  In the most accessible terms this paper presents a convex-geometric approach
to the study of fuzzy vectors. Motivated by several key results from the theory
of convex bodies, we establish a representation theorem of fuzzy vectors
through support functions, in which a necessary and sufficient condition for a
function to be the support function of a fuzzy vector is provided. As
applications, symmetric and skew fuzzy vectors are postulated, based on which a
Mare\v{s} core of each fuzzy vector is constructed through convex bodies and
support functions, and it is shown that every fuzzy vector over the
$n$-dimensional Euclidean space has a unique Mare\v{s} core if, and only if,
the dimension $n=1$.
