Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth, $L^1$-depth and projection depth.

翻译：统计深度函数根据元素在概率分布或数据集中的中心性，对空间中的元素进行排序。由于许多深度函数在实数线上由中位数达到最大值，它们为更一般数据类型（本文中为模糊数据）的中位数型位置估计提供了自然定义方法。本文分析了基于深度中位数、基于支撑函数的中位数，以及文献中模糊数据中位数概念之间的关系。我们利用了先前论文中定义的模糊数据特定深度函数：Tukey深度、单纯形深度、$L^1$深度和投影深度的改进版本。