3 research outputs found
Matroidal structure of generalized rough sets based on symmetric and transitive relations
Rough sets are efficient for data pre-process in data mining. Lower and upper
approximations are two core concepts of rough sets. This paper studies
generalized rough sets based on symmetric and transitive relations from the
operator-oriented view by matroidal approaches. We firstly construct a
matroidal structure of generalized rough sets based on symmetric and transitive
relations, and provide an approach to study the matroid induced by a symmetric
and transitive relation. Secondly, this paper establishes a close relationship
between matroids and generalized rough sets. Approximation quality and
roughness of generalized rough sets can be computed by the circuit of matroid
theory. At last, a symmetric and transitive relation can be constructed by a
matroid with some special properties.Comment: 5 page
Rough matroids based on coverings
The introduction of covering-based rough sets has made a substantial
contribution to the classical rough sets. However, many vital problems in rough
sets, including attribution reduction, are NP-hard and therefore the algorithms
for solving them are usually greedy. Matroid, as a generalization of linear
independence in vector spaces, it has a variety of applications in many fields
such as algorithm design and combinatorial optimization. An excellent
introduction to the topic of rough matroids is due to Zhu and Wang. On the
basis of their work, we study the rough matroids based on coverings in this
paper. First, we investigate some properties of the definable sets with respect
to a covering. Specifically, it is interesting that the set of all definable
sets with respect to a covering, equipped with the binary relation of inclusion
, constructs a lattice. Second, we propose the rough matroids based
on coverings, which are a generalization of the rough matroids based on
relations. Finally, some properties of rough matroids based on coverings are
explored. Moreover, an equivalent formulation of rough matroids based on
coverings is presented. These interesting and important results exhibit many
potential connections between rough sets and matroids.Comment: 15page