Table 3 Interval-valued spherical fuzzy aggregated decision matrix.
\(\:{\varvec{C}}_{1}\) | \(\:{\varvec{C}}_{2}\) | \(\:{\varvec{C}}_{3}\) | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\:{\mathfrak{m}}^{\varvec{l}}\) | \(\:{\mathfrak{m}}^{\varvec{u}}\) | \(\:{\mathfrak{n}}^{\varvec{l}}\) | \(\:{\mathfrak{n}}^{\varvec{u}}\) | \(\:{\mathcal{a}}^{\varvec{l}}\) | \(\:{\mathcal{a}}^{\varvec{u}}\) | \(\:{\mathfrak{m}}^{\varvec{l}}\) | \(\:{\mathfrak{m}}^{\varvec{u}}\) | \(\:{\mathfrak{n}}^{\varvec{l}}\) | \(\:{\mathfrak{n}}^{\varvec{u}}\) | \(\:{\mathcal{a}}^{\varvec{l}}\) | \(\:{\mathcal{a}}^{\varvec{u}}\) | \(\:{\mathfrak{m}}^{\varvec{l}}\) | \(\:{\mathfrak{m}}^{\varvec{u}}\) | \(\:{\mathfrak{n}}^{\varvec{l}}\) | \(\:{\mathfrak{n}}^{\varvec{u}}\) | \(\:{\mathcal{a}}^{\varvec{l}}\) | \(\:{\mathcal{a}}^{\varvec{u}}\) | |
\(\:{\varvec{A}}_{1}\) | \(\:0.39\) | \(\:0.50\) | \(\:0.71\) | \(\:0.74\) | \(\:0.21\) | \(\:0.29\) | \(\:0.31\) | \(\:0.42\) | \(\:0.78\) | \(\:0.80\) | \(\:0.19\) | \(\:0.26\) | \(\:0.27\) | \(\:0.37\) | \(\:0.85\) | \(\:0.86\) | \(\:0.14\) | \(\:0.21\) |
\(\:{\varvec{A}}_{2}\) | \(\:0.39\) | \(\:0.52\) | \(\:0.70\) | \(\:0.73\) | \(\:0.21\) | \(\:0.29\) | \(\:0.37\) | \(\:0.49\) | \(\:0.76\) | \(\:0.78\) | \(\:0.17\) | \(\:0.25\) | \(\:0.21\) | \(\:0.29\) | \(\:0.87\) | \(\:0.88\) | \(\:0.16\) | \(\:0.21\) |
\(\:{\varvec{A}}_{3}\) | \(\:0.38\) | \(\:0.50\) | \(\:0.71\) | \(\:0.73\) | \(\:0.21\) | \(\:0.28\) | \(\:0.28\) | \(\:0.38\) | \(\:0.79\) | \(\:0.81\) | \(\:0.19\) | \(\:0.25\) | \(\:0.29\) | \(\:0.39\) | \(\:0.84\) | \(\:0.86\) | \(\:0.14\) | \(\:0.21\) |
\(\:{\varvec{A}}_{4}\) | \(\:0.38\) | \(\:0.50\) | \(\:0.71\) | \(\:0.73\) | \(\:0.21\) | \(\:0.28\) | \(\:0.38\) | \(\:0.48\) | \(\:0.76\) | \(\:0.78\) | \(\:0.17\) | \(\:0.25\) | \(\:0.26\) | \(\:0.35\) | \(\:0.85\) | \(\:0.87\) | \(\:0.15\) | \(\:0.21\) |
\(\:{\varvec{A}}_{5}\) | \(\:0.33\) | \(\:0.45\) | \(\:0.73\) | \(\:0.75\) | \(\:0.22\) | \(\:0.29\) | \(\:0.35\) | \(\:0.47\) | \(\:0.77\) | \(\:0.79\) | \(\:0.17\) | \(\:0.26\) | \(\:0.17\) | \(\:0.23\) | \(\:0.89\) | \(\:0.90\) | \(\:0.18\) | \(\:0.22\) |
\(\:{\varvec{A}}_{6}\) | \(\:0.32\) | \(\:0.43\) | \(\:0.74\) | \(\:0.76\) | \(\:0.23\) | \(\:0.30\) | \(\:0.34\) | \(\:0.46\) | \(\:0.77\) | \(\:0.79\) | \(\:0.17\) | \(\:0.25\) | \(\:0.27\) | \(\:0.37\) | \(\:0.85\) | \(\:0.86\) | \(\:0.14\) | \(\:0.21\) |
