  This paper further investigates the set-valued information system. First, we
bring forward three tolerance relations for set-valued information systems and
explore their basic properties in detail. Then the data compression is
investigated for attribute reductions of set-valued information systems.
Afterwards, we discuss the data compression of dynamic set-valued information
systems by utilizing the precious compression of the original systems. Several
illustrative examples are employed to show that attribute reductions of
set-valued information systems can be simplified significantly by our proposed
approach.
