Soft Computing

, Volume 23, Issue 10, pp 3217–3228 | Cite as

The characterizations of upper approximation operators based on coverings

  • Pei Wang
  • Qingguo LiEmail author


In this paper, We propose a condition of symmetry for the covering \(\mathscr {C}\) in a covering-based approximation space \((U,\mathscr {C})\). By using this condition, we obtain general, topological and intuitive characterizations of the covering \({\mathscr {C}}\) for two types of covering-based upper approximation operators being closure operators. We investigate axiomatic systems for \(\overline{apr}_{S}\) and discuss the relationships among upper approximation operators. We also give a description of \((U,{\mathscr {C}})\) in terms of information exchange systems when these operators are closure ones. We also solve an open problem raised by Ge et al.


Closure operator Covering-based upper approximation operator Partition Third condition of symmetry 



This work is supported by the Natural Science Foundation of China (No. 11371130) and the Natural Science Foundation of Guangxi (Nos. 2014GXNSFBA118015, 2016CSOBDP0004, 2016JC2014 and KY2015YB244).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

Human and animal rights

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


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and EconometricsHunan UniversityChangshaChina
  2. 2.Guangxi Universities Key Lab of Complex System Optimization and Big Data ProcessingYulin Normal UniversityYulinChina

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