Monte Carlo Methods in Fuzzy Optimization

✍ Scribed by James J. Buckley, Leonard J. Jowers

• Publisher: Springer
• Year: 2008
• Tongue: English
• Leaves: 252
• Series: Studies in Fuzziness and Soft Computing
• Category: Library

✦ Synopsis

Monte Carlo Methods in Fuzzy Optimization is a clear and didactic book about Monte Carlo methods using random fuzzy numbers to obtain approximate solutions to fuzzy optimization problems. The book includes various solved problems such as fuzzy linear programming, fuzzy regression, fuzzy inventory control, fuzzy game theory, and fuzzy queuing theory. The book will appeal to engineers, researchers, and students in Fuzziness and applied mathematics.

✦ Table of Contents

cover.jpg......Page 1
front-matter.pdf......Page 2
Part I......Page 14
Part IV......Page 15
Previous Research......Page 16
MATLAB/C++ Programs......Page 17
Fuzzy Sets......Page 19
Fuzzy Numbers......Page 20
Alpha-Cuts......Page 21
Inequalities......Page 22
Extension Principle......Page 23
Interval Arithmetic......Page 24
Fuzzy Arithmetic......Page 25
Extension Principle......Page 26
Differences......Page 27
Min/Max of a Fuzzy Number......Page 28
Buckley's Method......Page 30
Kerre's Method......Page 31
Chen's Method......Page 32
Undominated Fuzzy Vectors......Page 34
Buckley's Method......Page 36
Chen's Method......Page 37
Random Numbers......Page 39
Quasi-random Sequences......Page 40
Random Number Generator......Page 41
Random Vectors: Real Numbers......Page 42
Random Vectors: Non-negative Integers......Page 44
Random Triangular/Trapezoidal Fuzzy Numbers......Page 45
Generated from Implicit Quadratic Functions......Page 46
Generated from Parametric Quadratic Functions, Bézier Fuzzy Numbers......Page 48
Comparison of Random Fuzzy Vectors......Page 50
Random Fuzzy Vectors......Page 51
Run Test......Page 53
Frequency Test......Page 57
Search Space $[a,b]$ for QBGFNs......Page 60
Search Space $\Omega$ for TFNs......Page 62
Other Search Spaces......Page 63
Crisp Linear Program......Page 64
Fuzzy Linear Program......Page 65
Kerre's Method......Page 66
Chen's Method......Page 68
Comparison of Solutions......Page 70
Fully Fuzzified Linear Programming......Page 73
Product Mix Problem......Page 74
Kerre's Method......Page 75
Chen's Method......Page 77
Comparison of Solutions......Page 78
Diet Problem......Page 80
Fuzzy Monte Carlo Method......Page 81
Comparison of Solutions......Page 83
Multiobjective Fully Fuzzified Linear Programming......Page 86
Example Problem......Page 87
Fuzzy Monte Carlo Method......Page 88
Compare Solutions......Page 91
$\overline{A}$ $\overline{X}$+ $\overline{B}$= $\overline{C}$......Page 94
Other Solutions......Page 96
Fuzzy Monte Carlo Method......Page 99
Fuzzy Quadratic Equation......Page 103
Fuzzy Monte Carlo Method......Page 105
Fuzzy Matrix Equation......Page 108
Fuzzy Monte Carlo Method......Page 115
Summary and Conclusions......Page 119
Introduction......Page 121
Random Fuzzy Vectors......Page 122
First Choice of Intervals......Page 123
Second Choice of Intervals......Page 124
Comparison of Solutions......Page 126
Summary and Conclusions......Page 127
Introduction......Page 130
Univariate Fuzzy Nonlinear Regression......Page 131
Fuzzy Monte Carlo Method......Page 132
First Choice of Intervals......Page 133
Second Choice of Intervals......Page 135
First Choice of Intervals......Page 136
Second Choice of Intervals......Page 137
Comparison of Solutions......Page 138
Summary and Conclusions......Page 139
Universal Approximator......Page 141
Evolutionary Algorithm......Page 142
Fuzzy Monte Carlo Method......Page 143
First Application......Page 144
Second Application......Page 147
Third Application......Page 149
Fourth Application......Page 151
Summary and Conclusions......Page 155
Introduction......Page 157
Error Measures......Page 158
Example Problem......Page 159
First Choice of Intervals......Page 160
Second Choice of Intervals......Page 161
Comparison of Solutions......Page 162
Summary and Conclusions......Page 163
MATLAB Program......Page 164
Two-Person Zero-Sum Games......Page 167
Fuzzy Two-Person Zero-Sum Games......Page 168
Fuzzy Monte Carlo......Page 171
Max/Min of Fuzzy Numbers......Page 172
Fuzzy Monte Carlo Solution Method......Page 173
Conclusions and Future Research......Page 174
Queuing Model......Page 176
Fuzzy Queuing Model......Page 178
Maximum of Fuzzy Profit......Page 181
Fuzzy Monte Carlo Solution......Page 182
Summary and Conclusions......Page 184
Min-Cost Capacitated Network......Page 186
Fuzzy Monte Carlo Method......Page 189
Fuzzy Shortest Path Problem......Page 190
Monte Carlo Method......Page 191
Max-Flow Problem......Page 193
Fuzzy Max-Flow Problem......Page 194
Fuzzy Monte Carlo Solution......Page 195
Inventory Problem......Page 197
Monte Carlo Method......Page 200
Monte Carlo Solution......Page 201
Inventory Model......Page 203
Monte Carlo Solution......Page 209
Inventory Model......Page 211
Monte Carlo Method......Page 212
Transportation Problem......Page 215
Fuzzy Transportation Problem......Page 216
Fuzzy Integers......Page 220
A Fuzzy Integer Programming Problem......Page 221
Fuzzy Monte Carlo Solution......Page 222
A Dynamic Programming Problem......Page 224
A Fuzzy Dynamic Programming Problem......Page 225
Fuzzy Monte Carlo Solution......Page 226
Introduction......Page 228
Job Times Fuzzy Numbers......Page 229
Fuzzy Monte Carlo Method......Page 231
Max/Min $f(\overline{X})$......Page 234
Max/Min $f(\overline{X},\overline{Y})$......Page 235
Summary......Page 237
Future Research......Page 238
Conclusions......Page 239
back-matter.pdf......Page 240