Some Researches On Rough Matroids

An excellent introduction to the topic of rough matroids is due to Zhu and Wang. Rough matroid, as an important generation of rough set theory and matroid theory, not only has fundations in theory and application fields of the rough set theory, but also has succeed the complete axiom systems and the effectively processing method in practical applications of matroid theory. Thus, rough matroid is a more efficient tool for dealing with uncertain problems in information systems than rough set, and it also plays a vital role in other fields such as combinatorial optimization and algorithm design. At present, as a new research field, the study of rough matroids in the aspects of theory and application is not mature yet. Then some naturely existing and meaningful issues should be sequentially studied and solved. On the basis of Zhu’s work, we study some researches on rough matroids by means of combining rough set theory with matroid theory in this thesis. The main contributions of this work are listed as follows:(1) Some main research findings of combining rough set theory with matroid theory are proposed. We establish some types of matroidal structures of rough sets through the properties of rough sets, and the characters and applications of these types of matroidal structure are studied by means of rough set theory. Meanwhile, the connectedness of a matroid is an important definition in matroid theory, and the approches of judging a matroid is connected or not are very complex. Based on this, we present an approach to judge the connectedness of a matroid with constructive method by means of rough set theory. Finally, through some special matroids, some types of rough approximation operators are defined and their properties are explored.(2) The properties and equal formulations of rough matroids based on relations are investigated. By combining the rough set theory and matroid theory, we do some further discuss of the rough matroids based on relations. Moreover, the concept of rough matroid as a generalization of matroid, then some equal formulations can be given by matroid theory.(3) The definition and properties of rough matroids based on covering are proposed. Covering-based rough sets are generation of classical rough sets. Then we can generalize the definition of rough matroids based on relations to coverings based on Zhu’s work. Meanwhile, the properties and equal formulations of rough matroids based on coverings are presented.