Preface	6
	Contents	9
	Introduction	13
	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
	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
	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
	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
	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
	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
	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
	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
	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
	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
	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
	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
	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
	Index	505