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Chaos, entropy and a generalized extension principle. (English) Zbl 0827.58037
Summary: We show a relationship between a very simple criterion, positive topological entropy and Li-Yorke chaos. A general definition of fuzzification and level set, based on t-norms/conorms and their diagonal functions, is introduced. The chaos theorem of Benhabib and Day for set valued mappings is considerably strengthened and generalised.

MSC:
37D45Strange attractors, chaotic dynamics
94D05Fuzzy sets and logic in connection with communication
54C70Topological entropy
03E72Fuzzy set theory