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An Introduction to Grey Systems: Foundations, Methodology and Applications,
by Sifeng Liu and Yi Lin, Copyrighted by the IIGSS 1998. 426 + viii pages.
ISBN: 0-9665908-0-5 Hardcover (US$80.00 + shipping and handling $15.00, express mail $10 extra
ISBN: 0-9665908-1-3 Papercover (US$60.00 + shipping and handling $15.00, express mail $10 extra
Table of Contents
1. Introduction
2. Grey Numbers and Their Operations
2.1. Grey Numbers
2.2. Whitenization of Grey Numbers and Degree of Greyness
2.3. Operations of Interval Grey Numbers
3. Grey Equations and Grey Matrices
3.1. Grey Algebraic Equations and Grey Differential Equations
3.2. Grey Matrices and Their Operations
3.3. Several Special Grey Matrices
3.4. Singularities of Grey Matrices
3.5. Grey Characteristic Values and Vectors
4. Generations of Grey Sequences
4.1. Introduction
4.2. Generations Based on Average
4.3. Operations of Sequences
4.4. Smooth Sequences
4.5. Stepwise and Smooth Ratios
4.6. Accumulating Generation and Inverse Accumulating Generation Operators
4.7. Randomness of Sequences of Accumulating Generations
4.8. Grey Exponentiality of Accumulating Generations
5. Grey Incidence Analysis
5.1. Introduction
5.2. Grey Incidence Factors and Set of Grey Incidence Operators
5.3. Metric Space
5.4. Axioms and Degrees of Grey Indcidences
5.5. The Absolute Degree of Grey Incidences
5.6. The Relative Degree of Grey Incidences
5.7. The Synthetic Degree of Grey Incidences
5.8. The Order of Grey Incidences
5.9. Preference Analysis
5.10 Practical Applications
6. Grey Clusters and Grey Statistical Evaluations
6.1. Introduction
6.2. Clusters of Grey Incidences
6.3. Clusters with Variable Weights
6.4. Clusters with Fixed Weights
6.5. Grey Statistics
7. Grey Systems Modeling
7.1. The Thought of Five-Step-Modeling
7.2. Grey Differential Equations
7.3. Model: GM(1,1)
7.4. Model: Remnant GM(1,1)
7.5. Model Group of Type GM(1,1)
7.6. GM(1,N) and GM(0,N)
7.7. GM(2,1) and Verhulst Model
7.8. G-E Combined Models
8. Grey Prediction
8.1. Test of Grey Prediction Models
8.2. Predictions of Sequences
8.3. Interval Predictions
8.4. Disaster Predictions
8.5. Seasonal Disaster Predictions
8.6. Stock-Market-Like Predictions
8.7. Systems Predictions
8.8. Practical Applications
9. Grey Decisions
9.1. Introduction
9.2. Grey Target Decisions
9.3. Grey Incidence Decisions
9.4. Grey Development Decisions
9.5. Grey Statistical Decisions
9.6. Grey Cluster Decisions
9.7. Multiple-Target-Situation Decisions with a Synthesized Target
9.8. Grey Stratified Decisions
10. Grey Programming
10.1. Introduction
10.2. Linear Programming Models with Grey Parameters
10.3. Grey Linear Programming of Prediction Type
10.4. Several Theorems on Positioned Solutions of LPGP
10.5. Satisfactory Solutions of Grey Linear Programming
10.6. Quasi-Optimal Solutions of Grey Linear Programming
10.7. Grey 0-1 Programming
10.8. Grey Nonlinear Programming without Constraints
10.9. Grey Nonlinear Programming with Constraints
11. Grey Control
11.1. Introduction
11.2. Grey Linear Control Systems
11.3. Grey Transfer Functions and Special Links
11.4. Matrices of Grey Transfer Functions
11.5. Control with Abandonment
11.6. Control of Grey Incidences
11.7. Control of Grey Predictions
11.8. Practical Applications
12. Numerical Computations of Commonly Used Models
12.1. Elementary Functions
12.2. Major Prediction Models
12.3. Major Decision-Making Models
Appendix
References
Index
General Systems Theory -- Approaches and Applications
Edited by Yi Lin and Yonghao Ma, 334+ vi pages.
Copyrighted by IIGSS 1995
ISSN: 1078-6236 Papercover (US$29.95.00 + shipping and handling $15.00, express mail $10 extra