\(\:{\varvec{A}}_{7}\) | \(\:0.35\) | \(\:0.47\) | \(\:0.73\) | \(\:0.75\) | \(\:0.23\) | \(\:0.30\) | \(\:0.26\) | \(\:0.35\) | \(\:0.80\) | \(\:0.82\) | \(\:0.20\) | \(\:0.26\) | \(\:0.29\) | \(\:0.39\) | \(\:0.84\) | \(\:0.86\) | \(\:0.14\) | \(\:0.21\) |
\(\:{\varvec{A}}_{8}\) | \(\:0.28\) | \(\:0.38\) | \(\:0.76\) | \(\:0.78\) | \(\:0.26\) | \(\:0.32\) | \(\:0.31\) | \(\:0.42\) | \(\:0.78\) | \(\:0.80\) | \(\:0.19\) | \(\:0.26\) | \(\:0.25\) | \(\:0.34\) | \(\:0.86\) | \(\:0.87\) | \(\:0.15\) | \(\:0.21\) |
\(\:{\varvec{A}}_{9}\) | \(\:0.22\) | \(\:0.31\) | \(\:0.79\) | \(\:0.81\) | \(\:0.29\) | \(\:0.34\) | \(\:0.30\) | \(\:0.41\) | \(\:0.79\) | \(\:0.81\) | \(\:0.19\) | \(\:0.26\) | \(\:0.25\) | \(\:0.34\) | \(\:0.86\) | \(\:0.87\) | \(\:0.15\) | \(\:0.21\) |
\(\:{\varvec{A}}_{10}\) | \(\:0.35\) | \(\:0.47\) | \(\:0.73\) | \(\:0.75\) | \(\:0.23\) | \(\:0.30\) | \(\:0.28\) | \(\:0.38\) | \(\:0.80\) | \(\:0.82\) | \(\:0.21\) | \(\:0.27\) | \(\:0.21\) | \(\:0.29\) | \(\:0.87\) | \(\:0.88\) | \(\:0.16\) | \(\:0.21\) |
\(\:\varvec{m}\varvec{a}\varvec{x}\) | \(\:0.39\) | \(\:0.52\) | \(\:0.79\) | \(\:0.81\) | \(\:0.29\) | \(\:0.34\) | \(\:0.38\) | \(\:0.49\) | \(\:0.80\) | \(\:0.82\) | \(\:0.21\) | \(\:0.27\) | \(\:0.29\) | \(\:0.39\) | \(\:0.89\) | \(\:0.90\) | \(\:0.18\) | \(\:0.22\) |
\(\:\varvec{m}\varvec{i}\varvec{n}\) | \(\:0.22\) | \(\:0.31\) | \(\:0.70\) | \(\:0.73\) | \(\:0.21\) | \(\:0.28\) | \(\:0.26\) | \(\:0.35\) | \(\:0.76\) | \(\:0.78\) | \(\:0.17\) | \(\:0.25\) | \(\:0.17\) | \(\:0.23\) | \(\:0.84\) | \(\:0.86\) | \(\:0.14\) | \(\:0.21\) |
\(\:{\varvec{C}}_{4}\) | \(\:{\varvec{C}}_{5}\) | \(\:{\varvec{C}}_{6}\) | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\:{\mathfrak{m}}^{\varvec{l}}\) | \(\:{\mathfrak{m}}^{\varvec{u}}\) | \(\:{\mathfrak{n}}^{\varvec{l}}\) | \(\:{\mathfrak{n}}^{\varvec{u}}\) | \(\:{\mathcal{a}}^{\varvec{l}}\) | \(\:{\mathcal{a}}^{\varvec{u}}\) | \(\:{\mathfrak{m}}^{\varvec{l}}\) | \(\:{\mathfrak{m}}^{\varvec{u}}\) | \(\:{\mathfrak{n}}^{\varvec{l}}\) | \(\:{\mathfrak{n}}^{\varvec{u}}\) | \(\:{\mathcal{a}}^{\varvec{l}}\) | \(\:{\mathcal{a}}^{\varvec{u}}\) | \(\:{\mathfrak{m}}^{\varvec{l}}\) | \(\:{\mathfrak{m}}^{\varvec{u}}\) | \(\:{\mathfrak{n}}^{\varvec{l}}\) | \(\:{\mathfrak{n}}^{\varvec{u}}\) | \(\:{\mathcal{a}}^{\varvec{l}}\) | \(\:{\mathcal{a}}^{\varvec{u}}\) | |
