In this article, we prove that the generalized difference between $A,B\in {\mathbb{R}}_{{\mathcal{F}}_{\mathcal{C}}},$ i.e., fuzzy numbers with continuous endpoints, is given by an interactive difference. To be more precise, we construct a certain joint possibility distribution I such that the generalized difference coincides with the sup-I extension of the subtraction. As an immediate consequence, we have that every notion of difference between $A,B\in {\mathbb{R}}_{{\mathcal{F}}_{\mathcal{C}}},$ that has so far appeared in the literature, can be derived from a sup-J extension for some particular choice of J. Moreover, we show that both the generalized and the generalized Hukuhara derivative of a function $f:\mathbb{R}\to {\mathbb{R}}_{{\mathcal{F}}_{\mathcal{C}}}$ at $x\in \mathbb{R}$ can be expressed as the limit for h → 0 of a difference quotient, where the difference is an interactive difference for each h. For short, we say that the generalized (as well as the generalized Hukuhara) difference is interactive.

在本文中，我们证明了 $\mathrm{一种}，乙\in {\mathbb{[R}}_{{\mathcal{F}}_{\mathcal{C}}}，$即，具有连续端点的模糊数由交互差异给出。更准确地说，我们构造了某种联合可能性分布I，以使广义差异与减法的sup- I扩展一致。作为直接结果，我们认为$\mathrm{一种}，乙\in {\mathbb{[R}}_{{\mathcal{F}}_{\mathcal{C}}}，$即迄今在文献中出现，可从SUP-导出Ĵ扩展的一些特定选择Ĵ。而且，我们表明函数的广义和广义Hukuhara导数$F：\mathbb{[R}\to {\mathbb{[R}}_{{\mathcal{F}}_{\mathcal{C}}}$ 在 $X\in \mathbb{[R}$可以表示为 商的h →0的极限，其中该差是每个h的交互式差。简而言之，我们说广义（以及广义Hukuhara）差异是交互的。