Abstract
Rough sets are efficient to extract rules from information systems. Matroids generalize the linear independency in vector spaces and the cycle in graphs. Specifically, matroids provide well-established platforms for greedy algorithms, while most existing algorithms for many rough set problems including attribute reduction are greedy ones. Therefore, the combination between rough sets and matroids may bring new efficient solutions to those important and difficult problems. In this paper, 2-circuit matroids, abstracted from matroidal characteristics of rough sets, are studied and axiomatized. A matroid is induced by an equivalence relation, and its characteristics including the independent set and duality are represented with rough sets. Based on these rough set representations, this special type of matroid is defined as 2-circuit matroids. Conversely, an equivalence relation is induced by a matroid, and its relationship with the above induction is further investigated. Finally, a number of axioms of the 2-circuit matroid are obtained through rough sets. These interesting and diverse axioms demonstrate the potential for the connection between rough sets and matroids.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
