Geometric lattice structure of covering-based rough sets through matroids

09/29/2012
by   Aiping Huang, et al.
0

Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role in covering reductions. In this paper, we construct four geometric lattice structures of covering-based rough sets through matroids, and compare their relationships. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by the covering, and its characteristics including atoms, modular elements and modular pairs are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, sufficient and necessary conditions for three types of covering upper approximation operators to be closure operators of matroids are presented. We exhibit three types of matroids through closure axioms, and then obtain three geometric lattice structures of covering-based rough sets. Third, these four geometric lattice structures are compared. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely geometric lattice, to study covering-based rough sets.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/16/2013

Geometric lattice structure of covering and its application to attribute reduction through matroids

The reduction of covering decision systems is an important problem in da...
research
09/25/2012

Lattice structures of fixed points of the lower approximations of two types of covering-based rough sets

Covering is a common type of data structure and covering-based rough set...
research
12/16/2013

Connectedness of graphs and its application to connected matroids through covering-based rough sets

Graph theoretical ideas are highly utilized by computer science fields e...
research
07/02/2012

Characteristic matrix of covering and its application to boolean matrix decomposition and axiomatization

Covering is an important type of data structure while covering-based rou...
research
09/29/2012

Topological characterizations to three types of covering approximation operators

Covering-based rough set theory is a useful tool to deal with inexact, u...
research
10/02/2012

Relationship between the second type of covering-based rough set and matroid via closure operator

Recently, in order to broad the application and theoretical areas of rou...
research
11/28/2009

Covering rough sets based on neighborhoods: An approach without using neighborhoods

Rough set theory, a mathematical tool to deal with inexact or uncertain ...

Please sign up or login with your details

Forgot password? Click here to reset