ISBN: 3790814288
TITLE: Fuzzy Reasoning in Decision Making and Optimization
AUTHOR: Carlsson
TOC:

1. Fuzzy Sets and Fuzzy Logic
1.1 Fuzzy sets 1
1.2 Operations on fuzzy sets 7
1.3 The extension principle 12
1.4 t-norm-based operations on fuzzy numbers 19
1.5 Product-sum of triangular fuzzy numbers 21
1.6 Hamacher-sum of triangular fuzzy numbers 24
1.7 t-norm-based addition of fuzzy numbers 28
1.8 A functional relationship between t-norm-based addition and multiplication 30
1.9 On generahzation of Nguyen's theorems 33
1.10 Measures of possibility and necessity 35
1.11 A law of large numbers for fuzzy numbers 38
1.12 Metrics for fuzzy numbers 44
1.13 Possibilistic mean value and variance of fuzzy numbers 46
1.14 Auxiliary lemmas 53
1.15 Fuzzy implications 57
1.16 Linguistic variables 60
2. Fuzzy Multicriteria Decision Making
2.1 Averaging operators 65
2.2 Obtaining maximal entropy OWA operator weights 73
2.3 OWA Operators for Ph.D. student selection 78
2.4 Possibility and necessity in weighted aggregation 85
2.5 Benchmarking in linguistic importance weighted aggregations 92
3. Fuzzy Reasoning
3.1 The theory of approximate reasoning 101
3.2 Aggregation in fuzzy system modeling 104
3.3 Multiple fuzzy reasoning schemes 107
3.4 Some properties of the compositional rule of inference 111
3.5 Computation of the compositional rule of inference under t-norms 115
3.6 On the generalized method-of-case inference rule 119
4. Fuzzy Optimization
4.1 Possibilistic linear equality systems 123
4.2 Sensitivity analysis of a^~x = b^~ and a~^delta x = b^~^delta 130
4.3 Possibilistic systems with trapezoid fuzzy numbers 134
4.4 Flexible linear programming 136
4.5 Fuzzy linear programming with crisp relations 142
4.6 Possibilistic linear programming 144
4.7 Possibilistic quadratic programming 148
4.8 Multiobjective possibilistic linear programming 150
5. Fuzzy Reasoning for Fuzzy Optimization
5.1 Fuzzy reasoning for FMP 157
5.1.1 Extension to nonlinear FMP 161
5.1.2 Relation to classical LP problems 162
5.1.3 Crisp objective and fuzzy coefficients in constraints 163
5.1.4 Fuzzy objective function and crisp constraints 164
5.1.5 Relation to Zimmermann's soft constraints 164
5.1.6 Relation to Buckley's possibilistic LP 166
5.2 Optimization with linguistic variables 170
5.3 Multiobjective optimization with lingusitic variables 177
5.4 Interdependent multiple criteria decision making 179
5.4.1 The linear case 184
5.4.2 Application functions 186
5.5 MOP with interdependent objectives 190
5.6 Additive linear interdependences 193
5.7 Additive nonlinear interdependences 199
5.8 Compound interdependences 201
5.9 Biobjective interdependent decision problems 203
6. Applications in Management
6.1 Nordic Paper Inc. 207
6.1.1 Outline of a macro algorithm 209
6.2 A fuzzy approach to real option valuation 212
6.2.1 Probabilistic real option valuation 213
6.2.2 A hybrid approach to real option valuation 215
6.3 The Woodstrat project 219
6.3.1 Fuzzy hyperknowledge support systems 220
6.3.2 Cognitive maps for hyperknowledge representation 231
6.3.3 Adaptive FCM for strategy formation 232
6.4 Soft computing methods for reducing the bullwhip effect 236
6.4.1 The bullwhip effect, some additional details 240
6.4.2 Explanations for the bullwhip effect: standard results 242
6.4.3 Demand signal processing 243
6.4.4 Order batching 244
6.4.5 Price variations 246
6.4.6 A fuzzy approach to demand signal processing 247
6.4.7 A fuzzy logic controller to demand signal processing 248
6.4.8 A hybrid soft computing platform for taming the bullwhip effect 250
7. Future Trends in Fuzzy Reasoning and Decision Making
7.1 Software agents and agent-based systems 255
7.2 Intelligence and software agents 261
7.3 Scenario agents 264
7.3.1 The scenario agent: basic functionality 267
7.4 Scenarios and scenario planning: key features 268
7.5 Forecasting 272
7.6 Industry foresight 275
7.7 The scenario agent 278
7.7.1 Support for OW scenarios 279
7.7.2 Support for model-based scenarios 281
7.7.3 Support for scenario building and foresight 285
7.8 Interpretation agent 287
7.8.1 The interpretation agent: basic functionality 288
7.9 Coping with imprecision 290
7.10 Interpretation in a business environment 293
7.11 Mental models and cognitive maps 295
7.12 A preliminary description of an interpretation agent 296
7.13 An interpretation agent: details 300
7.13.1 Interpretation support for OW scenarios 302
7.13.2 Interpretation support for model-based scenarios 305
7.13.3 Interpretation support for decision models 309
7.13.4 Interpretation support for data sources 312
7.13.5 Generic interpretation of agent structures 313
7.13.6 Approximate reasoning and sense-making 313
7.13.7 Support for sense-making and interpretation 314
Bibliography 319
Index 337
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