title: Matroidal structure of generalized rough sets based on tolerance relations.
abstract: Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as combinatorial optimization and rough sets. In this paper, we construct a matroidal structure of the generalized rough set based on a tolerance relation. First, a family of sets are constructed through the lower approximation of a tolerance relation and they are proved to satisfy the circuit axioms of matroids. Thus we establish a matroid with the family of sets as its circuits. Second, we study the properties of the matroid including the base and the rank function. Moreover, we investigate the relationship between the upper approximation operator based on a tolerance relation and the closure operator of the matroid induced by the tolerance relation. Finally, from a tolerance relation, we can get a matroid of the generalized rough set based on the tolerance relation. The matroid can also induce a new relation. We investigate the connection between the original tolerance relation and the induced relation.
authors.affiliation: Laboratory of Granular Computing, Minnan Normal University, Zhangzhou 363000, China.
authors.forename: Hui
authors.initials: H
authors.lastname: Li
authors.affiliation: Laboratory of Granular Computing, Minnan Normal University, Zhangzhou 363000, China.
authors.forename: Yanfang
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Laboratory of Granular Computing, Minnan Normal University, Zhangzhou 363000, China.
authors.forename: William
authors.identifier: 0000-0001-8898-9244
authors.initials: W
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007256:Information Systems; D008962:Models, Theoretical