Optimal Models and Methods with Fuzzy Quantities

✍ Scribed by Cao, Bing-Yuan

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 454
• Series: Studies in Fuzziness and Soft Computing 248
• Category: Library

✦ Synopsis

The book contains ten chapters as follows, Prepare Knowledge, Regression and Self-regression Models with Fuzzy Coefficients; Regression and Self-regression Models with Fuzzy Variables, Fuzzy Input/output Model, Fuzzy Cluster Analysis and Fuzzy Recognition, Fuzzy Linear Programming, Fuzzy Geometric Programming, Fuzzy Relative Equation and Its Optimizing, Interval and Fuzzy Differential Equations and Interval and Fuzzy Functional and Their Variation.

It can not only be used as teaching materials or reference books for under-graduates in higher education, master graduates and doctor graduates in the courses of applied mathematics, computer science, artificial intelligence, fuzzy information process and automation, operations research, system science and engineering, and the like, but also serves as a reference book for researchers in these fields, particularly, for researchers in soft science.

✦ Table of Contents

Cover......Page 1
Front Matter......Page 2
General Model for Fu-Fu EVM......Page 7
Algorithm System......Page 14
Chance Operator of Fu-Ro Variables......Page 17
Membership Function......Page 37
Application to Purchasing Problem in a Large-Scale Integrated Steel Plant......Page 51
Level-2 Fuzzy Set, Type-2 Fuzzy Sets and Fu-Fu Variable......Page 3
Linear Fu-Fu EVM and Step Method......Page 8
Linear Fu-Ra EVM and Fuzzy Satisfied Method......Page 13
Fuzzy Sets......Page 21
General Model for Fu-Fu CCM......Page 23
Non-linear Fuzzy EVM and Fuzzy Simulation-Based PSO......Page 28
Fuzzy Arithmetic......Page 36
General Model for Fu-Fu DCM......Page 39
Linear Fu-Ro DCM and -Constraint Method......Page 55
Linear Fuzzy DCM and Ideal Point Method......Page 58
Non-linear Fuzzy DCM and Fuzzy Simulation-Based PSO with Shrinkage Factor......Page 63
Application of Farm Structure Optimization Problem......Page 66
Multi-objective Decision Making with Fuzzy Constraints......Page 72
Farm Structure Optimization Problem under Fuzzy Environment......Page 75
Physics-Based Model System......Page 4
Chance Operator of Fu-Fu Variables......Page 6
General Model for Fu-Ra EVM......Page 10
Non-linear Fu-Ra EVM and Fu-Ra Simulation-Based GA......Page 19
General Model for Fu-Ro CCM......Page 34
Non-linear Fu-Ra CCM and Fu-Ra Simulation-Based Adaptive Weight GA......Page 46
Modelling......Page 52
General Model for Fu-Ro DCM......Page 53
Non-linear Fu-Ro DCM and Fu-Ro Simulation Based Parallel TS......Page 64
Assumptions......Page 68
Possibility Distribution......Page 70
mean-Variance Portfolio Selection Model......Page 73
Another Way to Deal with Fuzzy Random......Page 81
Possibility, Necessity and General Fuzzy Measure......Page 82
Application to Inventory Problems......Page 86
Mathematical Model System......Page 5
Research Ideas and Paradigm: 5MRP......Page 18
Linear Fu-Fu CCM and Lexicographic Method......Page 25
Linear Fu-Fu DCM and Weight Sum Method......Page 40
Nonlinear Fu-Fu DCM and Fu-Fu Simulation Based Adaptive SA......Page 45
Another Way to Deal with Fu-Fu Multi-objective Decision Making Model......Page 60
Fuzzy Set Theory......Page 20
Basic Concepts of Fuzzy Sets......Page 26
Fuzzy Number......Page 33
Non-linear Fu-Ro CCM and Fu-Ro Simulation-Based Parametric TS......Page 47
Modelling for Integrated Reuse Logistics Network under Fuzzy Rough Environment......Page 71
Uncertain Linear Multi-objective Model......Page 74
Application to Beer Company......Page 76
Model Analysis System......Page 9
Membership Function......Page 56
Definition of Fuzzy Variable......Page 77
Expected Value Operator of Fuzzy Variables......Page 87
General Model for Fuzzy EVM......Page 95
Linear Fuzzy EVM and Two-Stage Method......Page 97
Non-linear Fuzzy EVM and Fuzzy Simulation-Based PSO......Page 102
General Model for Fuzzy CCM......Page 110
