Matroidal structure of generalized rough sets based on symmetric and transitive relations
This work provides a theoretical framework for data mining pre-processing, but it appears incremental as it extends existing matroidal approaches to specific types of relations.
The paper tackles the problem of analyzing generalized rough sets based on symmetric and transitive relations by constructing a matroidal structure, establishing a relationship between matroids and rough sets, and enabling computation of approximation quality and roughness using matroid circuits.
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.