Rough sets and matroidal contraction

TL;DR

This paper explores the integration of rough sets with matroid theory, focusing on the contraction of the dual matroid and its properties, advancing data mining preprocessing techniques.

Contribution

It establishes a matroidal structure for rough sets via lower approximation and analyzes the contraction of the dual matroid in this context.

Findings

Matroidal structure derived from rough sets using lower approximation.

Properties of the dual matroid, including independent sets, bases, and rank function.

Relationships between contractions of the dual matroid and equivalence class complements.

Abstract

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 matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough set is established through the lower approximation operator. Second, the dual of the matroid and its properties such as independent sets, bases and rank function are investigated. Finally, the relationships between the contraction of the dual matroid to the complement of a single point set and the contraction of the dual matroid to the complement of the equivalence class of this point are studied.