Inaccessibility of part of the database is a research topic hardly addressed in the literature about distributed databases. However, there are various application areas, where the database has to remain operable even if part of the database is inaccessible. In particular, queries to the database should be processed in an appropriate way. This means that the final and all intermediate results of a query in a distributed database system must be regarded as potentially vague.
In this paper we propose hybrid representations for vague sets, vague multisets, and vague lists, which address the accessible elements in an enumerating part and the inaccessible elements in a descriptive part. These representations allow to redefine the usual query language operations for vague sets, vague multisets, and vague lists. The main advantage of our approach is that the descriptive part of the representation can be used to improve the enumerating part during query processing.