Table 1 The tabular demonstration of IVBCFSS.
From: Interval-valued bipolar complex fuzzy soft sets and their applications in decision making
\(\left(\mathfrak{L},\Gamma \right)\) | \({j}_{1}\) | \({j}_{2}\) | … | \({j}_{{\tilde{s}}}\) |
|---|---|---|---|---|
\({\iota }_{1}\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{11}}^{L+}, {\rm O}_{{\mathfrak{L}}_{11}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{11}}^{L+}, {\rm O}_{{\mathfrak{L}}_{11}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{11}}^{L-}, {\rm O}_{{\mathfrak{L}}_{11}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{11}}^{L-}, {\rm O}_{{\mathfrak{L}}_{11}}^{U-}\right]\end{array}\right)\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{12}}^{L+}, {\rm O}_{{\mathfrak{L}}_{12}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{12}}^{L+}, {\rm O}_{{\mathfrak{L}}_{12}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{12}}^{L-}, {\rm O}_{{\mathfrak{L}}_{12}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{12}}^{L-}, {\rm O}_{{\mathfrak{L}}_{12}}^{U-}\right]\end{array}\right)\) | … | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{1{{\tilde{s}}}}}^{U-}\right]\end{array}\right)\) |
\({\iota }_{2}\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{21}}^{L+}, {\rm O}_{{\mathfrak{L}}_{21}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{21}}^{L+}, {\rm O}_{{\mathfrak{L}}_{21}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{21}}^{L-}, {\rm O}_{{\mathfrak{L}}_{21}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{21}}^{L-}, {\rm O}_{{\mathfrak{L}}_{21}}^{U-}\right]\end{array}\right)\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{22}}^{L+}, {\rm O}_{{\mathfrak{L}}_{22}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{22}}^{L+}, {\rm O}_{{\mathfrak{L}}_{22}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{22}}^{L-}, {\rm O}_{{\mathfrak{L}}_{22}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{22}}^{L-}, {\rm O}_{{\mathfrak{L}}_{22}}^{U-}\right]\end{array}\right)\) | … | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{2{{\tilde{s}}}}}^{U-}\right]\end{array}\right)\) |
\({\iota }_{3}\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{31}}^{L+}, {\rm O}_{{\mathfrak{L}}_{31}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{31}}^{L+}, {\rm O}_{{\mathfrak{L}}_{31}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{31}}^{L-}, {\rm O}_{{\mathfrak{L}}_{31}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{31}}^{L-}, {\rm O}_{{\mathfrak{L}}_{31}}^{U-}\right]\end{array}\right)\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{32}}^{L+}, {\rm O}_{{\mathfrak{L}}_{32}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{32}}^{L+}, {\rm O}_{{\mathfrak{L}}_{32}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{32}}^{L-}, {\rm O}_{{\mathfrak{L}}_{32}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{32}}^{L-}, {\rm O}_{{\mathfrak{L}}_{32}}^{U-}\right]\end{array}\right)\) | … | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{3{{\tilde{s}}}}}^{U-}\right]\end{array}\right)\) |
… | … | … | … | … |
\({\iota }_{{\tilde{r}}}\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{L+}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{L+}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{L-}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{L-}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}1}}^{U-}\right]\end{array}\right)\) | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{L+}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{L+}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{L-}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{L-}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}2}}^{U-}\right]\end{array}\right)\) | … | \(\left(\begin{array}{c}\left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{U+}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{L+}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{U+}\right], \\ \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{U-}\right]+\iota \left[{\rm N}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{L-}, {\rm O}_{{\mathfrak{L}}_{{{\tilde{r}}}{{\tilde{s}}}}}^{U-}\right]\end{array}\right)\) |
