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Table 7 Effect of the parameters \(p\) and \(\lambda\) on the ranking order for the pattern recognition problem

From: Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

Values of \(p\) and \(\lambda\)

Generalized chordal distance

Non-Archimedean chordal distance

\(\left( {P_{1} ,Q} \right)\)

\(\left( {P_{2} ,Q} \right)\)

\(\left( {P_{3} ,Q} \right)\)

\(\left( {P_{1} ,Q} \right)\)

\(\left( {P_{2} ,Q} \right)\)

\(\left( {P_{3} ,Q} \right)\)

p = 1

\(\lambda = 0\)

0.5101

0.2469

0.5172

0.5162

0.3976

0.5312

\(\lambda = 0.4\)

0.3605

0.2141

0.3722

\(\lambda = 0.6\)

0.1624

0.0667

0.1703

\(\lambda = 0.8\)

0.1422

0.0472

0.1510

\(\lambda = 1\)

0.1187

0.0266

0.1275

Ranking

\(P_{2} < P_{1} < P_{3}\)

\(P_{2} < P_{1} < P_{3}\)

p = 2

\(\lambda = 0\)

0.8527

0.5334

0.8649

0.5374

0.4272

0.5431

\(\lambda = 0.4\)

0.4642

0.2973

0.4723

\(\lambda = 0.6\)

0.1628

0.1042

0.1718

\(\lambda = 0.8\)

0.1478

0.0529

0.1619

\(\lambda = 1\)

0.1214

0.0482

0.1362

Ranking

\(P_{2} < P_{1} < P_{3}\)

\(P_{2} < P_{1} < P_{3}\)

p = 5

\(\lambda = 0\)

0.8755

0.5773

0.8799

0.5441

0.4363

0.5662

\(\lambda = 0.4\)

0.4770

0.3009

0.4846

\(\lambda = 0.6\)

0.1739

0.1124

0.1826

\(\lambda = 0.8\)

0.1581

0.0606

0.1685

\(\lambda = 1\)

0.1313

0.0584

0.1445

Ranking

\(P_{2} < P_{1} < P_{3}\)

\(P_{2} < P_{1} < P_{3}\)

p = 10

\(\lambda = 0\)

0.8932

0.6077

0.9038

0.5526

0.4423

0.5692

\(\lambda = 0.4\)

0.4876

0.3135

0.4962

\(\lambda = 0.6\)

0.1861

0.1352

0.1947

\(\lambda = 0.8\)

0.1621

0.0771

0.1742

\(\lambda = 1\)

0.1444

0.0609

0.1589

Ranking

\(P_{2} < P_{1} < P_{3}\)

\(P_{2} < P_{1} < P_{3}\)

p = 50

\(\lambda = 0\)

0.9210

0.6679

0.9442

0.5692

0.4649

0.5773

\(\lambda = 0.4\)

0.4946

0.3215

0.5016

\(\lambda = 0.6\)

0.1928

0.1497

0.2040

\(\lambda = 0.8\)

0.1701

0.0808

0.1777

\(\lambda = 1\)

0.1470

0.0737

0.1612

Ranking

\(P_{2} < P_{1} < P_{3}\)

\(P_{2} < P_{1} < P_{3}\)