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Applications of Complex Fuzzy Sets in Time-Series Prediction Open Access


Other title
Machine Learning Algorithms
Time Series Prediction
Complex Fuzzy Sets and Logic
Neuro-Fuzzy Systems
Type of item
Degree grantor
University of Alberta
Author or creator
Yazdanbakhsh Poodeh, Omolbanin
Supervisor and department
Dick, Scott (Electrical and Computer Engineering)
Examining committee member and department
Reformat, Marek (Electrical and Computer Engineering)
Pedrycz, Witold (Electrical and Computer Engineering)
Department of Electrical and Computer Engineering
Software Engineering and Intelligent Systems
Date accepted
Graduation date
2017-11:Fall 2017
Doctor of Philosophy
Degree level
Complex fuzzy sets are a recent extension of type-1 fuzzy sets, whose membership functions have the unit disc of the complex plane as their co-domain. In the same vein, complex fuzzy logic is a new multi-valued logic whose truth valuation set is the unit disc. Prior research has indicated that machine-learning algorithms built using complex fuzzy logic could be very accurate in time-series forecasting. This Ph.D. dissertation investigates different designs of machine learning algorithms based on complex fuzzy logic to develop reliable and fast algorithms for time-series prediction. The machine learning algorithms designed in this dissertation are inferred from Adaptive Neuro-Complex Fuzzy Inferential System (ANCFIS). ANCFIS was the first neuro-fuzzy system to combine complex fuzzy sets and rule interference for time-series forecasting. ANCFIS uses a hybrid learning rule where consequent parameters are updated on the forward pass, and antecedent parameters on the backward pass. Some recent findings, however, indicate that published results on ANCFIS are sub-optimal. First, we propose to improve the performance of the ANCFIS by changing how we define an input window, or even using sub-sampled windows. We compare the performance of ANCFIS using three different approaches to defining an input window, across six time-series data sets. Then, we evaluate the performance of ANCFIS for univariate time-series prediction using a photovoltaic power data set. We compare the results of ANCFIS against well-known machine learning and statistical learning algorithms. As ANCFIS has not been designed to work with multivariate time-series, we extend the ANCFIS learning architecture to the multivariate case. We investigate single-input-single-output, multiple-input-single-output, and multiple-input-multiple-output variations of the architecture, exploring their performances on four multi-variate time-series. We also explore modifications to the forward- and backward-pass computations in the architecture. We find that our best designs are superior to the published results on these data sets, and at least as accurate as kernel-based prediction algorithms. We also propose and evaluate a randomized-learning approach to training this neuro-fuzzy system. A number of recent results have shown that assigning fixed, random values to a subset of the adaptive parameters in a neural network model is an effective, simpler, and far faster alternative to optimizing those same parameters. We study mechanisms by which randomized learning may be combined with our system, and evaluate the system on both univariate and multivariate time-series. In general, we find that our proposed architecture is far faster than the original system, with no statistically significant difference in accuracy. Finally, we propose a machine learning algorithm, which is designed for fast training of a compact, accurate forecasting model. We use the Fast Fourier Transform algorithm to identify the dominant frequencies in a time-series, and then create complex fuzzy sets to match them as the antecedents of a complex fuzzy rule. Consequent linear functions are then learned via recursive least-squares. We evaluate this algorithm on both univariate and multivariate time-series, finding that this incremental-learning algorithm is as accurate and compact as its slower predecessor, and can be trained much more quickly.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
O. Yazdanbakhsh and S. Dick, "A Systematic Review of Complex Fuzzy Sets and Logic," Fuzzy Sets and Systems, 2017O. Yazdanbakhsh and S. Dick, "Time-Series Forecasting via Complex Fuzzy Logic," Frontiers of Higher Order Fuzzy Sets, A. Sadeghian and H. Tahayori, Eds., Heidelberg, Germany: Springer, 2015O. Yazdanbakhsh, A. Krahn and S. Dick., "Predicting Solar Power Output using Complex Fuzzy Logic," Fuzzy Information Processing Society (NAFIPS), Annual Meeting of the North American Edmonton, Alberta, 2013O. Yazdanbakhsh and S. Dick, "Multi-variate time-series forecasting using complex fuzzy logic," Fuzzy Information Processing Society (NAFIPS) held jointly with 5th World Conference on Soft Computing (WConSC),Washington, Seattle, 2015, pp. 1-6O. Yazdanbahksh and S. Dick, "Forecasting of multivariate time-series via complex fuzzy logic," IEEE Transactions on Systems, Man and Cybernetics: SystemsO. Yazdanbakhsh and S. Dick, "ANCFIS-ELM: A Machine Learning Algorithm based on Complex Fuzzy Sets," World Congress on Computational Intelligence, Vancouver, Canada, 2016.

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