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Two-Stage Composition of Probabilistic Preferences

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Abstract

A strategy of multicriteria decision aid in which initial acceptance of all the alternatives is followed by an automatic classification of them is here proposed. This classification is used in the next step to limit to the alternatives in the upper class the comparisons employed to choose the best alternative. A procedure to perform the classification through successive divisions is proposed. It is also studied the replacement, in the calculation of the preference score according to each criterion, which is a central step in the Composition of Probabilistic Preferences, of the probability of being preferable simultaneously to all alternatives by the average of the probabilities of being preferable to each one. Another development brought is the calculation of preference probabilities based on empirical cumulative distributions, derived from the observed preference counts. Procedures for effectively bringing to practice each of these proposals are presented and the results of applying them to different practical situations are discussed.

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Funding

Funding was provided by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior.

Author information

Authors and Affiliations

  1. Engineering School, Fluminense Federal University, Passo da Patria St., 156, Niterói, RJ, 24210-240, Brazil

    Annibal Parracho Sant’Anna & Gilson Brito Alves Lima

  2. Votorantim Energia, Av. das Nações Unidas, 8501, São Paulo, SP, 05425-070, Brazil

    Leonardo Augusto da Fonseca Parracho Sant’Anna

  3. Brazilian War College, Fortaleza de São João, Av. João Luiz Alves s/n, Rio de Janeiro, RJ, 22291-090, Brazil

    Luiz Octávio Gavião

Authors
  1. Annibal Parracho Sant’Anna
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  2. Gilson Brito Alves Lima
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  3. Leonardo Augusto da Fonseca Parracho Sant’Anna
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  4. Luiz Octávio Gavião
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Corresponding author

Correspondence to Annibal Parracho Sant’Anna.

Appendices

Appendix A: Evaluations of 20 Modes of Failure by 30 Experts

See Tables 19, 20 and 21.

Table 19 Evaluations by the criterion of severity
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Table 20 Evaluations by the criterion of occurrence
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Table 21 Evaluations by the criterion of detectability
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Appendix B: Evaluations of 14 Techniques by 23 Experts

See Tables 22, 23 and 24.

Table 22 Evaluations by the criterion of efficiency
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Table 23 Evaluations by the criterion of efficacy
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Table 24 Evaluations by the criterion of complexity
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Appendix C: Evaluations of 80 Plants

