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International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(4): 338-348

Published online December 25, 2021

https://doi.org/10.5391/IJFIS.2021.21.4.338

© The Korean Institute of Intelligent Systems

Dynamic Type-2 Fuzzy Time Warping (DT2FTW): A Hybrid Model for Uncertain Time-Series Prediction

Aref Safari1, Rahil Hosseini1 , and Mahdi Mazinani2

1Department of Computer Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
2Department of Electronic Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran

Correspondence to :
Rahil Hosseini (rahil.hosseini@qodsiau.ac.ir)

Received: April 4, 2020; Revised: June 22, 2021; Accepted: August 31, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Prediction of time series is associated with nondeterministic pattern analysis for uncertain conditions. Therefore, it is necessary to develop high-quality prediction methods for real-world applications. Type-2 fuzzy systems can handle high-order uncertainties, such as sequential dependencies associated with time series. Precise and reliable prediction can help to develop reasonable strategies and assist specialists in planning the best policies for modeling events in uncertain time series. In this study, a hybrid model (dynamic type-2 fuzzy time warping [DT2FTW]) was proposed for handling high-order uncertainties in time-series prediction. A type-2 fuzzy intelligent system was developed alongside a dynamic time warping algorithm for predicting the patterns’ similarity in long-time series for time-series prediction. The results demonstrate that the proposed DT2FTW model yields more reliable predictions on global standard benchmarks such as the Mackey-Glass, Dow Jones, and NASDAQ time-series. The results also confirm that the proposed DT2FTW model has lower error rates than its counterpart algorithms in terms of the root mean square error (RMSE), mean absolute error (MAE), and mean percentage error (MPE). In addition, the results confirm the superiority of the proposed model with an average area under the ROC curve (AUC) of 94%, with the 95% confidence interval (92%-95%).

Keywords: Dynamic time warping, Interval type-2 fuzzy system, Time-series prediction

No potential conflict of interest relevant to this article was reported.

Aref Safari received his M.Sc. degree in artificial intelligence. He is now working on his Ph.D. thesis to model the uncertainty of non-stationary time-series. His research interests are soft computing, time-series analysis, and pattern analysis.

E-mail: safari.aref@gmail.com


Rahil Hosseini received her Ph.D. degree in computational Iintelligence from Kingston University. She is a faculty member at Department of Computer Engineering. Her main research interests include pattern recognition, fuzzy modeling and data mining.

E-mail: rahilhosseini@gmail.com


Mahdi Mazinani received his Ph.D. degree in electrical engineering from Kingston University. Currently, he is a faculty member of the Department of Electrical Engineering. His main research interests include probability theory and pattern recognition.

E-mail: mahdi mazinani@yahoo.com


Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(4): 338-348

Published online December 25, 2021 https://doi.org/10.5391/IJFIS.2021.21.4.338

Copyright © The Korean Institute of Intelligent Systems.

Dynamic Type-2 Fuzzy Time Warping (DT2FTW): A Hybrid Model for Uncertain Time-Series Prediction

Aref Safari1, Rahil Hosseini1 , and Mahdi Mazinani2

1Department of Computer Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
2Department of Electronic Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran

Correspondence to:Rahil Hosseini (rahil.hosseini@qodsiau.ac.ir)

Received: April 4, 2020; Revised: June 22, 2021; Accepted: August 31, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Prediction of time series is associated with nondeterministic pattern analysis for uncertain conditions. Therefore, it is necessary to develop high-quality prediction methods for real-world applications. Type-2 fuzzy systems can handle high-order uncertainties, such as sequential dependencies associated with time series. Precise and reliable prediction can help to develop reasonable strategies and assist specialists in planning the best policies for modeling events in uncertain time series. In this study, a hybrid model (dynamic type-2 fuzzy time warping [DT2FTW]) was proposed for handling high-order uncertainties in time-series prediction. A type-2 fuzzy intelligent system was developed alongside a dynamic time warping algorithm for predicting the patterns’ similarity in long-time series for time-series prediction. The results demonstrate that the proposed DT2FTW model yields more reliable predictions on global standard benchmarks such as the Mackey-Glass, Dow Jones, and NASDAQ time-series. The results also confirm that the proposed DT2FTW model has lower error rates than its counterpart algorithms in terms of the root mean square error (RMSE), mean absolute error (MAE), and mean percentage error (MPE). In addition, the results confirm the superiority of the proposed model with an average area under the ROC curve (AUC) of 94%, with the 95% confidence interval (92%-95%).

