Graphs and Questionnaires (eBook)

eBook Download: PDF

1980 | 1. Auflage
430 Seiten
Elsevier Science (Verlag)
978-0-08-087143-1 (ISBN)

Infos

Graphs and Questionnaires

Inhalt

Front Page 1
Grahphs and Questionnaires 4
Copyright Page 5
Contents 10
Preface 6
Preface to the French Edition 7
Chapter I. Fundamental properties of graphs 16
1.1 Ordered pairs and product sets 16
1.2 The graph concept 17
1.3 Elementary operations and transitive closures 23
1.4 Connectivity, equivalence and preorder 26
1.5 Graph representations 32
1.6 Paths, circuits and cocircuits 37
Exercises 41
Chapter II. Latticoids and arborescences 44
2. 1 Circuitless graphs 44
2. 2 Arborescences and trees 48
2. 3 Arborescences and data processing 56
2. 4 Transportation networks 63
Exercises 65
Chapter III. Operations on graphs 66
3.1 General definitions 66
3.2 Unary operations 67
3.3 Transformations 68
3.4 Cartesian operations 73
3.5 Latticoid operations 90
Exercises 92
Chapter IV. General properties of questionnaires 96
4.1 Preliminaries 96
4.2 The concept of a questionnaire 97
4.3 Routing 108
4.4 Probabilities in a latticoid questionnaire 116
4.5 Routing length 126
Exercises 129
Chapter V. The construction of questionnaires 132
5.1 Operations on questionnaires 132
5.2 Valuations on the answers and the arcs 141
5.3 L-optimal supports 145
5.4 Properties of arborescent questionnaires 152
Exercises 162
Chapter VI. Optimal routing 164
6.1 Determination of an L-optimal questionnaire 164
6.2 Necessary conditions for L-optimality 164
6.3 A sufficient condition for L-optimality 170
6.4 Huffman's algorithm 172
6.5 Questionnaires and coding 177
6.6 Equiprobable polychotomic questionnaires 180
Exercises 187
Chapter VII. Informational study of questionnaires 190
7.1 Introduction to information 190
7.2 Axiomatics of information 197
7.3 Properties of information 206
7.4 Processed information and transmitted information 216
7.5 Other definitions of information 222
Exercises 230
Chapter VIII. Information and routing length 232
8.1 Information and routing in questionnaires 232
8.2 Contribution of information 256
8.3 Quasi-questionnaires 267
Exercises 282
Chapter IX. Conditioning of the questions and answers 284
9.1 Limitations and extensions 284
9.2 Utilities of the answers 284
9.3 Cost of the questions 290
9.4 Questionnaires in the sense of Campbell 299
9.5 Questionnaires in the broad sense 303
9.6 Realizable questionnaires 309
9.7 Questionnaires in practice 321
Chapter X. Interrogations, comparisons, sortings 328
10.1 Indirect interrogations and pseudo-questionnaires 328
10.2 Comparisons and questions 340
10.3 Questionnaires €or sorting 348
Problems 358
Solutions to Problems 370
Tables 412
Bibliography 416
Index 436
Main Symbols 444

Produkt-Details

• Erscheint lt. Verlag: 1.1.1980
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-087143-7 / 0080871437
• ISBN-13: 978-0-08-087143-1 / 9780080871431