Abstract

Extensions of the well-known definition of chaos due to Li and Yorke for difference equations in ℝ1 are reviewed for difference equations in ℝn 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 (ξ n, D) of fuzzy sets on the base space ℝn, 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.

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