Fuzzy sets in decision analysis, operations research and statistics:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer Acad. Publ.
1998
|
| Series: | The handbooks of fuzzy sets series
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 453 S. graph. Darst. |
| ISBN: | 0792381122 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Series Foreword xiii
Didier Dubois, Henri Prade
Preface xv
Roman Slowiriski
Contributing Authors xxi
Part I DECISION MAKING
1
Fuzzy Preference Modeling 3
Patrice Perny, Marc Roubens
1.1 Preference Modeling and Decision Aid 3
1.2 Preference Structures 5
1.2.1 Basic Notions of Crisp Preference Modeling 5
1.2.2 Fuzzy Preference Modeling 8
1.2.3 Particular Solutions 13
1.2.4 Transitivity of (P, I, J) 15
1.3 Preference Modeling for MCDA 16
1.3.1 Multicriteria Decision Problems 16
1.3.2 The Use of Fuzzy Sets in the Definition of Criteria 17
1.3.3 Construction of Preference Relations from Criterion Values 19
1.3.4 The Construction of Preference Relations from Ill known
Consequences 22
References 27
vi DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS
2
Fuzzy Aggregation of Numerical Preferences 31
Michel Grabisch, Sergei A. Orlovski, Ronald R. Yager
2.1 The Aggregation Problem 31
2.2 Construction of One Comprehensive Criterion 34
2.2.1 Introduction 34
2.2.2 Properties for Aggregation 35
2.2.3 Common Aggregation Operators 37
2.2.4 Ordered Weighted Averaging (OWA) Operators 41
2.2.5 Fuzzy Integrals 42
2.2.6 Relation between Operators and Characterization of
Operators 44
2.2.7 Behavioral Analysis of Operators 47
2.2.8 Identification of Operators 51
2.2.9 Aggregation of Fuzzy Numbers 55
2.3 Aggregation of Fuzzy Preferences in Problems of Multiattribute
Choice 56
2.3.1 Introduction 56
2.3.2 Pareto Principle 56
2.3.3 Relation of Relative Importance 59
2.3.4 The Agreement Discordance Principle for Aggregation 61
References 64
3
The Use of Fuzzy Preference Models in Multiple 69
Criteria Choice, Ranking and Sorting
Janos Fodor, Sergei A. Orlovski, Patrice Perny, Marc Roubens
3.1 Choice Based on a Fuzzy Binary Relation 69
3.2 Choice Methods Based on Scoring Functions 76
3.3 Choice Functions Based on Covering Relations 78
3.4 Choice Functions Based on Transitive Closures 83
3.5 Choice Functions Based on Kernels 86
3.6 Ranking and Sorting from Fuzzy Relations 91
3.6.1 Ranking Methods 91
3.6.2 Sorting Methods 95
References 96
CONTENTS vii
4
Group Decision Making Under Fuzziness 103
Janusz Kacprzyk, Hannu Nurmi
4.1 Introduction 103
4.1.1 Group Decision Making, Social Choice and Consensus
Reaching Basic Issues and the Role of Fuzziness 104
4.1.2 Fuzzy Linguistic Quantifiers and the Ordered
Weighted Averaging (OWA) Operators 108
4.2 Group Decision Making Under Fuzzy Preferences and a Fuzzy
Majority 112
4.2.1 Direct Derivation of a Solution 113
4.2.2 Indirect Derivation of a Solution the Consensus Winner 122
4.3 Degrees of Consensus under Fuzzy Preferences and a Fuzzy Majority 127
4.4 Concluding Remarks 131
References 132
5
Elements of Fuzzy Game Theory 137
Antoine Billot
5.1 Introduction: Rational Behavior and Games 137
5.2 Games and Fuzziness 139
5.2.1 General Statements about Boolean Game Theory 139
5.2.2 General Statements about Fuzzy Game Theory 141
5.3 Fuzzy Information and Fuzzy Coalitions 142
5.3.1 Fuzzy Information 142
5.3.2 Fuzzy Behavior 143
5.4 IMonCooperative Fuzzy Game Theory 145
5.4.1 Fixed Points and Nash Equilibrium 145
5.4.2 Prudent Behavior and Equilibria 154
5.5 Cooperative Fuzzy Game Theory 159
5.5.1 Fuzzy Structures with Boolean Preferences 160
5.5.2 Boolean Structures with Fuzzy Preferences 166
References l7^
viii DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS
Part II MATHEMATICAL PROGRAMMING
6
Fuzzy Linear Programming with Single or Multiple 179
Objective Functions
Heinrich Rommel]anger, Roman Slowinski
6.1 Introduction 179
6.2 Linear Programming with Soft Constraints 181
6.3 Modeling of Fuzzy Data 186
6.4 Aggregation of the Left Hand Sides of Fuzzy Constraints 189
6.5 Inequality Relations 189
6.6. Maximizing Fuzzy Objectives 191
6.7 Extended Addition, based on Yager s T norm Tp 197
6.8 Solution Process for Getting a Compromise Solution 199
6.9 Applications of Fuzzy Linear Programming 205
References 207
7
Fuzzy Nonlinear Programming with Single or Multiple 215
Objective Functions
Masatoshi Sakawa
7.1 Nonlinear Programming with a Fuzzy Goal and Constraints 215
7.2 Multiobjective Nonlinear Programming with Fuzzy Goals 217
