Maly, JanWoltran, StefanMitschang, BernhardNicklas, DanielaLeymann, FrankSchöning, HaraldHerschel, MelanieTeubner, JensHärder, TheoKopp, OliverWieland, Matthias2017-06-212017-06-212017978-3-88579-660-2Ranking sets of objects based on an order between the single elements has been thoroughly studied in the literature. In particular, it has been shown that it is in general impossible to find a total ranking – jointly satisfying properties as dominance and independence – on the whole power set of objects. However, in many formalisms from the area of knowledge representation one does not need to order the entire power set, since certain sets are already ruled out due to hard constraints or are not satisfying some background theory. In this paper, we address the question whether an order on a given subset of the power set of elements satisfying different variants of dominance and independence can be found. We first show that this problem is tractable when we look for partial rankings, but becomes NP-complete for total rankings.enRanking Sets. ComplexityText/Conference Paper1617-5468