A systematic review of complex fuzzy sets and logic.

Complex fuzzy sets and logic are an extension of type-1 fuzzy sets wherein memberships may be complex-valued. This has been an area of growing research focus in the fuzzy systems community for over a decade, with successful applications in time series forecasting and other areas. We conduct a systematic review of this topic to provide a framework to position new research in the field, consolidate the available theoretical results, catalogue the current applications of complex fuzzy sets and logic, identify the key open questions facing researchers in this area, and suggest possible future directions for research in this field.