Advertisement

Approximation via a double-matroid structure

  • Xiaonan LiEmail author
  • Huangjian Yi
  • Zhaohao Wang
Foundations
  • 36 Downloads

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.

Keywords

Approximation Granular computing Information systems Rough sets 

Notes

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).

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.

References

  1. 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
  2. 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
  3. Chen XY, Li QG (2007) Construction of rough approximations in fuzzy setting. Fuzzy Sets Syst 159:2641–2653MathSciNetCrossRefzbMATHGoogle Scholar
  4. Chiaselotti G, Ciucci D, Gentile T, Infusino FG (2016) The granular partition lattice of an information table. Inf Sci 373:57–78MathSciNetCrossRefzbMATHGoogle Scholar
  5. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191–209CrossRefzbMATHGoogle Scholar
  6. Lee T (1987) An information-theoretic analysisof relational databases- part 1: data dependencies and metric. IEEE Trans Softw Eng SE-13 10:1049–1061CrossRefGoogle Scholar
  7. Li XN, Liu SY (2012) Matroidal approaches to rough sets via closure operators. Int J Approx Reason 53:513–527MathSciNetCrossRefzbMATHGoogle Scholar
  8. Li XN, Yi HJ, Liu SY (2016) Rough sets and matroids from a lattice-theoretic viewpoint. Inf Sci 342:37–52MathSciNetCrossRefzbMATHGoogle Scholar
  9. Li XN, Yi HJ, She YH, Sun BZ (2017a) Generalized three-way models based on subset-evaluation. Int J Approx Reason 83:142–159MathSciNetCrossRefzbMATHGoogle Scholar
  10. Li XN, Sun BZ, She YH (2017b) Generalized matroids based on three-way decision models. Int J Approx Reason 90:192–207MathSciNetCrossRefzbMATHGoogle Scholar
  11. Mao H (2014) Characterization and reduction of concept lattices through matroid theory. Inf Sci 281:338–354MathSciNetCrossRefzbMATHGoogle Scholar
  12. Marek VW, Skowron A (2014) Rough sets and matroids. In: Peters JF, Skowron A (eds) Transactions on rough sets XVII, LNCS, vol 8375, pp 74–81Google Scholar
  13. Oxley JG (1992) Matroid theory. Oxford University Press, New YorkzbMATHGoogle Scholar
  14. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356CrossRefzbMATHGoogle Scholar
  15. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data, system theory, knowledge engineering and problem solving, vol 9. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  16. Skowron A (1996) Tolerance approximation spaces. Fundam Inform 27:245–253MathSciNetzbMATHGoogle Scholar
  17. 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
  18. 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
  19. Wang SP, Zhu QX, Zhu W, Min F (2014) Rough set characterization for 2-circuit matroid. Fundam Inform 129:377–393MathSciNetzbMATHGoogle Scholar
  20. Welsh D (1976) Matroid theory. Academic press, LondonzbMATHGoogle Scholar
  21. Yao YY (2004) A partition model of granular computing. In: Peters JF et al (eds) Transactions on rough sets I, LNCS, vol 3100, pp 232–253Google Scholar
  22. Yao YY, Yao BX (2012) Covering based rough set approximations. Inf Sci 200:91–107MathSciNetCrossRefzbMATHGoogle Scholar
  23. Zhu W, Wang SP (2013) Rough matroids based on relations. Inf Sci 232:241–252MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© 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

Personalised recommendations