Matroidal structure of generalized rough sets based on symmetric and transitive relations

TL;DR

This paper explores the matroidal structure of generalized rough sets based on symmetric and transitive relations, providing new insights into their approximation properties and relationships.

Contribution

It constructs a matroidal framework for generalized rough sets and links matroid properties with rough set approximations, advancing theoretical understanding.

Findings

Matroidal structure of generalized rough sets established

Approximation quality can be analyzed via matroid circuits

Relation between matroids and rough sets clarified

Abstract

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.