# The characterizations of upper approximation operators based on coverings

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## Abstract

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.

## Keywords

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

### Acknowledgements

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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