Rough sets is born for analyzing the uncertainty data in information systems. However, many important problems of rough sets are NP-hard, most of which needs greedy algorithms to solve. Matroid, a sophisticated mathematical structure, provides a well platform for greedy algorithms. Hence, it is necessary to integrate rough set with matroid. In this paper, we establish a spanning matroidal structure is established and some characteristics of the matroidal structure are investigated in different ways. Moreover, some axiomatic characterizations of matroid are obtained through rough set. Firstly, a family of sets is defined by the upper approximation operator and prove it to satisfy spanning set axiom. So a matroid is induced by rough set in this way. We call the matroid spanning matroid. Secondly, some characteristics of spanning matroid, such as closed sets, spanning sets and bases, are investigated with rough set and matrix approaches, respectively. Thirdly, we investigate the axiomatic characterization of the upper approximation operator based on equivalence relation from matroids. Finally, based on rough sets, we obtain some axiomatic characterizations of spanning matroid in different ways.
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