Table 13 Sensitivity score values and ranking.

From: WASPAS-based multi-expert decision algorithm for physical education using circular pythagorean fuzzy aggregation with prioritized weights

\(\:\varvec{\gamma\:}\)

\(\:{\mathcal{A}}_{1}\)

\(\:{\mathcal{A}}_{2}\)

\(\:{\mathcal{A}}_{3}\)

\(\:{\mathcal{A}}_{4}\)

\(\:{\mathcal{A}}_{5}\)

Ranking

\(\:{\varvec{\gamma\:}}_{1}=0.1\)

0.4741

0.4945

0.4347

0.4963

0.2648

\(\:{\mathcal{A}}_{4}>{\mathcal{A}}_{2}>{\mathcal{A}}_{1}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{2}=0.2\)

0.4833

0.5197

0.4670

0.5182

0.3006

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{3}=0.3\)

0.4923

0.5430

0.4967

0.5386

0.3343

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{4}=0.4\)

0.5101

0.5644

0.5241

0.5575

0.3661

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{5}=0.5\)

0.5094

0.5843

0.5493

0.5752

0.3962

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{6}=0.6\)

0.5176

0.6027

0.5726

0.5918

0.4245

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{7}=0.7\)

0.5255

0.6199

0.5942

0.6073

0.4514

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{8}=0.8\)

0.5332

0.6358

0.6142

0.6218

0.4767

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{5}\)

\(\:{\varvec{\gamma\:}}_{9}=0.9\)

0.5407

0.6508

0.6329

0.6355

0.5008

\(\:{\mathcal{A}}_{2}>{\mathcal{A}}_{4}>{\mathcal{A}}_{3}\:>{\mathcal{A}}_{1}\:>{\mathcal{A}}_{5}\)