Fuzzy mathematics in economics and engineering: with 27 tables
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Heidelberg ; New York
Physica-Verl.
2002
|
| Schriftenreihe: | Studies in fuzziness and soft computing
91 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009638418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 272 S. graph. Darst. |
| ISBN: | 3790814563 |
Internformat
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| 264 | 1 | |a Heidelberg ; New York |b Physica-Verl. |c 2002 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 Introduction 1
Bibliography 3
2 Fuzzy Sets 5
2.1 Fuzzy Sets 5
2.1.1 Fuzzy Numbers 5
2.1.2 Alpha Cuts 7
2.1.3 Inequalities 9
2.1.4 Discrete Fuzzy Sets 9
2.2 Fuzzy Arithmetic 9
2.2.1 Extension Principle 9
2.2.2 Interval Arithmetic 10
2.2.3 Fuzzy Arithmetic 11
2.3 Fuzzy Functions 12
2.3.1 Extension Principle 13
2.3.2 Alpha Cuts and Interval Arithmetic 13
2.3.3 Differences 14
2.4 Possibility Theory 15
Bibliography 17
3 Solving Fuzzy Equations 19
3.1 Il + B=C 19
3.2 New Solutions 22
3.3 Systems of Fuzzy Linear Equations 24
3.4 Applications 33
3.4.1 Fuzzy Linear Equation 33
3.4.2 Fuzzy Quadratic Equation 34
3.4.3 System of Linear Equations 35
3.5 Fuzzy Input Output Analysis 39
3.5.1 The Open Model 39
3.5.2 Fuzzy Model 41
3.6 Summary and Conclusions 43
Bibliography 45
viii CONTENTS
4 Fuzzy Mathematics in Finance 47
4.1 Future Value 48
4.2 Present Value 50
4.3 Annuities 53
4.3.1 Future Value 53
4.3.2 Present Value 54
4.4 Portfolio Analysis 55
4.4.1 NPV Method 55
4.4.2 IRR Method 59
4.5 Summary and Conclusions 62
Bibliography 65
5 Fuzzy Non—Linear Regression 69
5.1 Univariate Non Linear Fuzzy Regression 70
5.1.1 Testing the EA 71
5.1.2 Application 72
5.2 Multivariate Non Linear Fuzzy Regression 74
5.2.1 Testing 75
5.2.2 Application 75
5.3 Conclusions and Results 76
Bibliography 77
6 Operations Research 81
6.1 Fuzzy Linear Programming 81
6.1.1 Maximize Z 82
6.1.2 Fuzzy Inequality 85
6.1.3 Evolutionary Algorithm 88
6.1.4 Applications 89
6.1.5 Summary and Conclusions 97
6.2 Fuzzy PERT 98
6.2.1 Job Times Fuzzy Numbers 102
6.2.2 Job Times Discrete Fuzzy Sets 104
6.2.3 Summary 104
6.3 Fuzzy Inventory Control 105
6.3.1 Demand Not Fuzzy 109
6.3.2 Fuzzy Demand Ill
6.3.3 Backorders 117
6.3.4 Evolutionary Algorithm 118
6.4 Fuzzy Queuing Theory 118
6.4.1 Service 120
6.4.2 Arrivals 121
6.4.3 Finite or Infinite System Capacity 122
6.4.4 Machine Servicing Problem 124
6.4.5 Fuzzy Queuing Decision Problem 126
6.4.6 Summary and Conclusions 129
CONTENTS ix
6.5 Fuzzy Network Analysis 129
6.5.1 Fuzzy Shortest Route 130
6.5.2 Fuzzy Min Cost Capacitated Network 132
6.5.3 Evolutionary Algorithm 136
6.5.4 Summary and Conclusions 137
6.6 Summary and Conclusions 137
Bibliography 139
7 Fuzzy Differential Equations 145
7.1 Fuzzy Initial Conditions 146
7.1.1 Electrical Circuit 150
7.1.2 Vibrating Mass 153
7.1.3 Dynamic Supply and Demand 155
7.2 Other Fuzzy Parameters 158
7.3 Summary and Conclusions 161
Bibliography 163
8 Fuzzy Difference Equations 165
8.1 Difference Equations 166
8.2 Fuzzy Initial Conditions 167
8.2.1 Classical Solution 167
8.2.2 Extension Principle Solution 169
8.2.3 Interval Arithmetic Solution 172
8.2.4 Summary 174
8.3 Recursive Solutions 175
8.4 Applications 176
8.4.1 National Income 176
8.4.2 Transmission of Information 178
8.4.3 Fuzzy Fibonacci Numbers 179
8.5 Summary and Conclusions . , 180
Bibliography 183
9 Fuzzy Partial Differential Equations 185
9.1 Elementary Partial Differential Equations 185
9.2 Classical Solution 187
9.3 Extension Principle Solution 190
9.4 Summary and Conclusions 194
Bibliography 197
10 Fuzzy Eigenvalues 199
10.1 Fuzzy Eigenvalue Problem 199
10.1.1 Algorithm 203
10.2 Fuzzy Input Output Analysis 206
10.3 Fuzzy Hierarchical Analysis 209
10.3.1 The Amax Method 210
x CONTENTS
10.3.2 Fuzzy Amax Method 212
10.3.3 Fuzzy Geometric Row Mean Method 222
10.4 Summary and Conclusions 224
Bibliography 227
11 Fuzzy Integral Equations 229
11.1 Resolvent Kernel Method 230
11.1.1 Classical Solution 231
11.1.2 Second Solution Method 235
