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This analysis investigates how Zadeh's extension affects sensitivity and Lyapunov stability in fuzzy sets under a semiflow framework.
For a given metric space X, the symbol ℱ(X) denotes the family of all normal upper semicontinuous fuzzy sets on X with compact support. A semiflow is a continuous function f:T×X → X, where T is an abelian topological monoid. We study when f^:T×ℱ(X) → ℱ(X) is strongly sensitive, multi-sensitive or positive Lyapunov stable, where f^ is the Zadeh's extension of the semiflow f and ℱ(X) is endowed with level-wise and Skorokhod metrics.
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Fernández et al. (2025) studied this question.
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