A new hybrid fuzzy time series forecasting model based on combing fuzzy C-Means clustering and particle swam optimization

FEX index is split in two parts for independent testing. The first part is used as
a training dataset and the second part is used as a testing dataset. From historical data in
the past few days, we can forecast the new TAIFEX index for the next day. In this paper
the historical data of TAIFEX between March 8, 1998 and September 23, 1998 was used as
a training dataset and the remaining data was used in the testing phase. To forecast for
testing dataset, the highest votes(wh) for MV scheme in model [22] are used as 3. Other
parameters are taken similar to training set. For instance, for forecasting the new data of
date 9/24/1998, the data under days from 8/3/1998 to 9/23/1998 are utilized as the training
dataset. Similarly, a new data of date 9/25/1998 can be forecasting based on the data of
dates between 8/3/1998 and 9/24/1998. A comparison of results for actual data and the
forecasting results between the proposed model and the models [15, 22, 24] which use 16
intervals with the 3rd - order FTS. The results in Table 13 indicate that the proposed model
is more precise than four compared models based on 3rd - order FTS and also gets the
smallest MSE of 116.37.
4.4. Experimental results for forecasting the vehicle road accidents
In addition, the proposed model is also used for forecasting the vehicle road accidents in
Belgium [1] from 1974 to 2004 and there is made a comparison of the forecasting results with
the previous works [1, 19, 20, 39]. A comparison of the forecasting results using RMSE (24) is
shown in Table 14. It is evident that the proposed method gets better forecasting results than
the forecasting models above. More detailedly comparison, for the same number of interval of
13, the proposed model obtains the smallest RMSE value of 1.96 among two models [20, 39]
using the 3rd - order FTS. Beside that, the proposed model also has far smaller RMSE value
than model [19] and model [39] based on first - order FTS with different number of intervals.
To sum up, demonstrations above show that the proposed model outperform the existing
models based on both the first- order and high -order FTS model with different number of
intervals in forecasting the vehicle road accidents.
288 NGHIEM VAN TINH, NGUYEN CONG DIEU
Table 12. A comparison of the forecasting results of the proposed method with the existing models
based on the high - order FTS under number of intervals = 16
Date Actual data H01b L08 HPSO MPTSO THPSO NPSO Proposed
model
8/3/1998 7552 N/A N/A N/A N/A N/A N/A N/A
8/4/1998 7560 7450 N/A N/A N/A N/A N/A N/A
8/5/1998 7487 7450 N/A N/A N/A N/A N/A N/A
8/6/1998 7462 7500 N/A N/A N/A N/A 7452.54 N/A
8/7/1998 7515 7500 N/A N/A N/A N/A 7331.62 N/A
8/10/1998 7565 7450 N/A N/A N/A N/A 7285.63 7361.5
8/11/1998 7360 7300 N/A N/A N/A N/A 7331.62 7361.5
8/12/1998 7330 7300 7329 7289.56 7325.28 7325 7291.67 7328.16
8/13/1998 7291 7300 7289.5 7320.77 7287.48 7287.5 7217.15 7290.41
—– —– —– —– —– —– —– —– —–
9/29/1998 6806 6850 6796 6800.07 6781.01 6794.3 7331.62 6810.92
9/30/1998 6787 6750 6796 7289.56 6781.01 6794.3 7285.63 6789.25
MSE 5437.58 105.02 103.61 92.17 55.96 35.86 5.1
Table 13. A comparison of the MSE value for testing phase based on 3rd-order FTS under 16
intervals using wh = 3.
Date Actual data Model [25] Model [23] Model [16] Proposed model
9/24/1998 6890 6959.07 6861.0 6916.62 6886
9/25/1998 6871 6833.52 6897.8 6886.0 6874
9/28/1998 6840 6896.95 6912.8 6892.4 6852
9/29/1998 6806 6863.76 6858.4 6871.54 6825.88
9/30/1998 6787 6823.38 6800.5 6859.12 6791.2
MSE 2815.69 1957.42 2635.23 116.37
Table 14. A comparison of the forecasting results between proposed model and various models based
on first - order and high - order FLRs
Year Actual data Model [20] Model [21] Model [1] Model [40] Proposed model
1st-order 3rd-order
1974 1574 —- — —- —- —- —-
1975 1460 1497 —- 1458 —- 1445 —-
1976 1536 1497 —- 1467 —- 1548 —-
1977 1597 1497 1497 1606 1594 1582 1597
1978 1644 1497 1497 1592 1643 1609 1642
—- —– —– —– —– —– —- —-
2003 1035 995 997 1097 1036 1041 1039
2004 953 995 997 929 954 954 950
RMSE 83.12 46.78 37.66 19.2 16.68 1.96
A NEW HYBRID FUZZY TIME SERIES FORECASTING MODEL 289
5. CONCLUSION AND FUTURE WORK
In this study, a new FTS forecasting model which combines FCM and PSO algorithm
is proposed for forecasting real-world time series. The advantages of the proposed model
are that it combines the PSO and FCM to get the optimum partition of the intervals for
increasing the forecasting accuracy rates. The time variant - fuzzy relationship groups were
established to overcome the shortcomings of the conventional FTS model which also uses the
fuzzy relationship groups. In addition to that the paper also proposes a new defuzzification
method for calculating the forecasting output values, which has been the main contribution
issue for improving forecasting accuracy of the proposed model. From the empirical study
on three datasets of forecasting enrollments, TAIFEX forecasting and car road accidents
forecasting, the experimental results show that the proposed model outperforms other ex-
isting forecasting models with various orders and different interval lengths. The detail of
comparison was presented in Tables 8 - 14 and Figs. 3 - 4.
Even though, the proposed method shows that the superior forecasting capability com-
pared with existing forecasting models, there still remain some aspects which needs to be
mentioned, such as the computational complexity when combining many methods in fo-
recasting model and the forecasting of multi-factor problems. To continue evaluating the
performance of the forecasting model and overcoming those weaknesses. There are two sug-
gestions for future research as the proposed model need to combine with some more effective
optimal techniques to deal with more complicated and multi-factor factors problems for
decision-making such as: weather forecasting, monthly inflation, and so on. Moreover, we
will study some methods for automatically determining the optimal order of the fuzzy logical
relationship for forecasting real-world time series. The main contributions of this paper are
summarized as below:
1) The appearance of fuzzy sets on the right - hand side of the fuzzy relationship group is
considered in the process of determining the FRGs, which makes a more effective use
of the historical data and become more reasonable in reality;
2) The forecasting accuracy of FTS model constructed on basis of unequal-sized intervals
that are formed by combining FCM with PSO is prominently improved;
3) The information on the right - hand side of all fuzzy logical relationships are considered
to calculate the forecasting output by the new defuzzification technique.
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Received on December 22, 2018
Revised on April 25, 2019