This chapter reviews the development of the definitions of chaos from the wellknown Li-Yorke definition of chaos for difference equations in 葶
to those for difference equations in 葶
with either a snap-back repeller or saddle point as well as for maps in Banach spaces and complete metric spaces, among which Devaney’s definition will be used in this book in the proof that chaos exists in anti-controlled fuzzy systems. Finally, a definition of chaos for maps in a space of fuzzy sets, namely, the metric space (ξ
) of fuzzy sets on the base space 葶
, is given, aiming to lay a theoretical foundation for further studies on the interactions between fuzzy logic and chaos theory. Some illustrative examples are presented.