Abstract:  Double-quantitative rough approximation, containing two types of quan-
titative information, indicated stronger generalization ability and more accurate data
processing capacity than the single-quantitative rough approximation. In this paper,
the neighborhood-based double-quantitative rough set models are firstly presented in a
set-valued information system. Secondly, the attribute reduction method based on the
lower approximation invariant is addressed, and the relevant algorithm for the approx-
imation attribute reduction is provided in the set-valued information system. Finally,
to illustrate the superiority and the effectiveness of the proposed reduction approach,
experimental evaluation is performed using three datasets coming from the University of
California-Irvine (UCI) repository.

Key words: Attribute reduction, Double quantification, Fuzzy similarity relation, Set-
valued information system