Table 2 Properties of upper approximation operations (Zhu and Wang 2012, 2007; Zhang and Luo 2013)
| Â | \(\overline{C}_{1}\) | \(\overline{C}_{2}\) | \(\overline{C}_{3}\) | \(\overline{C}_{4}\) | \(\overline{C}_{5}\) | \(\overline{C}_{6}\) | \(\overline{C}_{7}\) | \(\overline{C}_{8}\) | \(\overline{C}_{9}\) | \(\overline{C}_{10}\) |
|---|---|---|---|---|---|---|---|---|---|---|
1H | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) |
2H | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) |
3H | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) |
4H | – | \(\checkmark \) | \(\checkmark \) | – | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) |
5H | \(\checkmark \) | – | – | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | – | – | – |
6H | – | \(\checkmark \) | \(\checkmark \) | – | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) |
7H | – | – | – | – | – | – | – | – | – | – |