An investigation of complex fuzzy sets for large-scale learning

Abstract

Complex fuzzy sets are an extension of type-1 fuzzy sets with complex-valued membership functions. Over the last 20 years, time-series forecasting has emerged as the most important application of complex fuzzy sets, with neuro-fuzzy systems employing them shown to be accurate and compact forecasting models. In the complex fuzzy sets literature, two dominant approaches to designing forecasters can be observed: sinusoidal membership functions versus complex-valued Gaussian membership functions. To date, however, there has never been a systematic investigation that compares the performance of these two membership types (or their combination) within a common architecture.We propose a new neuro-fuzzy architecture using complex fuzzy sets that has been designed for large-scale learning problems. This architecture employs randomized learning to speed up network training. In designing this architecture, we empirically compared sinusoidal complex fuzzy sets and complex Gaussian fuzzy sets. Across multiple variations of the architecture, we find that the complex Gaussian fuzzy sets lead to significantly more accurate forecasts on moderate-to-large time series datasets, while still keeping the overall size of the network compact.