<p>This work delves into the characterization of strong fuzzy metric spaces by using domain-theoretical methods. Unlike the conventional approach of using formal ball posets in fuzzy metric spaces, which typically form continuous domains or directed complete posets, this paper introduces a new concept of T-closed balls in strong fuzzy metric spaces. Under the reverse inclusion order, T-closed ball posets are algebraic, and thus naturally continuous. Specifically, we demonstrate that strong fuzzy metric spaces are T-complete if and only if the T-closed ball posets constitute Scott domains. This conclusion obviates the typical dependence on minimal t-norms in the domain characterizations of fuzzy metric spaces. Additionally, we present alternative strategies via standard closed balls and formal balls, to address the characterization of standard complete fuzzy ultrametric spaces. These contributions provide new avenues for establishing connections between fuzzy metric spaces and the associated ordered structures.</p>