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
This is a preview of subscription content, log in to check access.
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.
This article does not contain any studies with human participants or animals performed by any of the authors.
Bisi C, Chiaselotti G, Ciucci D, Gentile T, Infusino FG (2017) Micro and macro models of granular computing induced by the indiscernibility relation. Inf Sci 388–389:247–273MathSciNetCrossRefGoogle Scholar
Cattaneo G, Ciucci D (2009) Lattices with interior and closure operators and abstract approximation spaces. In: Peters JF et al (eds) Transactions on rough sets X, LNCS, vol 5656. Springer, Heidelberg, pp 67–116CrossRefGoogle Scholar
Wang GY, Skowron A, Yao YY, Ślȩzak D, Polkowski L (eds) (2017) Thriving rough sets: 10th anniversary- Honoring professor Z. Pawlak’s life and legacy and 35 years of rough sets. Springer, ChamzbMATHGoogle Scholar
Wang SP, Zhu QX, Zhu W, Min F (2012) Matroidal structure of rough sets and its characterization to attribute reduction. Knowl-Based Syst 36:155–161CrossRefGoogle Scholar