Main Data
Author: Sifeng Liu, Yi Lin
Title: Grey Information Theory and Practical Applications
Publisher: Springer-Verlag
ISBN/ISSN: 9781846283420
Edition: 1
Price: CHF 166.60
Publication date: 01/01/2006
Category: Informatik, EDV Buch
Language: English
Technical Data
Pages: 508
Kopierschutz: DRM
Geräte: PC/MAC/eReader/Tablet
Formate: PDF
Table of contents
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.
Table of contents
1.1 Scientific Background for the Appearance of Grey Systems Theory13
1.2 Fundamental Concepts and Principles of Grey Systems15
1.3 Comparison Between Several Nondeterministic Methods19
1.4 Main Contents in Grey Systems Theory20
1.5 Role of Grey Systems Theory in the Development of Science22
1.6 Positions of Grey Systems Theory in the Spectrum of Interdisciplinary Sciences23
1.7 Grey Systems in the Content of Uncertain Information25
Grey Numbers and Their Operations34
2.1 Grey Numbers34
2.2 Whitenization of Grey Numbers and Degree of Greyness37
2.3 Operations of Interval Grey Numbers41
2.4 Measures of Grey Numbers44
2.5 Information Content of Grey Numbers49
Grey Equations and Grey Matrices55
3.1 Grey Algebraic Equations and Grey Di erential Equations55
3.2 Grey Matrices and Their Operations56
3.3 Several Special Grey Matrices60
3.4 Singularities of Grey Matrices62
3.5 Grey Characteristic Values and Vectors64
Generation of Grey Sequences67
4.1 Introduction67
4.2 Generation Based on Average69
4.3 Operators of Sequences71
4.4 Smooth Sequences80
4.5 Stepwise and Smooth Ratios83
4.6 Accumulating and Inverse Accumulating Generation Operators85
4.7 Randomness of Sequences of Accumulating Generations89
4.8 Grey Exponentiality of Accumulating Generations91
Grey Incidence Analysis95
5.1 Introduction95
5.2 Grey Incidence Factors and Set of Grey Incidence Operators97
5.3 Metric Spaces100
5.4 Degrees of Grey Incidences103
5.5 Absolute Degree of Grey Incidence111
5.6 Relative Degree of Grey Incidence123
5.7 Synthetic Degree of Grey Incidence127
5.8 Order of Grey Incidences128
5.9 Preference Analysis130
5.10 Practical Applications142
Grey Clusters and Grey Statistical Evaluations149
6.1 Introduction149
6.2 Clusters of Grey Incidences150
6.3 Clusters with Variable Weights154
6.4 Clusters with Fixed Weights163
6.5 Grey Evaluation Based on Triangular Whitenization Functions172
6.6 Grey Statistics174
6.7 Entropy of Coe cient Vector of Grey Evaluations179
6.8 Practical Examples184
Grey Systems Modeling200
7.1 The Thought of Five-Step-Modeling200
7.2 Grey Di erential Equations203
7.3 Model: GM(1,1)206
7.4 Model: Remnant GM(1,1)226
7.5 Model Group of GM(1,1) Type231
7.6 GM(1,N) and GM(0,N)237
7.7 GM(2,1) and Verhulst Model244
Grey Combined Models253
8.1 Econometric Models254
8.2 Cobb-Douglas Model262
8.3 Markov Model266
8.4 Combined Time Series Model270
8.5 Combined Predictions273
Grey Prediction282
9.1 Test of Grey Prediction Models282
9.2 Predictions of Sequences284
9.3 Interval Predictions288
9.4 Disaster Predictions296
9.5 Seasonal Disaster Predictions300
9.6 Stock-Market-Like Predictions306
9.7 Systems Predictions312
9.8 Practical Applications318
Grey Decisions322
10.1 Introduction322
10.2 Grey Target Decisions325
10.3 Grey Incidence Decisions332
10.4 Grey Development Decisions343
10.5 Grey Statistical Decisions348
10.6 Grey Cluster Decisions354
10.7 Multiple-Target-Situation Decisions with a Synthesized Target358
10.8 Grey Stratified Decisions365
Grey Programming374
11.1 Introduction374
11.2 Linear Programming Models with Grey Parameters376
11.3 Grey Linear Programming of Prediction Type380
11.4 Several Theorems on Positioned Solutions of LPGP384
11.5 Satisfactory Solutions of Grey Linear Programming389
11.6 Quasi-Optimal Solutions of Grey Linear Programming396
11.7 Grey 0-1 Programming402
11.8 Grey Nonlinear Programming Without Constraints411
11.9 Grey Nonlinear Programming with Constraints414
Grey Input and Output421
12.1 Basic Concepts for Grey Input and Output421
12.2 P-F Theorems of Grey Non-Negative Matrices424
12.3 Responsibility and Infiuence Coefficients430
12.4 Optimal Input-Output Models434
12.5 Dynamic Input-Output Models440
12.6 Practical Applications444
Grey Control450
13.1 Introduction450
13.2 Grey Linear Control Systems453
13.3 Grey Transfer Functions and Special Links457
13.4 Matrices of Grey Transfer Functions462
13.5 Control with Abandonment464
13.6 Control of Grey Incidences465
13.7 Control of Grey Predictions466
13.8 Practical Applications468