For a given metric space X, we consider the set of all normal fuzzy sets on X, denoted by $\mathcal{F}(X)$. In this work, we study expanding, positively expansive and weakly positively expansive dynamical systems $(X,f)$ and how they are reflected in the dynamical system $(\mathcal{F}(X),\hat{f})$, where $\hat{f}$ is the Zadeh's extension of f and $\mathcal{F}(X)$ has one of the following metrics: the levelwise metric, the endograph metric, the sendograph metric and the Skorokhod metric. We mainly show that if we consider the following conditions:

(i)

$(X,f)$ is positively expansive (resp. expanding);

(ii)

$(\mathcal{K}(X),\bar{f})$ is positively expansive (resp. expanding);

(iii)

$({\mathcal{F}}_{\infty }(X),\hat{f})$ is positively expansive (resp. expanding);

(iv)

$({\mathcal{F}}_0(X),\hat{f})$ is positively expansive (resp. expanding).

对于给定的度量空间X，我们考虑集合就一切正常模糊集的X，表示由$\mathcal{F}(X)$. 在这项工作中，我们研究了膨胀、正膨胀和弱正膨胀动力系统$(X,F)$ 以及它们如何反映在动力系统中 $(\mathcal{F}(X),\widehat{F})$， 在哪里 $\widehat{F}$是f的 Zadeh 扩展，并且$\mathcal{F}(X)$具有以下度量之一：levelwise 度量、endograph 度量、sendograph 度量和 Skorokhod 度量。我们主要表明，如果我们考虑以下条件：

（一世）

$(X,F)$ 是积极扩张的（分别是扩张）；

(二)

$(\mathcal{钾}(X),\bar{F})$ 是积极扩张的（分别是扩张）；

(三)

$({\mathcal{F}}_{\infty }(X),\widehat{F})$ 是积极扩张的（分别是扩张）；

(四)

$({\mathcal{F}}_0(X),\widehat{F})$ 是积极扩张的（分别是扩张）。