\(\:{\varvec{A}}_{1}\) | \(\:0.42\) | \(\:0.55\) | \(\:0.56\) | \(\:0.59\) | \(\:0.30\) | \(\:0.36\) | \(\:0.42\) | \(\:0.56\) | \(\:0.47\) | \(\:0.50\) | \(\:0.37\) | \(\:0.42\) | \(\:0.26\) | \(\:0.36\) | \(\:0.82\) | \(\:0.83\) | \(\:0.18\) | \(\:0.24\) |
\(\:{\varvec{A}}_{2}\) | \(\:0.42\) | \(\:0.55\) | \(\:0.56\) | \(\:0.59\) | \(\:0.30\) | \(\:0.36\) | \(\:0.62\) | \(\:0.78\) | \(\:0.37\) | \(\:0.41\) | \(\:0.28\) | \(\:0.33\) | \(\:0.29\) | \(\:0.40\) | \(\:0.81\) | \(\:0.82\) | \(\:0.18\) | \(\:0.25\) |
\(\:{\varvec{A}}_{3}\) | \(\:0.53\) | \(\:0.68\) | \(\:0.50\) | \(\:0.53\) | \(\:0.25\) | \(\:0.33\) | \(\:0.55\) | \(\:0.70\) | \(\:0.40\) | \(\:0.43\) | \(\:0.31\) | \(\:0.36\) | \(\:0.29\) | \(\:0.39\) | \(\:0.81\) | \(\:0.83\) | \(\:0.18\) | \(\:0.24\) |
\(\:{\varvec{A}}_{4}\) | \(\:0.56\) | \(\:0.71\) | \(\:0.48\) | \(\:0.53\) | \(\:0.24\) | \(\:0.32\) | \(\:0.58\) | \(\:0.72\) | \(\:0.39\) | \(\:0.42\) | \(\:0.29\) | \(\:0.35\) | \(\:0.35\) | \(\:0.46\) | \(\:0.78\) | \(\:0.80\) | \(\:0.16\) | \(\:0.24\) |
\(\:{\varvec{A}}_{5}\) | \(\:0.49\) | \(\:0.64\) | \(\:0.53\) | \(\:0.56\) | \(\:0.27\) | \(\:0.35\) | \(\:0.64\) | \(\:0.80\) | \(\:0.35\) | \(\:0.40\) | \(\:0.26\) | \(\:0.32\) | \(\:0.29\) | \(\:0.39\) | \(\:0.81\) | \(\:0.83\) | \(\:0.18\) | \(\:0.24\) |
\(\:{\varvec{A}}_{6}\) | \(\:0.56\) | \(\:0.71\) | \(\:0.48\) | \(\:0.53\) | \(\:0.24\) | \(\:0.32\) | \(\:0.61\) | \(\:0.77\) | \(\:0.37\) | \(\:0.41\) | \(\:0.28\) | \(\:0.33\) | \(\:0.32\) | \(\:0.43\) | \(\:0.79\) | \(\:0.81\) | \(\:0.16\) | \(\:0.24\) |
\(\:{\varvec{A}}_{7}\) | \(\:0.53\) | \(\:0.68\) | \(\:0.50\) | \(\:0.53\) | \(\:0.25\) | \(\:0.33\) | \(\:0.59\) | \(\:0.74\) | \(\:0.39\) | \(\:0.42\) | \(\:0.29\) | \(\:0.35\) | \(\:0.26\) | \(\:0.36\) | \(\:0.82\) | \(\:0.83\) | \(\:0.18\) | \(\:0.24\) |
\(\:{\varvec{A}}_{8}\) | \(\:0.42\) | \(\:0.55\) | \(\:0.56\) | \(\:0.59\) | \(\:0.30\) | \(\:0.36\) | \(\:0.58\) | \(\:0.72\) | \(\:0.39\) | \(\:0.42\) | \(\:0.29\) | \(\:0.35\) | \(\:0.29\) | \(\:0.40\) | \(\:0.81\) | \(\:0.82\) | \(\:0.18\) | \(\:0.25\) |
\(\:{\varvec{A}}_{9}\) | \(\:0.45\) | \(\:0.59\) | \(\:0.54\) | \(\:0.57\) | \(\:0.29\) | \(\:0.35\) | \(\:0.55\) | \(\:0.70\) | \(\:0.40\) | \(\:0.43\) | \(\:0.31\) | \(\:0.36\) | \(\:0.31\) | \(\:0.42\) | \(\:0.80\) | \(\:0.83\) | \(\:0.18\) | \(\:0.25\) |
