Liu / Lin Grey Information

Theory and Practical Applications
1. Auflage 2006
ISBN: 978-1-84628-342-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 508 Seiten

Rapid formation and development of new theories of systems science have become an important part of modern science and technology. For - ample, since the 1940s, there have appeared systems theory, information theory, fuzzy mathematics, cybernetics, dissipative structures, synergetics, catastrophe theory, chaos theory, bifurcations, ultra circulations, dynamics, and many other systems theories. Grey systems theory is also one of such systems theories that appeared initially in the 1980s. When the research of systems science and the method and technology of systems engineering are applied in various traditional disciplines, such as management science, decision science, and various scienti?c disciplines, a whole new group of new results and breakthroughs are obtained. Such a historical background has provided the environment and soil for grey systems theory to form and to develop rapidly in the past 20-plus years. More speci?cally, in 1982, Professor Deng Ju-Long published the ?rst research paper in the area of grey systems in the international journal entitled Systems and Control Letters, published by North-Holland Co. His paper was titled “Control Problems of Grey Systems. ” The publication of this paper signalled the birth of grey systems theory after many years of e ective research of the founding father. This new theory soon caught the attention of the international academic community and practitioners of science. Many well-known scholars, such as Chinese academicians Qian Xueshen, Song Jian, and Zhang Zhongjun. Professor Roger W.

Autoren/Hrsg.

Liu, Sifeng

Lin, Yi

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;Introduction;13
3.1;1.1 Scientific Background for the Appearance of Grey Systems Theory;13
3.2;1.2 Fundamental Concepts and Principles of Grey Systems;15
3.3;1.3 Comparison Between Several Nondeterministic Methods;19
3.4;1.4 Main Contents in Grey Systems Theory;20
3.5;1.5 Role of Grey Systems Theory in the Development of Science;22
3.6;1.6 Positions of Grey Systems Theory in the Spectrum of Interdisciplinary Sciences;23
3.7;1.7 Grey Systems in the Content of Uncertain Information;25
4;Grey Numbers and Their Operations;34
4.1;2.1 Grey Numbers;34
4.2;2.2 Whitenization of Grey Numbers and Degree of Greyness;37
4.3;2.3 Operations of Interval Grey Numbers;41
4.4;2.4 Measures of Grey Numbers;44
4.5;2.5 Information Content of Grey Numbers;49
5;Grey Equations and Grey Matrices;55
5.1;3.1 Grey Algebraic Equations and Grey Di erential Equations;55
5.2;3.2 Grey Matrices and Their Operations;56
5.3;3.3 Several Special Grey Matrices;60
5.4;3.4 Singularities of Grey Matrices;62
5.5;3.5 Grey Characteristic Values and Vectors;64
6;Generation of Grey Sequences;67
6.1;4.1 Introduction;67
6.2;4.2 Generation Based on Average;69
6.3;4.3 Operators of Sequences;71
6.4;4.4 Smooth Sequences;80
6.5;4.5 Stepwise and Smooth Ratios;83
6.6;4.6 Accumulating and Inverse Accumulating Generation Operators;85
6.7;4.7 Randomness of Sequences of Accumulating Generations;89
6.8;4.8 Grey Exponentiality of Accumulating Generations;91
7;Grey Incidence Analysis;95
7.1;5.1 Introduction;95
7.2;5.2 Grey Incidence Factors and Set of Grey Incidence Operators;97
7.3;5.3 Metric Spaces;100
7.4;5.4 Degrees of Grey Incidences;103
7.5;5.5 Absolute Degree of Grey Incidence;111
7.6;5.6 Relative Degree of Grey Incidence;123
7.7;5.7 Synthetic Degree of Grey Incidence;127
7.8;5.8 Order of Grey Incidences;128
7.9;5.9 Preference Analysis;130
7.10;5.10 Practical Applications;142
8;Grey Clusters and Grey Statistical Evaluations;149
8.1;6.1 Introduction;149
8.2;6.2 Clusters of Grey Incidences;150
8.3;6.3 Clusters with Variable Weights;154
8.4;6.4 Clusters with Fixed Weights;163
8.5;6.5 Grey Evaluation Based on Triangular Whitenization Functions;172
8.6;6.6 Grey Statistics;174
8.7;6.7 Entropy of Coe cient Vector of Grey Evaluations;179
8.8;6.8 Practical Examples;184
9;Grey Systems Modeling;200
9.1;7.1 The Thought of Five-Step-Modeling;200
9.2;7.2 Grey Di erential Equations;203
9.3;7.3 Model: GM(1,1);206
9.4;7.4 Model: Remnant GM(1,1);226
9.5;7.5 Model Group of GM(1,1) Type;231
9.6;7.6 GM(1,N) and GM(0,N);237
9.7;7.7 GM(2,1) and Verhulst Model;244
10;Grey Combined Models;253
10.1;8.1 Econometric Models;254
10.2;8.2 Cobb-Douglas Model;262
10.3;8.3 Markov Model;266
10.4;8.4 Combined Time Series Model;270
10.5;8.5 Combined Predictions;273
11;Grey Prediction;282
11.1;9.1 Test of Grey Prediction Models;282
11.2;9.2 Predictions of Sequences;284
11.3;9.3 Interval Predictions;288
11.4;9.4 Disaster Predictions;296
11.5;9.5 Seasonal Disaster Predictions;300
11.6;9.6 Stock-Market-Like Predictions;306
11.7;9.7 Systems Predictions;312
11.8;9.8 Practical Applications;318
12;Grey Decisions;322
12.1;10.1 Introduction;322
12.2;10.2 Grey Target Decisions;325
12.3;10.3 Grey Incidence Decisions;332
12.4;10.4 Grey Development Decisions;343
12.5;10.5 Grey Statistical Decisions;348
12.6;10.6 Grey Cluster Decisions;354
12.7;10.7 Multiple-Target-Situation Decisions with a Synthesized Target;358
12.8;10.8 Grey Stratified Decisions;365
13;Grey Programming;374
13.1;11.1 Introduction;374
13.2;11.2 Linear Programming Models with Grey Parameters;376
13.3;11.3 Grey Linear Programming of Prediction Type;380
13.4;11.4 Several Theorems on Positioned Solutions of LPGP;384
13.5;11.5 Satisfactory Solutions of Grey Linear Programming;389
13.6;11.6 Quasi-Optimal Solutions of Grey Linear Programming;396
13.7;11.7 Grey 0-1 Programming;402
13.8;11.8 Grey Nonlinear Programming Without Constraints;411
13.9;11.9 Grey Nonlinear Programming with Constraints;414
14;Grey Input and Output;421
14.1;12.1 Basic Concepts for Grey Input and Output;421
14.2;12.2 P-F Theorems of Grey Non-Negative Matrices;424
14.3;12.3 Responsibility and Infiuence Coefficients;430
14.4;12.4 Optimal Input-Output Models;434
14.5;12.5 Dynamic Input-Output Models;440
14.6;12.6 Practical Applications;444
15;Grey Control;450
15.1;13.1 Introduction;450
15.2;13.2 Grey Linear Control Systems;453
15.3;13.3 Grey Transfer Functions and Special Links;457
15.4;13.4 Matrices of Grey Transfer Functions;462
15.5;13.5 Control with Abandonment;464
15.6;13.6 Control of Grey Incidences;465
15.7;13.7 Control of Grey Predictions;466
15.8;13.8 Practical Applications;468
16;References;476
17;Index;505