 days (see Figure 1). Five existing approaches, moving average (MA), exponential smoothing (ES), BPN, ARIMA, and [PERSON]'s fuzzy and neural approach, were also applied to this real case. [PERSON] and [PERSON]'s fuzzy interpolation approach was not compared because it is too subjective. MA uses a number of historical actual data values to generate a forecast. The moving period of MA has a reference value. Increasing the number of periods averaged does smooth out fluctuations better, but it makes the method less sensitive to real changes in the data. For this reason, this study tried a variety of moving periods (from 3 to 7), in which the best option was kept for later analyses. ES is a weighted moving-average forecasting method, in which the latest estimate is equal to the old estimate adjusted by a fraction of the difference between the last period's actual value and the old estimate. The smoothing constant in ES ranged from 0 to 1, and was optimized by enumerating some possible values. ARIMA is the generalization of an autoregressive moving average (ARMA) model that is usually used to fit time series data [35]. ARIMA consists of three stages: identification, estimation, and checking. To identify the order in the ARIMA process, the minimum information criterion (MINIC) method was employed. The stationarity and seasonal stationarity in the data were examined with the augmented Mickey fuller (ADF) unit root tests [19]. BPN, also known as the multi-layer feed-forward neural network, is one of the most commonly used artificial neural networks. In BPN, inputs include the prices of \(K\) periods before. Here, \(K\) was set to be equal to the number of moving periods in MA for a fair comparison. The BPN was trained for 70, 000 epochs per replication with randomized initial weights. To evaluate the accuracy of each method, three measures including root mean squared error (RMSE), mean absolute error/deviation (MAE/D), and mean absolute percentage error (MAPE) were calculated. On the other hand, we assessed the precision of MA, ES, BPN, and ARIMA with 66:  
Figure 1: The collected dynamic random access memory (DRAM) price data. \[6\sigma=6\sqrt{\frac{\sum\limits_{i=K+1}^{T}{(F_{i}-A_{i})}^{2}}{T-K-K-1}} \tag{56}\]  
To the contrary, for evaluating the precision of [PERSON]'s fuzzy and neural approach or the agent-based fuzzy collaborative intelligence approach, the average range of fuzzy price forecasts was considered. In both ways, the probability of containing the actual value in the fuzzy or interval forecast was approximately 100%. See Table 1 for the performances of various approaches in the two aspects. From the tabulated results it can be seen that the difference between the forecasting results and the real data is very small. The magnitude of the errors ranged from 0.00% to 3.47% with an average of only 0.59%. In fitting the collected data, the agent-based fuzzy collaborative intelligence approach achieved a very good performance. Among the three accuracy measures, MAPE and RMSE are similar in nature. The performance of the agent-based fuzzy collaborative intelligence approach with respect to these two measures was obviously better than those of the compared approaches. The advantage of the agent-based fuzzy collaborative intelligence approach in the accuracy aspect was most obvious when it came to MAE. MAE is highly indicative when the values are very small. We notice that ARIMA achieves good performance in this regard. The collaboration in the proposed methodology is aimed at the adjustment of the forecast by referencing the forecasts of others. The same treatment can be applied to ARIMA to further improve the forecasting performance of price forecasting.