The experimental results show that the proposed method is better than the others on the accuracy of forecasting. It is simple and flexible in applying this method because we can determine the parameters of HA for reasonable intervals.
93.1 3709.8 04/12/1992 3651.4 3629.3 3740.9 3564.5 3693.1 3709.8 05/12/1992 3727.9 3629.3 3740.9 3564.5 3693.1 3709.8 07/12/1992 3755.8 3629.3 3740.9 3859.9 3693.1 3709.8 08/12/1992 3761 3629.3 3740.9 3859.9 3693.1 3709.8 09/12/1992 3776.6 3629.3 3740.9 3859.9 3693.1 3709.8 10/12/1992 3746.8 3629.3 3740.9 3859.9 3693.1 3709.8 11/12/1992 3734.3 3629.3 3740.9 3859.9 3693.1 3709.8 12/12/1992 3742.6 3629.3 3740.9 3859.9 3693.1 3709.8 14/12/1992 3696.8 3629.3 3740.9 3859.9 3693.1 3709.8 15/12/1992 3688.3 3629.3 3740.9 3564.5 3693.1 3709.8 16/12/1992 3674.9 3629.3 3740.9 3564.5 3693.1 3709.8 17/12/1992 3668.7 3629.3 3740.9 3564.5 3693.1 3709.8 18/12/1992 3658 3629.3 3740.9 3564.5 3693.1 3709.8 21/12/1992 3576.1 3629.3 3740.9 3564.5 3693.1 3709.8 22/12/1992 3578 3629.3 3477.1 3564.5 3519.4 3442.3 23/12/1992 3448.2 3629.3 3477.1 3564.5 3519.4 3442.3 24/12/1992 3456 3629.3 3477.1 3413.3 3519.4 3442.3 28/12/1992 3327.7 3629.3 3477.1 3413.3 3519.4 3442.3 29/12/1992 3377.1 3629.3 3368.1 3413.3 3519.4 3491.4 114.2 85.7 107.2 75.7 68.9 RMSE 580 The partitioning method based on Hedge Algebras for fuzzy time series forecasting Also Applying FL for UNE [15] with intervals, the forecasting result is presented in the following Table 6: Table Comparing forecasting result on UNE Date Actual data Wang 2013 Chen 2013 Wang 2014 Lu 2015 The proposed method 02/01/2013 7.7 7.39 7.60 7.62 7.58 7.51 03/01/2013 7.5 7.39 7.60 7.62 7.58 7.51 04/01/2013 7.5 7.39 7.60 7.62 7.58 7.51 05/01/2013 7.5 7.39 7.60 7.62 7.58 7.51 06/01/2013 7.5 7.39 7.60 7.62 7.58 7.51 07/01/2013 7.3 7.39 7.60 7.62 7.58 7.51 08/01/2013 7.2 7.39 7.12 7.13 7.07 6.99 09/01/2013 7.2 6.89 7.12 7.13 7.07 6.99 10/01/2013 7.2 6.89 7.12 7.13 7.07 6.99 11/01/2013 7.0 6.89 7.12 7.13 7.07 6.99 12/01/2013 6.7 6.89 7.12 7.13 7.07 6.99 0.20 0.18 0.19 0.17 0.16 RMSE Comparing forecasting results of the proposed method with some forecasting result of recently different methods on regular time series such as Alabama, TAIEX, UNE in Table 4, Table and Table show that the proposed method gives better forecasting performance Besides, the proposed method only use arithmetic operations with simple way to calculate forecasting result CONCLUSION This paper presented a novel method of partitioning the universe of discourse, and used this method in the method of using fuzzy time series to forecast time series, to improve forecasting performance The proposed method is formed by mean of the linguistic terms that are used to qualitatively describe the historical values of fuzzy time series Based on the linguistic terms, the number of intervals, corresponding to the number of linguistic terms, and length of intervals, corresponding to the fuzziness intervals, are determined 581 Hoang Tung, Nguyen Dinh Thuan, Vu Minh Loc From the experimental results on the regular time series, compare to forecasting result of different methods, we can see that when using the proposed method to model fuzzy time series gives better forecasting accuracy The proposed method also shows that it is rather simple because of using only arithmetic operations and simple way to calculate forecasting values REFERENCES Song Q., Chissom B.S - Fuzzy time series and its models, Fuzzy