Plant

I. P.

A. E.

Tariff

Inflow

I. P.

A. E.

Tariff

Inflow

Itumbiara

2082

1015

3.264

0.646

0.667

0.597

0.548

0.663

G. B. Munhoz

1676

576

2.641

1.536

0.601

0.481

0.571

0.658

S. Simao

1608

1281

3.175

0.421

0.59

0.667

0.551

0.665

Jupia

1551

886

2.709

0.158

0.58

0.563

0.569

0.667

Porto Primavera

1540

1017

2.873

0.140

0.579

0.597

0.563

0.667

Ita

1450

720

2.929

0.952

0.564

0.519

0.561

0.661

Marimbondo

1440

726

2.886

0.540

0.562

0.521

0.562

0.664

Salto Santiago

1420

723

3.034

1.005

0.559

0.52

0.557

0.661

Agua Vermelha

1396

746

2.678

0.478

0.555

0.526

0.570

0.664

Salto Segredo

1260

603

2.931

1.181

0.533

0.488

0.560

0.660

Salto Caxias

1240

605

3.169

0.747

0.53

0.489

0.552

0.663

Furnas

1216

598

2.033

1.080

0.526

0.487

0.594

0.661

Machadinho

1140

529

2.762

1.342

0.514

0.469

0.567

0.659

Emborcacao

1136

497

3.022

2.066

0.513

0.46

0.557

0.654

Salto Osorio

1078

522

2.573

0.959

0.504

0.467

0.574

0.661

Henry Borden

889

108

1.261

25.343

0.473

0.358

0.624

0.503

Campos Novos

880

378

2.44

3.272

0.472

0.429

0.579

0.646

Barra Grande

690

381

2.533

3.369

0.441

0.43

0.576

0.646

Cachoeira Dourada

658

415

3.646

0.615

0.436

0.439

0.533

0.664

Capivara

640

330

2.734

0.924

0.433

0.416

0.568

0.662

Taquarucu

554

201

2.67

0.874

0.419

0.383

0.570

0.662

Nova Ponte

510

276

2.833

3.344

0.412

0.402

0.564

0.646

Itauba

500

190

2.248

3.842

0.41

0.38

0.586

0.643

Mascarenhas Moraes

476

295

2.203

0.967

0.406

0.407

0.588

0.661

Jaguara

448

336

2.365

0.935

0.401

0.418

0.582

0.661

Chavantes

414

172

1.457

2.935

0.396

0.375

0.616

0.648

Miranda

390

202

2.976

2.877

0.392

0.383

0.559

0.649

Volta Grande

380

229

2.575

0.858

0.39

0.39

0.574

0.662

Nilo Pecanha

380

335

1.348

8.010

0.39

0.418

0.620

0.615

Corumba I

375

209

3.284

2.208

0.39

0.385

0.547

0.653

Rosana

372

177

1.977

0.777

0.389

0.376

0.597

0.663

N. Avanhandava

347

139

2.472

1.404

0.385

0.366

0.578

0.658

Porto Colombia

320

185

1.995

0.755

0.381

0.378

0.596

0.663

Promissao

264

104

2.389

1.503

0.372

0.357

0.581

0.658

G. Parigot Souza

252

109

1.168

51.327

0.37

0.358

0.627

0.333

Capim Branco II

240

131

3.297

2.704

0.368

0.364

0.547

0.650

Funil RJ

222

121

1.443

4.385

0.365

0.361

0.617

0.639

Igarapava

220

136

2.695

0.909

0.364

0.365

0.569

0.662

Passo Fundo

220

119

1.658

17.703

0.364

0.361

0.609

0.552

Capim Branco I

210

155

3.202

2.822

0.363

0.37

0.550

0.649

Manso

210

92

7.357

5.856

0.363

0.354

0.393

0.629

Funil–MG

180

89

1.625

3.280

0.358

0.353

0.610

0.646

Jacui

180

123

2.126

4.825

0.358

0.362

0.591

0.636

Ponte de Pedra

176

132

8.945

12.924

0.357

0.364

0.333

0.583

Ilha dos Pombos

164

115

1.304

2.258

0.355

0.36

0.622

0.653

Itiquira I e II

157

107

6.273

13.510

0.354

0.358

0.434

0.580

Passo Real

150

68

2.084

4.876

0.353

0.348

0.592

0.636

A. Souza Lima

143

66

1.158

2.215

0.352

0.347

0.627

0.653

Barra Bonita

141

45

1.139

2.499

0.352

0.341

0.628

0.651

Candonga

140

65

1.605

6.450

0.352

0.347

0.611

0.626

Guilman-Amorim

140

66

1.246

12.442

0.352

0.347

0.624

0.587

Fontes

132

104

1.348

31.632

0.35

0.357

0.620

0.462

Ibitinga

131

74

2.26

1.829

0.35

0.349

0.586

0.656

Monte Claro

130

59

1.515

3.705

0.35

0.345

0.614

0.643

Corumba IV

127

76

3.281

7.515

0.349

0.35

0.547

0.619

Dona Francisca

125

78

2.317

3.142

0.349

0.35

0.584

0.647

Masc. Escelsa

123

108

1.276

1.114

0.349

0.358

0.623

0.660

Quebra Queixo

120

59

1.704

12.870

0.348

0.345

0.607

0.584

Santa Clara-PR

117

70

1.851

9.809

0.348

0.348

0.601

0.604

Jauru

110

79

8.354

11.433

0.347

0.35

0.356

0.593

Euclides Cunha

109

49

1.696

11.360

0.346

0.343

0.607

0.594

Pereira Passos

100

51

1.345

6.391

0.345

0.343

0.620

0.626

A. A. Laydner

98

47

0.894

4.503

0.345

0.342

0.637

0.638

Paraibuna

85

50

0.929

14.605

0.343

0.343

0.636

0.572

Canoas I

83

57

1.894

2.081

0.342

0.345

0.600

0.654

Caconde

80

33

1.696

18.587

0.342

0.338

0.607

0.547

Piraju

79

42

1.212

4.402

0.342

0.341

0.625

0.639

Sa Carvalho

78

58

0.12

11.548

0.341

0.345

0.667

0.592

L. N. Garcez

74

55

1.672

2.203

0.341

0.344

0.608

0.653

Canoas II

72

48

1.771

2.164

0.34

0.342

0.604

0.653

Santa Branca

58

32

0.625

12.484

0.338

0.338

0.648

0.586

Rosal

55

30

1.161

30.786

0.338

0.338

0.627

0.467

Itutinga

52

28

1.608

7.527

0.337

0.337

0.610

0.619

Picada

50

27

1.3

27.280

0.337

0.337

0.622

0.490

Camargos

46

21

1.608

7.531

0.336

0.335

0.610

0.619

Sobragi

45

38

1.478

12.697

0.336

0.34

0.615

0.585

Ourinhos

44

24

1.599

2.898

0.336

0.336

0.611

0.649

Espora

32

24

4.672

16.188

0.334

0.336

0.495

0.562

Limoeiro

32

15

1.696

11.190

0.334

0.334

0.607

0.595

Jaguari

28

14

0.885

35.713

0.333

0.333

0.638

0.435

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Sant’Anna, A.P., Lima, G.B.A., Sant’Anna, L.A.d.F.P. et al. Two-Stage Composition of Probabilistic Preferences. Ann. Data. Sci. 7, 491–523 (2020). https://doi.org/10.1007/s40745-018-0177-9

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