  In practice, there are many dynamic covering decision information systems,
and knowledge reduction of dynamic covering decision information systems is a
significant challenge of covering-based rough sets. In this paper, we first
study mechanisms of constructing attribute reducts for consistent covering
decision information systems when adding objects using related families. We
also employ examples to illustrate how to construct attribute reducts of
consistent covering decision information systems when adding objects. Then we
investigate mechanisms of constructing attribute reducts for consistent
covering decision information systems when deleting objects using related
families. We also employ examples to illustrate how to construct attribute
reducts of consistent covering decision information systems when deleting
objects. Finally, the experimental results illustrates that the related
family-based methods are effective to perform attribute reduction of dynamic
covering decision information systems when object sets are varying with time.
