  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.