11.2 Symmetric Kernel Method 237
11.2.1 Classical Solution 237
11.2.2 Second Solution Method 239
11.3 Summary and Conclusions 240
Bibliography 241
12 Summary and Conclusions 243
12.1 Summary 243
12.1.1 Chapter 3: Solving Fuzzy Equations 243
12.1.2 Chapter 4: The Fuzzy Mathematics in Finance .... 244
12.1.3 Chapter 5: Fuzzy Non Linear Regression 244
12.1.4 Chapter 6: Operations Research 245
12.1.5 Chapter 7: Fuzzy Differential Equations 247
12.1.6 Chapter 8: The Fuzzy Difference Equations 248
12.1.7 Chapter 9: Fuzzy Partial Differential Equations .... 248
12.1.8 Chapter 10: Fuzzy Eigenvalues 249
12.1.9 Chapter 11: Fuzzy Integral Equations 249
12.2 Research Agenda 250
12.2.1 Chapter 3: Solving Fuzzy Equations 250
12.2.2 Chapter 4: The Fuzzy Mathematics of Finance .... 250
12.2.3 Chapter 5: Fuzzy Non Linear Regression 250
12.2.4 Chapter 6: Operations Research 250
12.2.5 Chapter 7: Fuzzy Differential Equations 251
12.2.6 Chapter 8: Fuzzy Difference Equations 252
12.2.7 Chapter 9: Fuzzy Partial Differential Equations .... 252
12.2.8 Chapter 10: Fuzzy Eigenvalues 252
12.2.9 Chapter 11: Fuzzy Integral Equations 252
12.3 Conclusions 252
13 Evolutionary Algorithms 253
13.1 Introduction 253
13.2 General Purpose Algorithm 253
Bibliography 257
Index 259
CONTENTS xi
List of Figures 267
List of Tables 271
|
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| id | DE-604.BV014072251 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:58:39Z |
| institution | BVB |
| isbn | 3790814563 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009638418 |
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| series | Studies in fuzziness and soft computing |
| series2 | Studies in fuzziness and soft computing |
| spellingShingle | Buckley, James J. 1936- Eslami, Esfandiar 1954- Feuring, Thomas 1964- Fuzzy mathematics in economics and engineering with 27 tables Studies in fuzziness and soft computing Fuzzy sets Fuzzy mathematics Econometrics Engineering mathematics Fuzzy-Menge (DE-588)4061868-7 gnd Integralgleichung (DE-588)4027229-1 gnd Finanzmathematik (DE-588)4017195-4 gnd Operations Research (DE-588)4043586-6 gnd Differentialgleichung (DE-588)4012249-9 gnd Evolutionärer Algorithmus (DE-588)4366912-8 gnd Lineare Gleichung (DE-588)4234490-6 gnd |
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| title | Fuzzy mathematics in economics and engineering with 27 tables |
| title_auth | Fuzzy mathematics in economics and engineering with 27 tables |
| title_exact_search | Fuzzy mathematics in economics and engineering with 27 tables |
| title_full | Fuzzy mathematics in economics and engineering with 27 tables James J. Buckley ; Esfandiar Eslami ; Thomas Feuring |
| title_fullStr | Fuzzy mathematics in economics and engineering with 27 tables James J. Buckley ; Esfandiar Eslami ; Thomas Feuring |
| title_full_unstemmed | Fuzzy mathematics in economics and engineering with 27 tables James J. Buckley ; Esfandiar Eslami ; Thomas Feuring |
| title_short | Fuzzy mathematics in economics and engineering |
| title_sort | fuzzy mathematics in economics and engineering with 27 tables |
| title_sub | with 27 tables |
| topic | Fuzzy sets Fuzzy mathematics Econometrics Engineering mathematics Fuzzy-Menge (DE-588)4061868-7 gnd Integralgleichung (DE-588)4027229-1 gnd Finanzmathematik (DE-588)4017195-4 gnd Operations Research (DE-588)4043586-6 gnd Differentialgleichung (DE-588)4012249-9 gnd Evolutionärer Algorithmus (DE-588)4366912-8 gnd Lineare Gleichung (DE-588)4234490-6 gnd |
| topic_facet | Fuzzy sets Fuzzy mathematics Econometrics Engineering mathematics Fuzzy-Menge Integralgleichung Finanzmathematik Operations Research Differentialgleichung Evolutionärer Algorithmus Lineare Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009638418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021858135 |
| work_keys_str_mv | AT buckleyjamesj fuzzymathematicsineconomicsandengineeringwith27tables AT eslamiesfandiar fuzzymathematicsineconomicsandengineeringwith27tables AT feuringthomas fuzzymathematicsineconomicsandengineeringwith27tables |