  Functions with uniform sublevel sets can represent orders, preference
relations or other binary relations and thus turn out to be a tool for
scalarization that can be used in multicriteria optimization, decision theory,
mathematical finance, production theory and operator theory. Sets which are not
necessarily convex can be separated by functions with uniform sublevel sets.
This report focuses on properties of real-valued and extended-real-valued
functions with uniform sublevel sets which are defined on a linear space
without assuming topological properties. The functions may be convex or
sublinear. They can coincide with a Minkowski functional or with an order unit
norm on a subset of the space. The considered functionals are applied to the
scalarization of vector optimization problems. These vector optimization
problems refer to arbitrary domination sets. The consideration of such sets is
motivated by their relationship to domination structures in decision making.
