Table 8 Ranking results of q-RF2LPMSM-based WASPAS with varying \(\theta \) values.

From: q-Rung orthopair fuzzy 2-tuple linguistic WASPAS algorithm for patients’ prioritization based on prioritized Maclaurin symmetric mean aggregation operators

\(\theta \)

\({{\text{\Shilling}}}_1\)

\({{\text{\Shilling}}}_2\)

\({{\text{\Shilling}}}_3\)

\({{\text{\Shilling}}}_4\)

\({{\text{\Shilling}}}_5\)

Ranking relation

\(\theta =0.0\)

0.00555

0.00469

0.00597

0.00450

0.00715

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.1\)

0.01996

0.01849

0.02042

0.01824

0.02224

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.2\)

0.03437

0.03229

0.03488

0.03198

0.03733

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.3\)

0.04878

0.04610

0.04933

0.04571

0.05242

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.4\)

0.06319

0.05990

0.06378

0.05942

0.06751

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.5\)

0.07660

0.07370

0.07820

0.07320

0.08259

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.6\)

0.09201

0.08750

0.09269

0.08693

0.09769

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.7\)

0.10642

0.10131

0.10714

0.10067

0.11277

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.8\)

0.12083

0.11511

0.12159

0.11440

0.12787

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =0.9\)

0.13524

0.12891

0.13604

0.12814

0.14296

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)

\(\theta =1.0\)

0.14965

0.14271

0.15050

0.14188

0.15804

\({{\text{\Shilling}}}_5>{{\text{\Shilling}}}_3>{{\text{\Shilling}}}_1>{{\text{\Shilling}}}_2>{{\text{\Shilling}}}_4\)