7.3 Interactive Fuzzy Multiobjective Approaches 225
7.4 Interactive Fuzzy Multiobjective Nonlinear Goal Programming 227
7.5 Interactive Fuzzy Multiobjective Nonlinear Programming 229
7.6 Multiobjective Nonlinear Programming with Fuzzy Parameters 233
7.7 Interactive Nonlinear Programming with Fuzzy Parameters 236
7.8 Interactive Fuzzy Nonlinear Programming with Fuzzy Parameters 240
References 246
8
Discrete Fuzzy Optimization 249
Stefan Chanas, Dorota Kuchta
8.1 Introduction 249
8.2 Fuzzy Optimization in Graphs and Networks 251
8.2.1 Max Flow Problem 251
8.2.2 Min Cost Flow Problem 253
CONTENTS ix
8.2.3 The Shortest Route Problem 255
8.3 Fuzzy Transportation and Assignment Problem 258
8.3.1 Integer Transportation Problem with Fuzzy Coefficients in
the Objective Function 258
8.3.2 Integer Transportation Problem with Fuzzy Demand and
Supply Values and a Fuzzy Goal 259
8.3.3 Fuzzy Assignment Problem 262
8.4 Fuzzy Network Planning 264
8.4.1 A Generalization of the CPM Method Chanas and
Kamburowski Approach 264
8.4.2 Fuzzy PERT 266
8.5 Fuzzy Scheduling on Machines 267
8.5.1 The Fuzzy N job M machine Flow Shop Problem 268
8.5.2 The Fuzzy Open Shop Problem (with Fuzzy Due Dates) 270
8.5.3 The Fuzzy Identical Machines Maximum Lateness Problem 271
8.5.4 General Fuzzy Job Shop Problems 271
8.6 Other Selected Problems 273
8.6.1 Fuzzy Set Covering Problem 273
8.6.2 Fuzzy Multiple Choice Knapsack Problem 274
8.6.3 General Fuzzy 0 1 Linear Problems 275
References 277
9
Fuzzy Dynamic Programming 281
Augustine 0. Esogbue, Janusz Kacprzyk
9.1 Introduction 281
9.2 Multistage Decision Making under Fuzziness 283
9.2.1 Multistage Decision Making under Fuzziness Bellman and
Zadeh s Approach 283
9.2.2 Essentials of Multistage Decision Making (Control) under
Fuzziness Bellman and Zadeh s Approach 285
9.3 Fuzzy Dynamic Programming for Multistage Decision Making with
a Fixed and Specified Termination Time 287
9.3.1 The Case of a Deterministic Dynamic System 287
9.3.2 The Case of a Stochastic Dynamic System 288
9.3.3 The Case of a Fuzzy Dynamic System 290
9.4 Fuzzy Dynamic Programming for Multistage Decision Making with
a Fuzzy Termination Time 291
9.4.1 The Case of a Deterministic Dynamic System 292
9.4.2 The Case of a Stochastic Dynamic System 293
9.4.3 Remarks on the Case of a Fuzzy Dynamic System 293
x DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS
9.5 Multistage Decision Making with an Implicitly Specified Termination
Time 294
9.6 Multistage Decision Making with an Infinite Termination Time 294
9.7 Stochastic Multistage Decision Making under Fuzzy Criteria 295
9.7.1 Fuzzy Criterion Sets and Fuzzy Dynamic Programming 295
9.7.2 Optimal Control Policy and Additional Studies in Fuzzy
Criterion Dynamic Programming 300
9.8 Computational Complexity Analysis of Fuzzy Dynamic Programs 300
9.8.1 Computational Analysis of Kacprzyk s Model 300
9.8.2 Stein s Approach 301
9.8.3 Comparative Summary 301
9.9 Brief Review of Applications of Fuzzy Dynamic Programming 301
9.10 Concluding Remarks 303
References 304
Part III STATISTICS AND DATA ANALYSIS
10
Fuzzy Set Theoretic Methods in Statistics 311
Jorg Gebhardt, Maria Angeles Gil, Rudolf Kruse
10.1 Introduction 311
10.2 Fuzziness in Random Experiments 312
10.3 An Approach to Fuzzy Valued Statistics with Fuzzy Experimental
Data 315
10.3.1 Fuzzy Random Variables 316
10.3.2 Fuzzy Probability Theory 318
10.3.3 Fuzzy Statistics 320
10.3.4 The SOLD System An Implementation 321
10.4 An Approach to Real Valued Statistics with Fuzzy Experimental
Data 324
10.4.1 Point Estimation from Fuzzy Data. Maximum Likelihood
Principle and an Operative Approximation 327
10.4.2 Testing Hypothesis with Fuzzy Data. Likelihood Ratio Test 333
10.5 Approaches to Modeling Fuzzy Bayes Statistical Decision Making 335
10.5.1 An Approach to Modeling Statistical Decision Making with
Fuzzy Data 335
10.5.2 An Approach to Modeling Statistical Decision Making with
Fuzzy Utilities 337
10.6 Concluding Remarks 340
References 341
CONTENTS xi
11
Fuzzy Regression Analysis 349
Phil Diamond, Hideo Tanaka
11.1 Introduction 349
11.1.1 Overview of Possibilistic Regression 352
11.1.2 Overview of Least Squares Methods 353
11.2 Possibilistic Regression 353
11.2.1 Interval Regression 354
11.2.2 Fuzzy Regression 360
11.2.3 Exponential Possibility Regression 362
11.3 Least Squares Regression 369
11.3.1 Celmins Model 369
11.3.2 Metric Distance 371
11.3.3 Korner s Method 377
