  Uncertainty relations are a distinctive characteristic of quantum theory that
impose intrinsic limitations on the precision with which physical properties
can be simultaneously determined. The modern work on uncertainty relations
employs \emph{entropic measures} to quantify the lack of knowledge associated
with measuring non-commuting observables. However, there is no fundamental
reason for using entropies as quantifiers; any functional relation that
characterizes the uncertainty of the measurement outcomes defines an
uncertainty relation. Starting from a very reasonable assumption of invariance
under mere relabelling of the measurement outcomes, we show that Schur-concave
functions are the most general uncertainty quantifiers. We then discover a
fine-grained uncertainty relation that is given in terms of the majorization
order between two probability vectors, \textcolor{black}{significantly
extending a majorization-based uncertainty relation first introduced in [M. H.
Partovi, Phys. Rev. A \textbf{84}, 052117 (2011)].} Such a vector-type
uncertainty relation generates an infinite family of distinct scalar
uncertainty relations via the application of arbitrary uncertainty quantifiers.
Our relation is therefore universal and captures the essence of uncertainty in
quantum theory.
