Towards Inductive Learning of Complex Fuzzy Inference Systems

Complex fuzzy logic is an extension to type-1 fuzzy sets that has recently been developed. To date, no practical applications of complex fuzzy logic have been developed, possibly due to the difficulty of eliciting expert knowledge for both the magnitude and phase of a complex fuzzy set. We believe that practical applications of complex fuzzy logic require inductive learning. We are taking a first step towards this by building an inductive learning algorithm ANCFIS (Adaptive Neuro Fuzzy Complex Inference System), which hybridizes the theory of complex fuzzy inference and ANFIS. We believe that complex fuzzy sets will be a remarkably efficient way of modeling approximately periodic data. Thus, our proposed application of ANCFIS is in time series forecasting. We present an introduction to ANCFIS, its structure and computational formulas. The ANCFIS architecture is tested against three commonly cited time series datasets. Preliminary results show that ANCFIS is indeed able to model relatively periodic data as expected.