The Application of Complex Fuzzy Sets to Large-Scale Time-Series Forecasting
Creators: Sobhi, Sayedabbas 
Publisher: name: University of Alberta Library
Year: 2022

<p>A number of architectures and time series forecasting algorithms use complex fuzzy sets, which are extensions of type-1 fuzzy sets. In the complex fuzzy set literature, the two most common forms of fuzzy sets are sinusoidal membership functions and complex Gaussian membership one. However, there have been no studies that combine both forms, either separately or in combination, to allow a direct comparison of their respective merits. Therefore, the first goal of this dissertation is to construct a suitable architecture to test both membership function forms, as well as their combination, on the time series forecasting task.</p>

<p>Previous architectures such as the Adaptive Neuro-Complex Fuzzy Inferential System (ANCFIS) have been shown to be accurate and compact forecasting algorithms. The Fast ANCFIS architecture was designed to speed up learning, and apply ANCFIS for data stream mining, by applying a fast Fourier transform to determine the parameters of sinusoidal membership functions. Randomized learning was proposed instead as an alternative strategy for speeding up learning in ANCFIS-ELM and RANCFIS. However, the learning algorithms and accuracy remained insufficient; none of the architectures were suitable for working with big data, which is an integral part of the real world today. Therefore, our second goal in this dissertation is to design a new CFS-based architecture that, while taking advantage of previous architectures, can also learn to forecast large-scale datasets efficiently and accurately.</p>

<p>We address both goals in this thesis by designing a new neuro-fuzzy architecture and evaluating it on multiple medium-to-large scale univariate and multivariate datasets (including a new condition-monitoring dataset for electric motors developed in the course of this dissertation work). It should be noted that one of the remarkable aspects of this thesis is that all our experiments on large-scale datasets are based on real sensor data. The Randomized Complex Neuro-Fuzzy Inferential System (RCNFIS) is a complex fuzzy set-based model implemented in three variants; we will furthermore discuss two stages in the design of this model. Our initial model focused on modelling univariate time series problems, using sinusoidal membership functions, complex Gaussian ones, or a combination of both. Our experiments with this model indicated that the complex Gaussian fuzzy sets led to a superior forecasting model than the sinusoidal ones, or their combination, across all datasets and all variants of the architecture. We then extended this model to forecast an arbitrary number of variates. We again found that, for all variants and all datasets, the complex Gaussian fuzzy sets led to superior forecasting models than the sinusoidal ones or the combination of both types. Additionally, we have applied statistical tests to prove all these claims (Z-test and Friedman). Finally, we found that these best RCNFIS models were more accurate than our previous architectures, while also being faster to train. They were furthermore more accurate than competing results on these datasets, either from the literature or our own experiments.</p>