Random-Like Multiple Objective Decision Making

By: Jiuping Xu, Liming Yao

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Paperback | 26 March 2011

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What are the random-like phenomena that can be found everywhere in real-life world? When carrying out a random sampling survey on the traffic situation, we often obtain some descriptive results such as approximately expedite, a little crowded and so on, therefore, the average level should be regarded as the random fuzzy phenomenon, which is one of the random-like phenomena. Decision makers usually need to make the decision for these problems with random-like phenomena. Which model should be constructed for them? How should we handle these models to find the optimal strategy? How can we apply these models to solve real-life problems with random-like phenomena? In order to answer these questions, this book provides an up-to-date methodology system 5MRP for random-like multiple objective decision making, which includes problem system with random-like phenomena, model system with random-like coefficients, research system with random-like uncertain methods. Some practical applications are also provided to illustrate the effectiveness of the proposed methodology system. Researchers, practitioners and students in systems science, economics, mathematics, information, engineering and MS/OR will get a lot of useful references from this research monograph.

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Non-Fiction Reference, Information & Interdisciplinary Subjects Research & Information Decision Theory Business & Management Management & Management Techniques Management Decision Making Operational Research Mathematics Optimisation Linear Programming

Random Set Theory	p. 1
Algebra and -Algebra	p. 1
Measurable Set and Measure Space	p. 4
Outer Measures	p. 8
Probability Space	p. 12
Product Probability Space	p. 14
Conditional Probability and Independence	p. 15
Random Variable	p. 16
Random Vector	p. 17
Probability Distribution	p. 18
Central Limit Theorem	p. 19
Monte Carlo Simulation	p. 25
Random Multiple Objective Decision Making	p. 35
Distribution Center Location Problem with Random Phenomena	p. 35
Two Kinds of Random Variables	p. 38
Discrete Random Variable	p. 38
Continuous Random Variable	p. 41
Random EVM	p. 45
General Model for Random EVM	p. 45
Linear Random EVM and the Weight Sum Method	p. 49
Nonlinear Random EVM and Random Simulation-Based SA	p. 52
Numerical Examples	p. 58
Random CCM	p. 61
General Model for Random CCM	p. 61
Linear Random CCM and the Lexicographic Method	p. 63
Nonlinear Random CCM and Random Simulation-Based ASA	p. 70
Numerical Examples	p. 75
Random DCM	p. 78
General Model for Random DCM	p. 79
Linear Random DCM and the Fuzzy Programming Method	p. 80
Nonlinear Random DCM and Random Simulation-Based PSA	p. 85
Numerical Examples	p. 89
Application to Chinese Fruit Beverage	p. 92
Background Statement	p. 92
Notations	p. 93
Modelling and Analysis	p. 93
Bi-Random Multiple Objective Decision Making	p. 101
Flow Shop Scheduling Problem with Ra-Ra Phenomena	p. 102
Ra-Ra Variable	p. 103
Discrete Ra-Ra Variable	p. 104
Continuous Ra-Ra Variable	p. 109
Ra-Ra EVM	p. 113
General Model for Ra-Ra EVM	p. 114
Linear Ra-Ra EVM and the Step Method	p. 126
Nonlinear Ra-Ra EVM and Ra-Ra Simulation-Based PSO	p. 132
Numerical Examples	p. 141
Ra-Ra CCM	p. 144
General Model for Ra-Ra CCM	p. 145
Linear Ra-Ra CCM and the Surrogate Worth Trade-Off Method	p. 150
Nonlinear Ra-Ra CCM and Ra-Ra Simulation-Based APSO	p. 157
Numerical Examples	p. 161
Ra-Ra DCM	p. 164
General Model for Ra-Ra DCM	p. 165
Linear Ra-Ra DCM and the Satisfying Trade-Off Method	p. 166
Nonlinear Ra-Ra DCM and Ra-Ra Simulation-Based Tribe-PSO	p. 170
Numerical Examples	p. 174
Application to GEELY Haoqing Automotive Holdings Group Limited Company	p. 178
Background Introduction	p. 178
Problem Description and Notation	p. 180
Modelling and Analysis	p. 181
Random Fuzzy Multiple Objective Decision Making	p. 189
Supply Chain Network Design with Ra-Fu Phenomena	p. 190
Random Fuzzy Variable	p. 192
Fuzzy Variable	p. 192
Ra-Fu Variable	p. 196
Ra-Fu EVM	p. 211
General Model for Ra-Fu EVM	p. 211
Linear Ra-Fu EVM and the Maximin Point Method	p. 213
Nonlinear Ra-Fu EVM and Ra-Fu Simulation-Based aw-GA	p. 218
Numerical Examples	p. 227
Ra-Fu CCM	p. 230
General Model for Ra-Fu CCM	p. 232
Linear Ra-Fu CCM and -Constraint Method	p. 236
Nonlinear Ra-Fu CCM and Ra-Fu Simulation-Based st-GA	p. 242
Numerical Examples	p. 250
Ra-Fu DCM	p. 252
General Model for Ra-Fu DCM	p. 254
Linear Ra-Fu DCM and Goal Programming Method	p. 255
Nonlinear Ra-Fu DCM and Ra-Fu Simulation-Based rw-GA	p. 260
Numerical Examples	p. 264
Application to Chinese Liquor	p. 266
Notations	p. 269
Modelling	p. 269
Comparison of st-GA and m-GA	p. 277
Random Rough Multiple Objective Decision Making	p. 279
Inventory Problem with Ra-Ro Phenomena	p. 280
Random Rough Variable	p. 282
Rough Set	p. 282
Ra-Ro Variable	p. 291
Ra-Ro EVM	p. 308
General Model for Ra-Ro EVM	p. 309
Linear Ra-Ro EVM and the Ideal Point Method	p. 312
Non-Linear Ra-Ro EVM and Ra-Ro Simulation-Based ECTS	p. 315
Numerical Examples	p. 322
Ra-Ro CCM	p. 325
General Model	p. 326
Linear Ra-Ro CCM and Two-Stage Method	p. 327
Nonlinear Ra-Ro CCM and Ra-Ro Simulation-Based PTS	p. 333
Numerical Examples	p. 339
Ra-Ro DCM	p. 342
General Model	p. 343
Linear Ra-Ro DCM and the Fuzzy Goal Method	p. 344
Nonlinear Ra-Ro DCM and Ra-Ro Simulation-Based RTS	p. 350
Numerical Examples	p. 354
The Inventory System of Wal-Mart Supermarket	p. 357
Background	p. 358
Assumptions	p. 359
Mathematical Model	p. 360
Sensitivity Analysis	p. 367
Methodological System for RLMODM	p. 371
Motivation of Researching RLMODM	p. 372
Physics-Based Model System	p. 375
Mathematical Model System	p. 377
Model Analysis System	p. 382
Algorithm System	p. 387
Research Ideas and Paradigm: 5MRP	p. 390
Future Research	p. 394
Some Mathematical Aids	p. 397
Series	p. 397
Some Useful Integrals	p. 398
Chebyshev's Inequality	p. 399
Cauchy's Equation	p. 399
Some Useful Lemmas	p. 400
Some Procedures	p. 403
The Procedure of Random Simulation-Based SA	p. 403
The Procedure of Ra-Ra Simulation-Based PSO	p. 406
The Procedure of Ra-Fu Simulation-Based GA	p. 409
The Procedure of Ra-Ro Simulation-Based TS	p. 416
References	p. 419
Index	p. 435
Table of Contents provided by Ingram. All Rights Reserved.

Random-Like Multiple Objective Decision Making

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