Related papers: Relationship between the second type of covering-b…
In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions,…
Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
The theory of rough sets is concerned with the lower and upper approximations of objects through a binary relation on a universe. It has been applied to machine learning, knowledge discovery and data mining. The theory of matroids is a…
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…
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…
Recently, the relationship between matroids and generalized rough sets based on relations has been studied from the viewpoint of linear independence of matrices. In this paper, we reveal more relationships by the predecessor and successor…
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…
We study the closure operators of polymatroids from a lattice theoretic point of view. We show that polymatroid closure operators relate to lattices enriched with a generating set in the same way that matroids relate to geometric lattices.…
Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set…
Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a…
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…
The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.\ when the goal is to decide if two common independent sets suffice or not.…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence…
Rough set theory is an important mathematical tool for dealing with uncertain or vague information. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood opera- tors. Moreover, the…
The relationship between the operator approximation property and the strong operator approximation property has deep significance in the theory of operator algebras. The original definitions of Effros and Ruan, unlike the classical…
A connected covering is a design system in which the corresponding {\em block graph} is connected. The minimum size of such coverings are called {\em connected coverings numbers}. In this paper, we present various formulas and bounds for…
The main result is Theorem MAT 11 which states that every finite closure operator is the ground set of a matroid. Its base sets consist of nonredundant covers of of the closure. These are minimal subsets that determine the closure operator…