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Table 2 Upper and lower approximations and the boundary region of the rough set X

From: Integrated measures for rough sets based on general binary relations

X

\( \underline{{R_{T}^{P} }} (X) \)

\( \underline{{R_{T}^{Q} }} (X) \)

\( \overline{{R_{T}^{P} }} (X) \)

\( \overline{{R_{T}^{Q} }} (X) \)

\( BN_{{R_{T}^{P} }} (X) \)

\( BN_{{R_{T}^{Q} }} (X) \)

X 1

{u 1, u 2}

{u 1, u 2}

{u 1, u 2, u 6, u 7}

{u 1, u 2, u 6, u 7}

{u 6, u 7}

{u 6, u 7}

X 2

\( \emptyset \)

\( \emptyset \)

{u 1, u 2, u 3, u 4, u 5}

{u 1, u 2, u 3, u 4}

{u 1, u 2, u 3, u 4, u 5}

{u 1, u 2, u 3, u 4}