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Approximation via a double-matroid structure

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Abstract

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.

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Notes

  1. For ease in working, we denote the partition \(\{1,2\},\{3,4\}\) by (12)(34), and the partition {1,2},{3},{4} simply by its non-trivial block (12).

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Acknowledgements

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).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, China

    Xiaonan Li

  2. School of Information and Technology, Northwest University, Xi’an, China

    Huangjian Yi

  3. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, China

    Zhaohao Wang

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  1. Xiaonan Li
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  2. Huangjian Yi
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  3. Zhaohao Wang
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Correspondence to Xiaonan Li.

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

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Communicated by A. Di Nola.

Dedicated to Professor Sanyang Liu on the occasion of his 60th birthday.

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Li, X., Yi, H. & Wang, Z. Approximation via a double-matroid structure. Soft Comput 23, 7557–7568 (2019). https://doi.org/10.1007/s00500-018-03749-8

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