Rough sets and matroidal contraction
This work addresses a theoretical problem in data mining and combinatorial optimization, but it is incremental as it builds on existing concepts without introducing new paradigms or broad applications.
The paper tackles the problem of integrating rough sets with matroid theory to analyze data structures, establishing a matroidal framework for rough sets and investigating properties like dual matroids and contractions, with results focusing on theoretical relationships rather than concrete numerical outcomes.
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.