# The characterizations of upper approximation operators based on special coverings

Open Mathematics (2017)

• Volume: 15, Issue: 1, page 193-202
• ISSN: 2391-5455

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## Abstract

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In this paper, we discuss the approximation operators [...] apr¯NS ${\overline{apr}}_{NS}$ and [...] apr¯S ${\overline{apr}}_{S}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.

## How to cite

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Pei Wang, and Qingguo Li. "The characterizations of upper approximation operators based on special coverings." Open Mathematics 15.1 (2017): 193-202. <http://eudml.org/doc/287980>.

@article{PeiWang2017,
abstract = {In this paper, we discuss the approximation operators [...] apr¯NS $\{\overline\{apr\} _\{NS\}\}$ and [...] apr¯S $\{\overline\{apr\} _S\}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.},
author = {Pei Wang, Qingguo Li},
journal = {Open Mathematics},
keywords = {Upper approximation operator; Closure operator; Base; Topology; upper approximation operator; closure operator; base; topology},
language = {eng},
number = {1},
pages = {193-202},
title = {The characterizations of upper approximation operators based on special coverings},
url = {http://eudml.org/doc/287980},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Pei Wang
AU - Qingguo Li
TI - The characterizations of upper approximation operators based on special coverings
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 193
EP - 202
AB - In this paper, we discuss the approximation operators [...] apr¯NS ${\overline{apr} _{NS}}$ and [...] apr¯S ${\overline{apr} _S}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.
LA - eng
KW - Upper approximation operator; Closure operator; Base; Topology; upper approximation operator; closure operator; base; topology
UR - http://eudml.org/doc/287980
ER -

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