127,256 research outputs found
Geometric lattice structure of covering and its application to attribute reduction through matroids
The reduction of covering decision systems is an important problem in data
mining, and covering-based rough sets serve as an efficient technique to
process the problem. Geometric lattices have been widely used in many fields,
especially greedy algorithm design which plays an important role in the
reduction problems. Therefore, it is meaningful to combine coverings with
geometric lattices to solve the optimization problems. In this paper, we obtain
geometric lattices from coverings through matroids and then apply them to the
issue of attribute reduction. First, a geometric lattice structure of a
covering is constructed through transversal matroids. Then its atoms are
studied and used to describe the lattice. Second, considering that all the
closed sets of a finite matroid form a geometric lattice, we propose a
dependence space through matroids and study the attribute reduction issues of
the space, which realizes the application of geometric lattices to attribute
reduction. Furthermore, a special type of information system is taken as an
example to illustrate the application. In a word, this work points out an
interesting view, namely, geometric lattice to study the attribute reduction
issues of information systems
Knowledge reduction of dynamic covering decision information systems with varying attribute values
Knowledge reduction of dynamic covering information systems involves with the
time in practical situations. In this paper, we provide incremental approaches
to computing the type-1 and type-2 characteristic matrices of dynamic coverings
because of varying attribute values. Then we present incremental algorithms of
constructing the second and sixth approximations of sets by using
characteristic matrices. We employ experimental results to illustrate that the
incremental approaches are effective to calculate approximations of sets in
dynamic covering information systems. Finally, we perform knowledge reduction
of dynamic covering information systems with the incremental approaches
- …