Table 5 Effects of parameter \({\varvec{q}}\) on decision results using Q-ROFHSEWG operator.

From: Optimizing construction company selection using einstein weighted aggregation operators for q-rung orthopair fuzzy hypersoft set

Parameter

Score value

Ranking

\({\varvec{q}} = 1\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.2232, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.2024, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.0856

\(\aleph^{\left( 3 \right)} > \aleph^{\left( 2 \right)}\) \(>\) \(\aleph^{\left( 1 \right)}\)

\({\varvec{q}} = 2\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.2540, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.2916, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.1626

\(\aleph^{\left( 3 \right)} > \aleph^{\left( 1 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 3\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.2072, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.2963, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.1896

\(\aleph^{\left( 3 \right)} > \aleph^{\left( 1 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 4\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.1567, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.2684, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.1836

\(\aleph^{\left( 1 \right)} > \aleph^{\left( 3 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 5\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.1178, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.2334, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.1654

\(\aleph^{\left( 1 \right)} > \aleph^{\left( 3 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 6\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.0899, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.2006, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.1449

\(\aleph^{\left( 1 \right)} > \aleph^{\left( 3 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 7\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.0699, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.1722, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.1258

\(\aleph^{\left( 1 \right)} > \aleph^{\left( 3 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 8\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.0555, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.1484, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.1091

\(\aleph^{\left( 1 \right)} > \aleph^{\left( 3 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 9\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.0449, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.1286, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.0948

\(\aleph^{\left( 1 \right)} > \aleph^{\left( 3 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)

\({\varvec{q}} = 10\)

\(S\left( {{\mathcal{L}}_{1} } \right)\) = \(-\) 0.0368, \(S\left( {{\mathcal{L}}_{2} } \right)\) = \(-\) 0.1120, \(S\left( {{\mathcal{L}}_{3} } \right)\) = \(-\) 0.0827

\(\aleph^{\left( 1 \right)} > \aleph^{\left( 3 \right)}\) \(>\) \(\aleph^{\left( 2 \right)}\)