In this paper we study some geometrical properties of the polytope of 3-tolerant fuzzy measures. To achieve this task, we profit that this polytope is an order polytope and hence many properties can be extracted from the subjacent poset. The main result in the paper is a straightforward procedure for obtaining a random 3-tolerant fuzzy measure. We also compute the volume and obtain some other properties of this polytope. These results can be also applied by duality to the polytope of 3-intolerant measures and they can also be easily extended to other subfamilies of fuzzy measures.

中文翻译：

---

关于三容忍模糊测度的多胞体

在本文中，我们研究了 3 容忍模糊测度的多胞体的一些几何性质。为了完成这个任务，我们获益于这个多胞体是一个有序多胞体，因此可以从下面的偏序集中提取许多属性。本文的主要结果是获得随机 3 容忍模糊测度的简单程序。我们还计算体积并获得此多面体的一些其他属性。这些结果也可以通过对偶性应用于 3 不容忍测度的多胞体，并且它们也可以很容易地扩展到模糊测度的其他子族。