Approximation via a double-matroid structure

  • Xiaonan LiEmail author
  • Huangjian Yi
  • Zhaohao Wang


Approximation is an important issue in rough set theory. In this study, we consider approximation by the matroidal approach. First, we study three lattices induced by an information system. Two of the three lattices are selected as the macrostructure and microstructure for approximation, respectively. Second, based on the two lattices, we define double-matroid lattices, where the upper and lower approximations with respect to an information system are depicted. Since the two lattices are geometric, we actually present approximation by the matroidal approach. Finally, we study the connection between our double-matroid lattices and granular partition lattices. Specifically, the comparison of these two structures is presented in both micro-level and macro-level.


Approximation Granular computing Information systems Rough sets 



The authors are grateful to Professor William Zhu for his help and the anonymous referees for their valuable suggestions. This work was supported by the National Natural Science Foundation of China (No. 61772019), the Shaanxi Province Natural Science Foundation Research Project (No. 2017JM1036), the Fundamental Research Funds for the Central Universities (No. JB170702) and the China Postdoctoral Science Foundation (No. 2016M602851).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of Information and TechnologyNorthwest UniversityXi’anChina
  3. 3.School of Mathematics and Computer ScienceShanxi Normal UniversityLinfenChina

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