In this paper we study scoring and order approach to concept interpretation in description logics. Only concepts are scored/ordered; roles remain crisp.
The concepts in scoring description logic are fuzzified; while the concepts in order description logic are interpreted as preorders on the domain. These description logics are used for preferential user-dependent search of the best instances.
In addition to the standard constructors we add top-k retrieval and aggregation of user preferences. We analyze the relationship between scoring and order concepts and we introduce a notion of order-preserving concept constructors.