Since 2009 when preference-approval structures were introduced in the social choice literature, they have been studied and applied to produce explicit voting rules, measure consensus (which in turn requires the construction of appropriate distances or metrics), or clustering, among other areas. This contribution builds on the notion of consistent preference-approval structures. We discuss their relationship to other literature and argue that their introduction is justified because they are at the root of a smooth extension of the Arrovian approach that acts on preference-approval structures, namely, approbatory social welfare functions. Also, our contribution lays out a general two-step procedure that generates approbatory social welfare functions. We prove that this parameterized process enables us to produce Borda-type extensions in this setting, inclusive of existing proposals for the aggregation of complete preorders. Fully developed examples are given, along with incompatible properties that bound the scope of utilization of the novel approbatory social welfare functions.