Zadeh’s extension of a strong sensitive semiflow

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.