Extensions of the well-known definition of chaos due to Li and Yorke for difference equations in ℝ
are reviewed for difference equations in ℝ
with either a snap-back repeller or saddle point as well as for mappings in Banach spaces and complete metric spaces. A further extension applicable to mappings in a space of fuzzy sets, namely the metric space (
) of fuzzy sets on the base space ℝ
, is then discussed and some illustrative examples are presented. The aim is to provide a theoretical foundation for further studies on the interaction between fuzzy logic and chaos theory.