Table 9 Ranking results of q-RF2LPDMSM-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

\(\theta =0.0\)

0.00008

0.00002

0.00006

0.00001

0.0001

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

\(\theta =0.1\)

0.01256

0.01141

0.01293

0.01114

0.01427

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

\(\theta =0.2\)

0.02504

0.02279

0.02581

0.02227

0.02844

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

\(\theta =0.3\)

0.03753

0.03418

0.03868

0.03334

0.04261

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

\(\theta =0.4\)

0.05001

0.04557

0.05155

0.04452

0.05678

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

\(\theta =0.5\)

0.06249

0.05696

0.06443

0.05565

0.07095

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

\(\theta =0.6\)

0.07497

0.06835

0.07730

0.06678

0.08512

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

\(\theta =0.7\)

0.08745

0.07973

0.09018

0.07791

0.09290

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

\(\theta =0.8\)

0.09999

0.09112

0.10305

0.08904

0.11346

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

\(\theta =0.9\)

0.11242

0.10251

0.11593

0.10017

0.12760

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

\(\theta =1.0\)

0.12490

0.11390

0.12880

0.11130

0.14180

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

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