\(\:{\varvec{A}}_{10}\) | \(\:0.45\) | \(\:0.59\) | \(\:0.54\) | \(\:0.57\) | \(\:0.29\) | \(\:0.35\) | \(\:0.59\) | \(\:0.74\) | \(\:0.39\) | \(\:0.42\) | \(\:0.29\) | \(\:0.35\) | \(\:0.28\) | \(\:0.38\) | \(\:0.82\) | \(\:0.84\) | \(\:0.19\) | \(\:0.26\) |
\(\:\varvec{m}\varvec{a}\varvec{x}\) | \(\:0.56\) | \(\:0.71\) | \(\:0.56\) | \(\:0.59\) | \(\:0.30\) | \(\:0.36\) | \(\:0.64\) | \(\:0.80\) | \(\:0.47\) | \(\:0.50\) | \(\:0.37\) | \(\:0.42\) | \(\:0.35\) | \(\:0.46\) | \(\:0.82\) | \(\:0.84\) | \(\:0.19\) | \(\:0.26\) |
\(\:\varvec{m}\varvec{i}\varvec{n}\) | \(\:0.42\) | \(\:0.55\) | \(\:0.48\) | \(\:0.53\) | \(\:0.24\) | \(\:0.32\) | \(\:0.42\) | \(\:0.56\) | \(\:0.35\) | \(\:0.40\) | \(\:0.26\) | \(\:0.32\) | \(\:0.26\) | \(\:0.36\) | \(\:0.78\) | \(\:0.80\) | \(\:0.16\) | \(\:0.24\) |
\(\:{\varvec{C}}_{7}\) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\:{\mathfrak{m}}^{\varvec{l}}\) | \(\:{\mathfrak{m}}^{\varvec{u}}\) | \(\:{\mathfrak{n}}^{\varvec{l}}\) | \(\:{\mathfrak{n}}^{\varvec{u}}\) | \(\:{\mathcal{a}}^{\varvec{l}}\) | \(\:{\mathcal{a}}^{\varvec{u}}\) | |||||||||||||
\(\:{\varvec{A}}_{1}\) | \(\:0.39\) | \(\:0.52\) | \(\:0.61\) | \(\:0.63\) | \(\:0.28\) | \(\:0.35\) | ||||||||||||
\(\:{\varvec{A}}_{2}\) | \(\:0.46\) | \(\:0.60\) | \(\:0.58\) | \(\:0.61\) | \(\:0.26\) | \(\:0.33\) | ||||||||||||
\(\:{\varvec{A}}_{3}\) | \(\:0.50\) | \(\:0.64\) | \(\:0.55\) | \(\:0.58\) | \(\:0.24\) | \(\:0.32\) | ||||||||||||
\(\:{\varvec{A}}_{4}\) | \(\:0.50\) | \(\:0.64\) | \(\:0.55\) | \(\:0.58\) | \(\:0.24\) | \(\:0.32\) | ||||||||||||
\(\:{\varvec{A}}_{5}\) | \(\:0.43\) | \(\:0.57\) | \(\:0.59\) | \(\:0.62\) | \(\:0.27\) | \(\:0.34\) | ||||||||||||
\(\:{\varvec{A}}_{6}\) | \(\:0.46\) | \(\:0.60\) | \(\:0.57\) | \(\:0.59\) | \(\:0.25\) | \(\:0.32\) | ||||||||||||
\(\:{\varvec{A}}_{7}\) | \(\:0.44\) | \(\:0.57\) | \(\:0.58\) | \(\:0.61\) | \(\:0.26\) | \(\:0.33\) | ||||||||||||
\(\:{\varvec{A}}_{8}\) | \(\:0.42\) | \(\:0.55\) | \(\:0.59\) | \(\:0.62\) | \(\:0.27\) | \(\:0.34\) | ||||||||||||
\(\:{\varvec{A}}_{9}\) | \(\:0.50\) | \(\:0.64\) | \(\:0.55\) | \(\:0.58\) | \(\:0.24\) | \(\:0.32\) | ||||||||||||
\(\:{\varvec{A}}_{10}\) | \(\:0.39\) | \(\:0.52\) | \(\:0.61\) | \(\:0.63\) | \(\:0.28\) | \(\:0.35\) | ||||||||||||
\(\:\varvec{m}\varvec{a}\varvec{x}\) | \(\:0.50\) | \(\:0.64\) | \(\:0.61\) | \(\:0.63\) | \(\:0.28\) | \(\:0.35\) | ||||||||||||
\(\:\varvec{m}\varvec{i}\varvec{n}\) | \(\:0.39\) | \(\:0.52\) | \(\:0.55\) | \(\:0.58\) | \(\:0.24\) | \(\:0.32\) | ||||||||||||