Keywords: Dynamic time warping, Interval type-2 fuzzy system, Time-series prediction

Fig 1.

Figure 1.

Block diagram of the proposed DT2FTW model.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 338-348https://doi.org/10.5391/IJFIS.2021.21.4.338

Fig 2.

Figure 2.

Error rate comparison of the DT2FTW model with its counterparts, for global time series: (a) NASDAQ, (b) Dow Jones, and (c) Mackey-Glass.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 338-348https://doi.org/10.5391/IJFIS.2021.21.4.338

Fig 3.

Figure 3.

Error rate of the DT2FTW model, for different noise levels: (a) = 1, (b) = 0.5, and (c) = 0.2, for the Mackey-Glass time series.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 338-348https://doi.org/10.5391/IJFIS.2021.21.4.338

Fig 4.

Figure 4.

Prediction fit results of the DT2FTW model, for different datasets: (a) NASDAQ, (b) Dow Jones, and (c)Mackey-Glass.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 338-348https://doi.org/10.5391/IJFIS.2021.21.4.338

Table 1 . Related fuzzy models for time-series prediction.

MethodLimitationAccuracy (%)
FCM time-series [17]No optimal parameter77.86
Fuzzy logic [18]No data reduction77.18
Fuzzy Markov [19]Complexity of model69.80
Fuzzy time-series [22]High-order uncertainty is not modeled77.00
Fuzzy neural [24]Weights are fixed79.24
Fuzzy-PSO [25]Limited to mid-range series80.12
Gustafson-Kessel fuzzy clustering [26]Insufficient results for long time-series82.93
PSO-fuzzy time-series [27]Not reliable for long time-series82.45
Fuzzy-NN time-series clustering [18]Time complexity is high84.73

Table 2 . T-test results for the DT2FTW and DTW.

Fold#DT2FTWDTW
10.90890.6414
20.90710.6149
30.90790.6212
40.91090.6311
50.91540.7063
60.92370.7195
70.93410.7431
80.94720.7621
90.94290.7901
100.95030.7811
Mean0.924840.70108

Table 3 . Comparison results for the DT2FTW model on the NASDAQ, Dow Jones, and Mackey-Glass data.

MethodNASDAQDow JonesMackey-Glass
MAERMSEMPEMAERMSEMPEMAERMSEMPE
Fuzzy clustering time-series [15]0.0290.0351.590.3200.0371.710.0270.0261.41
Fuzzy deep ANN time-series [16]0.0190.0191.520.0240.0281.640.0210.0171.39
DT2FTW0.0150.0131.390.0190.0171.410.0110.0091.19

Table 4 . Comparison of average performance of the DT2FTW model with its counterpart models (unit: %).

MethodAUCCIRecallPrecisionF-measure
Fuzzy-clustering8280–83828081
Fuzzy deep ANN9088–91929190
DT2FTW9492–95949593

Table 5 . Average complexity of the proposed DT2FTW model.

Pseudo-codeAverage complexity
Class type(6 * O(1)+O(N * M)+O(N2)
Training time(8 * O(1) + O(N2))
Calculating the outputO(N)
Calculating the errorO(1) + O(M * N)
The outputO(1) + O(N)

Table 6 . Time consumption of the DT2FTW model, for the three datasets.

SamplesMackey-GlassDow JonesNASDAQ
360:00:010:00:080:00:14
480:00:010:00:090:00:23
600:00:020:00:120:00:29
1120:00:040:00:210:00:37
2240:00:080:00:320:01:05
4480:00:160:00:550:02:23
1,2000:00:290:01:220:03:37

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