We present an approach to variable-strength conditional preferences for matchmaking and ranking objects in description logics. In detail, we introduce conditional preference bases, which consist of a description logic knowledge base and a finite set of variable-strength conditional preferences, and which are associated with a formal semantics based on ranking functions. We then define the notions of consistency and preferential entailment for conditional preference bases, which strictly generalize e-consistency and entailment in System Z+ in default reasoning from conditional knowledge bases, respectively. We also describe some semantic properties of preferential entailment. We then show how preferential entailment can be used to define a distance measure between two conditional preference bases. We also define functions for ranking objects relative to a conditional preference base, and we describe an application in the area of literature search. Finally, we provide algorithms for solving the main computational tasks related to conditional preference bases.