Gated sets in metric spaces play an important role in the study of convexity. In this paper, we investigate the notion of gated sets in the context of betweenness of fuzzy metric spaces. For this purpose, we analyze the validity of postulates presented by Huntington and Kline to the betweenness in GV fuzzy metric spaces. The postulates are different from the usual properties of metric betweenness, amounting to thirteen. Interestingly, the validity of most of these postulates to the betweenness need to be considered in fuzzy normed spaces. In particular, two of the postulates for this relation are valid when the space is 1-dimensional. Five of the postulates for this relation are centrally studied in connection with strict convexity. As a consequence, several characterizations on strict convexity in a GV fuzzy normed space under the minimum t-norm are established.

度量空间中的门控集在凸性研究中起着重要作用。在本文中，我们研究了在模糊度量空间之间的中间性情况下门集的概念。为此，我们分析了亨廷顿（Huntington）和克莱恩（Kline）提出的假设对GV模糊度量空间中的中间性的有效性。该假设与公制中间值的通常属性不同，共计13个。有趣的是，在模糊赋范空间中需要考虑大多数这些假设对中间性的有效性。特别是，当空间为一维时，此关系的两个假设有效。关于这种关系的五个假设是结合严格的凸度进行集中研究的。作为结果，