Abstract In this paper, we first show by a counterexample that the generalized Hukuhara differentiability of interval-valued function at a point is not fully equivalent to the one-sided differentiability of its endpoint functions, then present a complete characterization of the generalized Hukuhara differentiability of interval-valued functions. The obtained results include the existing cases in the literature and the new cases that correspond to the rather odd scenario of functions being gH-differentiable at a point, but not continuous in any deleted neighborhood of that point.

中文翻译：

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区间值函数的广义 Hukuhara 可微性并不完全等价于其端点函数的单边可微性

摘要 本文首先通过一个反例证明区间值函数在某一点的广义Hukuhara可微性并不完全等价于其端点函数的单边可微性，然后给出了一个点的广义Hukuhara可微性的完整刻画。 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?区间值函数。获得的结果包括文献中的现有案例和新案例，这些案例对应于函数在一点上可微的相当奇怪的情况，但在该点的任何删除邻域中不连续。