11.3.4 Hukuhara Fitting 378
11.3.5 Fitting Several Fuzzy Variables 380
11.3.6 Random Fuzzy Variables 382
11.3.7 Kriging 383
11.4 Concluding Remarks 385
References 386
Part IV RELIABILITY, MAINTENANCE
AND REPLACEMENT
12
Reliability 391
Etienne Kerre, Takehisa Onisawa, Bart Cappelle, Igor Gazdik
12.1 Introduction 391
12.2 Questions in Classical Reliability and their Possible Answers 393
12.3 Probabilistic Approach of System Reliability Analysis From Fuzzy
Theory Point of View 397
12.3.1 Failure Probability and Error Probability 397
12.3.2 Dependence 398
12.3.3 Scenario about Sequence of System Failure 400
12.3.4 System Reliability Evaluation 400
12.3.5 Use of Natural Language 401
12.4 Fuzzy Set Theory Approach 402
12.4.1 Fuzzy Probability Approach 402
12.4.2 Fault Tree Analysis by Fuzzy Failure Probability 405
12.4.3 Non Probabilistic Measure Approach 406
xii DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS
12.4.4 Fuzzy Fault Tree Analysis by Subjective Measure of
Reliability 409
12.4.5 Dependence Analysis 411
12.4.6 Natural Language Expressions of the Analysis Results 413
12.4.7 Determination of the Parameters nH and nG 413
12.4.8 Determination of the parameter r$ 414
12.4.9 Mutual Agreement of the Analysis Results 414
12.5 Conclusions 415
References 416
13
Maintenance and Replacement Models under a Fuzzy 421
Framework
Augustine 0. Esogbue, Warren E. Hearnes II
13.1 Economic Decision Analysis 421
13.2 Replacement Analysis 423
13.3 Fuzzy Concepts in Cash Flow Analysis 424
13.3.1 Nonprobabilistic Method in Cash Flow Analysis 425
13.3.2 Fuzzy Arithmetic and Interval Analysis 426
13.3.3 Some Sources of Uncertainty in Replacement Analysis 427
13.4 Economic Life of an Asset Model 428
13.5 Dynamic Programming Formulation of Economic Life of an Asset 432
13.6 The General Single Asset Replacement Problem 433
13.7 Inspection and Replacement Models 438
13.8 Maintenance Decisions 441
13.9 Summary 443
References 444
Index 449
|
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| indexdate | 2024-07-09T18:39:30Z |
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| isbn | 0792381122 |
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| series2 | The handbooks of fuzzy sets series |
| spelling | Fuzzy sets in decision analysis, operations research and statistics ed. by Roman Słowiński Boston [u.a.] Kluwer Acad. Publ. 1998 XXIV, 453 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The handbooks of fuzzy sets series 1 Ensembles flous Optimisation mathématique Prise de décision Decision-making Fuzzy sets Mathematical optimization Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Operations Research (DE-588)4043586-6 s Fuzzy-Menge (DE-588)4061868-7 s DE-604 Słowiński, Roman 1952- Sonstige (DE-588)12150798X oth The handbooks of fuzzy sets series 1 (DE-604)BV012607710 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008942994&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fuzzy sets in decision analysis, operations research and statistics The handbooks of fuzzy sets series Ensembles flous Optimisation mathématique Prise de décision Decision-making Fuzzy sets Mathematical optimization Fuzzy-Menge (DE-588)4061868-7 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4061868-7 (DE-588)4043586-6 |
| title | Fuzzy sets in decision analysis, operations research and statistics |
| title_auth | Fuzzy sets in decision analysis, operations research and statistics |
| title_exact_search | Fuzzy sets in decision analysis, operations research and statistics |
| title_full | Fuzzy sets in decision analysis, operations research and statistics ed. by Roman Słowiński |
| title_fullStr | Fuzzy sets in decision analysis, operations research and statistics ed. by Roman Słowiński |
| title_full_unstemmed | Fuzzy sets in decision analysis, operations research and statistics ed. by Roman Słowiński |
| title_short | Fuzzy sets in decision analysis, operations research and statistics |
| title_sort | fuzzy sets in decision analysis operations research and statistics |
| topic | Ensembles flous Optimisation mathématique Prise de décision Decision-making Fuzzy sets Mathematical optimization Fuzzy-Menge (DE-588)4061868-7 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Ensembles flous Optimisation mathématique Prise de décision Decision-making Fuzzy sets Mathematical optimization Fuzzy-Menge Operations Research |
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