We focus on handling conflicting and uncertain information in lightweight ontologies, where uncertainty is represented in a possibilistic logic setting. We use DL-Lite, a tractable fragment of Description Logic, to specify terminological knowledge (i.e., TBox). We assume the TBox to be stable and coherent, while its combination with a set of assertional facts (i.e., ABox) may be inconsistent. We address the problem of dealing with conflicts when the reliability relation between sources is only partially ordered. We propose to represent the uncertain ABox as a symbolic weighted base, where a strict partial preorder is applied on the weights. In this context, we provide a strategy for computing a single repair for the ABox, called the partial possibilistic repair. The idea is to consider all compatible bases of a partially preordered ABox (which intuitively encode total extensions of the partial preorder), compute their associated possibilistic repairs, before intersecting those repairs. We define the notion of π-accepted assertions and provide an equivalent characterization, therefore ensuring tractable computations of our method.