  It is well known that, under very weak assumptions, multiobjective
optimization problems admit $(1+\varepsilon,\dots,1+\varepsilon)$-approximation
sets (also called $\varepsilon$-Pareto sets) of polynomial cardinality (in the
size of the instance and in $\frac{1}{\varepsilon}$). While an approximation
guarantee of $1+\varepsilon$ for any $\varepsilon>0$ is the best one can expect
for singleobjective problems (apart from solving the problem to optimality),
even better approximation guarantees than $(1+\varepsilon,\dots,1+\varepsilon)$
can be considered in the multiobjective case since the approximation might be
exact in some of the objectives.
  Hence, in this paper, we consider partially exact approximation sets that
require to approximate each feasible solution exactly, i.e., with an
approximation guarantee of $1$, in some of the objectives while still obtaining
a guarantee of $1+\varepsilon$ in all others. We characterize the types of
polynomial-cardinality, partially exact approximation sets that are guaranteed
to exist for general multiobjective optimization problems. Moreover, we study
minimum-cardinality partially exact approximation sets concerning (weak)
efficiency of the contained solutions and relate their cardinalities to the
minimum cardinality of a $(1+\varepsilon,\dots,1+\varepsilon)$-approximation
set.
