Abstract
Let X be a compact metric space and [Formula: see text] a continuous map. Considering the space [Formula: see text] of all nonempty fuzzy sets on X endowed with the levelwise topology, we proved that its g-fuzzification is turbulent or erratic if the given system f is turbulent or erratic correspondingly and f is [Formula: see text]-expansive if and only if its g-fuzzification is [Formula: see text]-expansive.