
| TABLE II                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |                                                                                                                                                                                |                                                        |
| |--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------|
| Means of Original Data and frequency of intervals data   Interval Re-divide the interval   [900, 1100] 1   [1100, 1300] 6   [1300, 1500] 13  [1500, 1700] 9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | denotes the forecasting value of year (i), respectively.   | Ai - Fi | / Ai  AFER = ------------------ * 100 %   n   n   ∑ ( Ai - Fi ) 2   i=1  MSE = --------------------   n |                                                        |
| TABLE III                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |                                                                                                                                                                                |                                                        |
| FUZZY INTERVALS USING MEAN BASED PARTITIONING   Linguistics Intervals  u 1 [900, 1100]  u 2 [1100, 1133.33]  u 3 [1133.33, 1166.66]  u 4 [1166.66, 1199.99]  u 5 [1199.99, 1233.32]  u 6 [1233.32, 1266.65]  u 7 [1266.65, 1300.00]  u 8 [1300.00, 1315.38]  u 9 [1315.38, 1330.76]  u 10 [1330.76, 1346.14]  u 11 [1346.14, 1361.52]  u 12 [1361.52, 1376.90]  u 13 [1376.90, 1392.28]  u 14 [1392.28, 1407.66]  u 15 [1407.66, 1423.04]  u 16 [1423.04, 1438.42]  u 17 [1438.42, 1453.80]  u 18 [1453.80, 1469.18]  u 19 [1469.18, 1484.56]  u 20 [1484.56, 1500.00]  u 21 [1500.00, 1522.22]  u 22 [1522.22, 1544.44]  u 23 [1544.44, 1566.66]  u 24 [1566.66, 1588.88]  u 25 [1588.88, 1611.10]  u 26 [1611.10, 1633.32]  u 27 [1633.32, 1655.54]  u 28 [1655.54, 1677.76]  u 29 [1677.76, 1700.00]                                                                                                                     |                                                                                                                                                                                | In Table VI, we compare the forecasting results of the |
| proposed method with that of the existing methods.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | From                                                                                                                                                                           |                                                        |
| Table III, we can see that when the number of intervals in the  universe of discourse is twenty nine intervals are sub  partitioned base on means, the proposed method shows  smallest values of the MSE and AFER of the forecasting  results as compared to other methods of fuzzy time series  forecasting. That is, the proposed method can get a higher  forecasting accuracy rate for forecasting car road accidents  that the existing methods.  TABLE IV  THIRD ORDER FUZZY LOGICAL RELATIONSHIP GROUPS  Group 1: X1,X3,X7 -> X6 Group 2: X3,X7,X6 -> X4 Group 3: X7,X6,X4 -> X5 Group 4: X6,X4,X5 -> X3 Group 5: X4,X5,X3 -> X2 Group 6: X5,X3,X2 -> X5 Group 7: X3,X2,X5 -> X15 Group 8: X2,X5,X15 -> X10 Group 9: X5,X15,X10 -> X13 Group 10: X15,X10,X13 -> X19 Group 11: X10,X13,X19 -> X24 Group 12: X13,X19,X24 -> X20 Group 13: X19,X24,X20 -> X16 Group 14: X24,X20,X16 -> X13 Group 15: X20,X16,X13 -> X18 |                                                                                                                                                                                |                                                        |
| IV A COMPARISON OF DIFFERENT FORECASTING METHODS                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | Group 16: X16,X13,X18 -> X8                                                                                                                                                    |                                                        |
| In the following Table V summarizes the forecasting                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                |                                                        |
| results of the proposed method from 1974 to 2004, where the  universe of discourse is divided into twenty nine intervals  based on means based partitioning. In the following, we use  the average forecasting error rate (AFER) and mean square  error (MSE) to compare the forecasting results of different  forecasting methods, where Ai denotes the actual value and Fi                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | Group 17: X13,X18,X8 -> X12 Group 18: X18,X13,X12 -> X19 Group 19: X13,x12,x19, -> X18 Group 20: X12,X19,X18 -> X23                                                            |                                                        |