Linear Fuzzy CCM and Goal Programming Method......Page 113
Non-linear Fuzzy CCM and Fuzzy Simulation-Based PSO with Preference Order......Page 125
General Model for Fuzzy DCM......Page 129
Linear Fuzzy DCM and Ideal Point Method......Page 132
Non-linear Fuzzy DCM and Fuzzy Simulation-Based PSO with Shrinkage Factor......Page 137
Application of Farm Structure Optimization Problem......Page 140
Multi-objective Decision Making with Fuzzy Constraints......Page 146
Multi-objective Decision Making with Fuzzy Objectives......Page 149
Fuzzy Random Multiple Objective Decision Making......Page 152
Portfolio Selection Problem under a Fuzzy Random Environment......Page 153
Definition of Fu-Ra Variable......Page 155
Expected Value Operator of Fu-Ra Variables......Page 157
Chance Operator of Fu-Ra Variables......Page 159
General Model for Fu-Ra EVM......Page 161
Linear Fu-Ra EVM and Fuzzy Satisfied Method......Page 164
Non-linear Fu-Ra EVM and Fu-Ra Simulation-Based GA......Page 170
General Model for Fu-Ra CCM......Page 185
Linear Fu-Ra CCM and Surrogate Worth Trade-Off Method......Page 187
Non-linear Fu-Ra CCM and Fu-Ra Simulation-Based Adaptive Weight GA......Page 197
Fu-Ra DCM......Page 203
General Model for Fu-Ra DCM......Page 204
Linear Fu-Ra DCM and Satisfying Trade-Off Method......Page 206
Non-linear Fu-Ra DCM and Fu-Ra Simulation-Based Compromise GA......Page 215
Assumptions......Page 219
Chance Constrained Portfolio Selection Model......Page 221
mean-Variance Portfolio Selection Model......Page 224
Another Way to Deal with Fuzzy Random......Page 232
$(\alpha,\beta)$-Satisfied Solution for Fu-Ra Multi-objective Decision Making Model......Page 233
Application to Inventory Problems......Page 237
Raw Material Purchasing Problem under Bifuzzy Environment......Page 243
Level-2 Fuzzy Set, Type-2 Fuzzy Sets and Fu-Fu Variable......Page 245
Expected Value Operator of Fu-Fu Variables......Page 247
Chance Operator of Fu-Fu Variables......Page 248
General Model for Fu-Fu EVM......Page 249
Linear Fu-Fu EVM and Step Method......Page 250
Nonlinear Fu-Fu EVM and Fu-Fu Simulation Based SA......Page 260
General Model for Fu-Fu CCM......Page 265
Linear Fu-Fu CCM and Lexicographic Method......Page 267
Nonlinear Fu-Fu CCM and Fu-Fu Simulation Based Parallel SA......Page 276
General Model for Fu-Fu DCM......Page 281
Linear Fu-Fu DCM and Weight Sum Method......Page 282
Nonlinear Fu-Fu DCM and Fu-Fu Simulation Based Adaptive SA......Page 287
Application to Purchasing Problem in a Large-Scale Integrated Steel Plant......Page 293
Modelling......Page 294
Model Processing Specification......Page 297
Another Way to Deal with Fu-Fu Multi-objective Decision Making Model......Page 302
Integrated Logistics Problem under Fuzzy Rough Environment......Page 311
Definition of Fu-Ro Variable......Page 314
Expected Value Operator of Fu-Ro Variables......Page 324
Chance Operator of Fu-Ro Variables......Page 327
General Model for Fu-Ro EVM......Page 328
Linear Fu-Ro EVM and Minimax Point Method......Page 330
Non-linear Fu-Ro EVM and Fu-Ro Simulation-Based TS......Page 336
Fu-Ro CCM......Page 343
General Model for Fu-Ro CCM......Page 344
Linear Fu-Ro CCM and Fuzzy Goal Method......Page 346
Non-linear Fu-Ro CCM and Fu-Ro Simulation-Based Parametric TS......Page 357
General Model for Fu-Ro DCM......Page 363
Linear Fu-Ro DCM and -Constraint Method......Page 365
Non-linear Fu-Ro DCM and Fu-Ro Simulation Based Parallel TS......Page 374
Application to Integrated Logistics Network Design Problem......Page 380
Modelling for Integrated Reuse Logistics Network under Fuzzy Rough Environment......Page 381
Uncertain Linear Multi-objective Model......Page 384
Application to Beer Company......Page 386
Methodological System for FLMODM......Page 391
Motivation of Researching FLMODM......Page 392
Physics-Based Model System......Page 394
Mathematical Model System......Page 395
Model Analysis System......Page 399
Algorithm System......Page 404
Research Ideas and Paradigm: 5MRP......Page 408
Back Matter......Page 412