Sets and Systems 54 (3) (1993a) 269–277 Song Q., Chissom B.S - Forecasting enrollments with fuzzy time series – Part I, Fuzzy Sets and Systems 54 (1) (1993b) 1–9 Song Q., Chissom B S - Forecasting enrollments with fuzzy time series, Part II, Fuzzy Sets and Systems 62 (1) (1994) 1–8 Shyi-Ming Chen - Forecasting enrollments based on fuzzy time series, Fuzzy Sets and Systems 81 (1996) 311-319 Kunhuang Huarng - Efective lengths of intervals to improve forecasting in fuzzy time series, Fuzzy Sets and Systems 123 (2001) 387–394 Kunhuang Huarng - Heuristic models of fuzzy time series for forecasting, Fuzzy Sets and Systems 123 (2001) 369–386 Shyi-Ming Chen, Nien-Yi Chung - Forecasting enrollments using high-order fuzzy time series and genetic algorithms, International journal of intelligent systems 21 (2006) 485– 501 Tahseen Ahmed Jilani, Syed Muhammad Aqil Burney, and Cemal Ardil - Fuzzy metric approach for fuzzy time series forecasting based on frequency density based partitioning, International Journal of Computer, Information, Systems and Control Engineering (7)(2010) 39-44 Shyi-Ming Chen, Chia-Ching Hsu - A new method to forecast enrollments using fuzzy time Series, International Journal of Applied Science and Engineering (3) (2004) 234244 10 Kunhuang Huarng, Tiffany Hui-Kuang Yu - Ratio-based lengths of intervals to improve fuzzy time series forecasting, IEEE transactions on systems, man, and cybernetics—part b: cybernetics 36 (2) (2006) 328-340 11 Shyi-Ming Chen, Pei-Yuan Kao - TAIEX forecasting based on fuzzy time series, particle swarm optimization techniques and support vector machines, Information Sciences 247 (2013) 62–71 12 Lizhu Wang, Xiaodong Liu, Witold Pedrycz - Effective intervals determined by information granules to improve forecasting in fuzzy time series Expert Systems with Applications 40 (2013) 5673–5679 13 Lizhu Wang, Xiaodong Liu, Witold Pedrycz, Yongyun Shao - Determination of temporal information granules to improve forecasting in fuzzy time series, Expert Systems with Applications 41 (2014) 3134–3142 14 Eren Bas, Vedide Rezan Uslu, Ufuk Yolcu, Erol Egrioglu - A modified genetic algorithm for forecasting fuzzy time series, Applied Intelligence 41 (2014) 453-463 582 The partitioning method based on Hedge Algebras for fuzzy time series forecasting 15 Wei Lu, XueyanChen, WitoldPedrycz, XiaodongLiua, JianhuaYang - Using interval information granules to improve forecasting in fuzzy time series, International Journal of Approximate Reasoning 57 (2015) 1–18 16 Nguyen Cat Ho, Nguyen Van Long - Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras, Fuzzy Sets and Systems 158 (2007) 452 – 471 17 Cat Ho Nguyen, Witold Pedrycz, Thang Long Duong, Thai Son Tran - A genetic design of linguistic terms for fuzzy rule based classifiers, International Journal of Approximate Reasoning 54 (2013) 1-21 583 ... modified genetic algorithm for forecasting fuzzy time series, Applied Intelligence 41 (2014) 453-463 582 The partitioning method based on Hedge Algebras for fuzzy time series forecasting 15 Wei Lu,.. .The partitioning method based on Hedge Algebras for fuzzy time series forecasting Also Applying FL for UNE [15] with intervals, the forecasting result is presented in the following... novel method of partitioning the universe of discourse, and used this method in the method of using fuzzy time series to forecast time series, to improve forecasting performance The proposed method