An investigation of complex fuzzy sets for large-scale learning

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.