Let (X,f) be a dynamical system, (𝒦(X),¯f) be the system on hyperspace and (𝔽(X),˜fg) be its g-fuzzification. We study the relations among the various forms of sensitivity of the systems (X,f), (𝒦(X),¯f) and (𝔽1(X),˜fg). Firstly, we give a simpler proof of the theorem in [Wu & Chen, 2017] which states that (𝒦(X),¯f) is sensitive if and only if (𝔽1(X),˜fg) is sensitive. Then, we show that (1) all forms of sensitivity of (𝒦(X),¯f) are the same for (𝔽(X),˜fg), (2) all forms of sensitivity of (𝒦(X),¯f) partly imply the same for (X,f), and the converse holds in some cases.