| Preface | 6 |
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| Contents | 9 |
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| Introduction | 13 |
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| 1.1 Scientific Background for the Appearance of Grey Systems Theory | 13 |
| 1.2 Fundamental Concepts and Principles of Grey Systems | 15 |
| 1.3 Comparison Between Several Nondeterministic Methods | 19 |
| 1.4 Main Contents in Grey Systems Theory | 20 |
| 1.5 Role of Grey Systems Theory in the Development of Science | 22 |
| 1.6 Positions of Grey Systems Theory in the Spectrum of Interdisciplinary Sciences | 23 |
| 1.7 Grey Systems in the Content of Uncertain Information | 25 |
| Grey Numbers and Their Operations | 34 |
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| 2.1 Grey Numbers | 34 |
| 2.2 Whitenization of Grey Numbers and Degree of Greyness | 37 |
| 2.3 Operations of Interval Grey Numbers | 41 |
| 2.4 Measures of Grey Numbers | 44 |
| 2.5 Information Content of Grey Numbers | 49 |
| Grey Equations and Grey Matrices | 55 |
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| 3.1 Grey Algebraic Equations and Grey Di erential Equations | 55 |
| 3.2 Grey Matrices and Their Operations | 56 |
| 3.3 Several Special Grey Matrices | 60 |
| 3.4 Singularities of Grey Matrices | 62 |
| 3.5 Grey Characteristic Values and Vectors | 64 |
| Generation of Grey Sequences | 67 |
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| 4.1 Introduction | 67 |
| 4.2 Generation Based on Average | 69 |
| 4.3 Operators of Sequences | 71 |
| 4.4 Smooth Sequences | 80 |
| 4.5 Stepwise and Smooth Ratios | 83 |
| 4.6 Accumulating and Inverse Accumulating Generation Operators | 85 |
| 4.7 Randomness of Sequences of Accumulating Generations | 89 |
| 4.8 Grey Exponentiality of Accumulating Generations | 91 |
| Grey Incidence Analysis | 95 |
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| 5.1 Introduction | 95 |
| 5.2 Grey Incidence Factors and Set of Grey Incidence Operators | 97 |
| 5.3 Metric Spaces | 100 |
| 5.4 Degrees of Grey Incidences | 103 |
| 5.5 Absolute Degree of Grey Incidence | 111 |
| 5.6 Relative Degree of Grey Incidence | 123 |
| 5.7 Synthetic Degree of Grey Incidence | 127 |
| 5.8 Order of Grey Incidences | 128 |
| 5.9 Preference Analysis | 130 |
| 5.10 Practical Applications | 142 |
| Grey Clusters and Grey Statistical Evaluations | 149 |
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| 6.1 Introduction | 149 |
| 6.2 Clusters of Grey Incidences | 150 |
| 6.3 Clusters with Variable Weights | 154 |
| 6.4 Clusters with Fixed Weights | 163 |
| 6.5 Grey Evaluation Based on Triangular Whitenization Functions | 172 |
| 6.6 Grey Statistics | 174 |
| 6.7 Entropy of Coe cient Vector of Grey Evaluations | 179 |
| 6.8 Practical Examples | 184 |
| Grey Systems Modeling | 200 |
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| 7.1 The Thought of Five-Step-Modeling | 200 |
| 7.2 Grey Di erential Equations | 203 |
| 7.3 Model: GM(1,1) | 206 |
| 7.4 Model: Remnant GM(1,1) | 226 |
| 7.5 Model Group of GM(1,1) Type | 231 |
| 7.6 GM(1,N) and GM(0,N) | 237 |
| 7.7 GM(2,1) and Verhulst Model | 244 |
| Grey Combined Models | 253 |
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| 8.1 Econometric Models | 254 |
| 8.2 Cobb-Douglas Model | 262 |
| 8.3 Markov Model | 266 |
| 8.4 Combined Time Series Model | 270 |
| 8.5 Combined Predictions | 273 |
| Grey Prediction | 282 |
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| 9.1 Test of Grey Prediction Models | 282 |
| 9.2 Predictions of Sequences | 284 |
| 9.3 Interval Predictions | 288 |
| 9.4 Disaster Predictions | 296 |
| 9.5 Seasonal Disaster Predictions | 300 |
| 9.6 Stock-Market-Like Predictions | 306 |
| 9.7 Systems Predictions | 312 |
| 9.8 Practical Applications | 318 |
| Grey Decisions | 322 |
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| 10.1 Introduction | 322 |
| 10.2 Grey Target Decisions | 325 |
| 10.3 Grey Incidence Decisions | 332 |
| 10.4 Grey Development Decisions | 343 |
| 10.5 Grey Statistical Decisions | 348 |
| 10.6 Grey Cluster Decisions | 354 |
| 10.7 Multiple-Target-Situation Decisions with a Synthesized Target | 358 |
| 10.8 Grey Stratified Decisions | 365 |
| Grey Programming | 374 |
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| 11.1 Introduction | 374 |
| 11.2 Linear Programming Models with Grey Parameters | 376 |
| 11.3 Grey Linear Programming of Prediction Type | 380 |
| 11.4 Several Theorems on Positioned Solutions of LPGP | 384 |
| 11.5 Satisfactory Solutions of Grey Linear Programming | 389 |
| 11.6 Quasi-Optimal Solutions of Grey Linear Programming | 396 |
| 11.7 Grey 0-1 Programming | 402 |
| 11.8 Grey Nonlinear Programming Without Constraints | 411 |
| 11.9 Grey Nonlinear Programming with Constraints | 414 |
| Grey Input and Output | 421 |
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| 12.1 Basic Concepts for Grey Input and Output | 421 |
| 12.2 P-F Theorems of Grey Non-Negative Matrices | 424 |
| 12.3 Responsibility and Infiuence Coefficients | 430 |
| 12.4 Optimal Input-Output Models | 434 |
| 12.5 Dynamic Input-Output Models | 440 |
| 12.6 Practical Applications | 444 |
| Grey Control | 450 |
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| 13.1 Introduction | 450 |
| 13.2 Grey Linear Control Systems | 453 |
| 13.3 Grey Transfer Functions and Special Links | 457 |
| 13.4 Matrices of Grey Transfer Functions | 462 |
| 13.5 Control with Abandonment | 464 |
| 13.6 Control of Grey Incidences | 465 |
| 13.7 Control of Grey Predictions | 466 |
| 13.8 Practical Applications | 468 |
| References | 476 |
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| Index | 505 |
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