  The covering approximation space evolves in time due to the explosion of the
information, and the characteristic matrixes of coverings viewed as an
effective approach to approximating the concept should update with time for
knowledge discovery. This paper further investigates the construction of
characteristic matrixes without running the matrix acquisition algorithm
repeatedly. First, we present two approaches to computing the characteristic
matrixes of the covering with lower time complexity. Then, we investigate the
construction of the characteristic matrixes of the dynamic covering using the
incremental approach. We mainly address the characteristic matrix updating from
three aspects: the variations of elements in the covering, the immigration and
emigration of objects and the changes of attribute values. Afterwards, several
illustrative examples are employed to show that the proposed approach can
effectively compute the characteristic matrixes of the dynamic covering for
approximations of concepts.
