Type 2 Fuzzy Inference-Based Time Series Model
Abstract
:1. Introduction
2. Methodology
2.1. Collection and Selection of Data
2.2. Proposed Forecasting Model
2.3. Evaluation of the Performance
3. Empirical Analysis
4. Algorithm of the Proposed Method
- Step 1:
- The class interval of the universe of discourse is determined by using the sliding window method.
- Step 2:
- The observations are fuzzified into corresponding fuzzy sets.
- Step 3:
- Fuzzy logical relationship groups (FLRGs) are obtained.
- Step 4:
- Out-of-sample observations are mapped to FLRGs.
- Step 5:
- Operators and fuzzy rules obtained by using weighted subsethood-based algorithm are applied to the FLRGs for all the observations and obtain forecasts.
- Step 6:
- The forecasts are defuzzified.
- Step 7:
- Forecast values are computed for all data individually.
- Step 8:
- The method is compared with the previous method.
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Date (yyyy/mm/dd) | CPO Price | Fuzzy Sets |
---|---|---|
2012/10/1 | 424.20 | A7 |
2012/10/2 | 424.20 | A7 |
2012/10/3 | 407.40 | A3 |
2012/10/4 | 395.20 | A1 |
2012/10/5 | 411.00 | A4 |
2012/10/6 | 412.50 | A4 |
2012/10/7 | 412.50 | A4 |
2012/10/8 | 406.80 | A3 |
2012/10/9 | 418.50 | A5 |
2012/10/10 | 418.00 | A5 |
2012/10/11 | 430.00 | A8 |
2012/10/12 | 423.00 | A6 |
2012/10/13 | 415.50 | A5 |
2012/10/14 | 415.50 | A5 |
2012/10/15 | 417.40 | A5 |
2012/10/16 | 417.00 | A5 |
2012/10/17 | 414.90 | A5 |
2012/10/18 | 419.60 | A6 |
2012/10/19 | 425.80 | A7 |
2012/10/20 | 424.00 | A6 |
2012/10/21 | 424.00 | A6 |
2012/10/22 | 435.10 | A9 |
2012/10/23 | 424.70 | A7 |
2012/10/24 | 424.70 | A7 |
2012/10/25 | 435.20 | A9 |
2012/10/26 | 435.20 | A9 |
2012/10/27 | 434.30 | A9 |
2012/10/28 | 434.30 | A9 |
2012/10/29 | 428.60 | A7 |
2012/10/30 | 426.00 | A7 |
2012/10/31 | 424.70 | A7 |
Date (mm/dd) | Closing | High | Low |
---|---|---|---|
… | … | … | … |
10/11 | 430.00 | 431.10 | 419.20 |
10/12 | 423.00 | 428.80 | 412.80 |
10/13 | 415.50 | 420.30 | 413.80 |
… | … | … | … |
Date (mm/dd) | Forecasts | ||
---|---|---|---|
Closing | |||
10/12 | High | ||
Low | |||
Closing | |||
10/13 | High | ||
Low | |||
Closing | |||
10/14 | High | ||
Low |
Date (mm/dd) | Forecasts | ||
---|---|---|---|
Closing | |||
10/12 | High | ||
Low | |||
Closing | |||
10/13 | High | ||
Low | |||
Closing | |||
10/14 | High | ||
Low |
Year | Mean Square Error (MSE) | Root Mean Square Error (RMSE) | ||
---|---|---|---|---|
Proposed Method | Chen’s model | Proposed Method | Chen’s model | |
2012 | 0.0010 | 0.0010 | 0.518 | 0.520 |
2013 | 0.00067 | 0.0011 | 0.457 | 0.635 |
2014 | 0.0019 | 0.0027 | 0.637 | 0.855 |
2015 | 0.00069 | 0.00079 | 0.414 | 0.462 |
2016 | 0.0009 | 0.0015 | 0.567 | 0.754 |
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Share and Cite
Rahim, N.F.; Othman, M.; Sokkalingam, R.; Abdul Kadir, E. Type 2 Fuzzy Inference-Based Time Series Model. Symmetry 2019, 11, 1340. https://doi.org/10.3390/sym11111340
Rahim NF, Othman M, Sokkalingam R, Abdul Kadir E. Type 2 Fuzzy Inference-Based Time Series Model. Symmetry. 2019; 11(11):1340. https://doi.org/10.3390/sym11111340
Chicago/Turabian StyleRahim, Nur Fazliana, Mahmod Othman, Rajalingam Sokkalingam, and Evizal Abdul Kadir. 2019. "Type 2 Fuzzy Inference-Based Time Series Model" Symmetry 11, no. 11: 1340. https://doi.org/10.3390/sym11111340