Table 6 The lower approximations table with \(\beta =0.90, l=1\).
From: Soft ordered double quantitative approximations based three-way decisions and their applications
\(S^{\Diamond }\) | \(\sum \limits _{k=1}^{\left| D\right| } \left( \underline{S_{k}}\right) _{{\mathcal {D}}ominan \left( {\mathcal {T}}_{k}^{*},C\right) ^{+}}^{\beta \vee l \left( o\right) }\) | \(\sum \nolimits _{k=1}^{\left| D\right| } \left( \underline{S_{k}}\right) _{{\mathcal {D}}ominan \left( {\mathcal {T}}_{k}^{*},C\right) ^{-}}^{\beta \vee l\left( o\right) }\) |
|---|---|---|
\(S_{1}^{\Diamond }\) | \(\left\{ b_{1},b_{2},b_{3},b_{4},b_{6},b_{7},b_{9},b_{10},b_{12}\right\} \) | \(\left\{ b_{1},b_{2},b_{3},b_{4},b_{6},b_{12}\right\} \) |
\(S_{2}^{\Diamond }\) | \(\left\{ b_{1},b_{2},b_{3},b_{4},b_{5},b_{7},b_{8},b_{9},b_{10},b_{11},b_{12}\right\} \) | \(\left\{ b_{1},b_{2},b_{3},b_{4},b_{5},b_{8},b_{9},b_{10},b_{11},b_{12}\right\} \) |
\(S_{3}^{\Diamond }\) | \(\left\{ b_{1},b_{6},b_{7},b_{9},b_{11},b_{12}\right\} \) | \(\left\{ b_{1},b_{4},b_{6},b_{11},b_{12}\right\} \) |
\(S_{4}^{\Diamond }\) | \(\left\{ b_{1},b_{2},b_{3},b_{4},b_{5},b_{7},b_{8},b_{9},b_{10},b_{12}\right\} \) | \( \left\{ b_{1},b_{2},b_{3},b_{4},b_{5},b_{8},b_{9},b_{10},b_{12}\right\} \) |
