The book covers up-to-date theoretical and applied advances in grey systems theory from across the world and vividly presents the reader with the overall picture of this new theory and its frontier research. Many of the concepts, models and methods in the book are original by the authors, including simplified form of grey number, general grey number and the operations of grey numbers; the axiomatic system of buffer operators and a series of weakening and strengthening operators; a series of grey relational analysis models, including grey absolute, relative, synthetic, similarity, closeness, negative and three dimension degree, etc.; grey fixed weight clustering model, grey evaluation models based on center-point and end-point mixed possibility functions; original difference grey model (ODGM), even difference grey model (EDGM), discrete grey model (DGM), fractional grey models, self-memory grey models; multi-attribute intelligent grey target decision models, weight vector group with kernel and the weighted comprehensive clustering coefficient vector, and spectrum analysis of sequence operators, etc.
This book will be appropriate as a reference and/or professional book for courses of grey system theory for graduate students or high-level undergraduate students, majoring in areas of science, technology, agriculture, medicine, astronomy, earth science, economics, and management. It can also be utilized by researchers and practitioners in research institutions, business entities, and government agencies.
Author(s): Sifeng Liu, Yingjie Yang, Jeffrey Yi-Lin Forrest
Series: Series on Grey System
Publisher: Springer
Year: 2022
Language: English
Pages: 383
City: Singapore
Series Preface
Foreword by Dr. James M. Tien
Foreword by Dr. Keith William Hipel
Foreword by Dr. Hermann Haken
Foreword by Dr. Robert Vallée
Preface
Acknowledgements
Contents
1 Introduction
1.1 The Scientific Background of the Birth of Grey System Theory
1.2 The Founder of Grey System Theory
1.3 Development of Grey Systems Theory
1.3.1 Building a Basic Team
1.3.2 Establishment of Academic Organizations
1.3.3 Journals and Book Series on Grey System Theory
1.3.4 Grey System Theory Curriculums
1.3.5 Researchers of Grey System Theory Are All Over the World
1.3.6 Papers of Grey Systems Theory Are Growing Rapidly
1.4 Elementary Concepts of Grey System Theory
1.5 Fundamental Principles of Grey System Theory
1.6 Main Contents of Grey System Theory
References
2 Characteristics of Grey System Theory
2.1 A Kind of Poor Data Analysis Method with Strong Penetration
2.2 Characteristics of Uncertain Systems and the Simplicity Principle in Sciences
2.2.1 Incomplete Information
2.2.2 Inaccuracies in Data
2.2.3 The Scientific Principle of Simplicity
2.2.4 Precise Models Suffer from Inaccuracies
2.3 Comparison of Several Uncertainty Methods
2.4 Deep Applications of Grey System Theory in the Fields of Social Science, Natural Science and Engineering Technology
2.4.1 Successful Application of Grey System Theory in the Field of Social Sciences
2.4.2 Deep Application of Grey System Theory in the Field of Natural Science
2.4.3 A Large Number of Applications of Grey System Theory in the Field of Engineering Technology
References
3 Grey Numbers and Their Operations
3.1 Grey Numbers
3.2 The Whitenization of a Grey Number and Degree of Greyness
3.3 Degree of Greyness Defined by Axioms
3.4 The Operations of Interval Grey Numbers
3.5 General Grey Numbers and Their Operations
3.5.1 Reduced Form of Interval Grey Numbers
3.5.2 General Grey Number and Its Reduced Form
3.5.3 Synthesis of Degree of Greyness and Operations of General Grey Numbers
References
4 Sequence Operators and Grey Data Mining
4.1 Introduction
4.2 Systems Under Shocking Disturbances and Buffer Operators
4.2.1 The Trap for Shocking Disturbed System Forecasting
4.2.2 Axioms of Buffer Operators
4.2.3 Properties of Buffer Operators
4.3 Construction of Practically Useful Buffer Operators
4.3.1 Weakening Buffer Operators
4.3.2 Strengthening Buffer Operators
4.3.3 The General Form of Buffer Operator
4.4 Average Operator
4.5 The Quasi-Smooth Sequence and Stepwise Ratio Operator
4.6 Accumulating and Inverse Accumulating Operators
4.7 Exponentiality of Accumulating Sequence
References
5 Grey Relational Analysis Models
5.1 Introduction
5.2 Grey Relational Factors and Set of Grey Relational Operators
5.3 Grey Relational Axioms and Deng’s Grey Relational Analysis Model
5.4 Grey Absolute Relational Degree
5.5 Grey Relative and Synthetic Relational Degree
5.5.1 Relative Grey Relational Degree
5.5.2 Grey Synthetic Relational Degree
5.6 Grey Similarity, Closeness and Three-Dimensional Relational Degree
5.6.1 Grey Relational Analysis Models Based on Similarity and Closeness
5.6.2 Grey Three-Dimension Degree of Relational Degree
5.7 Negative Grey Relational Analysis Models
5.8 Superiority Analysis
5.9 Practical Application
References
6 Grey Clustering Evaluation Models
6.1 Introduction
6.2 Grey Relational Clustering Model
6.3 Common Possibility Functions
6.4 Variable Weight Grey Clustering Model
6.5 Fixed Weight Grey Clustering Model
6.6 Grey Clustering Evaluation Models Based on Mixed Possibility Functions
6.6.1 Grey Clustering Evaluation Model Based on End-Point Mixed Possibility Functions
6.6.2 Grey Clustering Evaluation Model Based on Center-Point Mixed Possibility Functions
6.7 Practical Applications
References
7 Series of GM Models
7.1 Introduction
7.2 The Four Basic Forms of GM(1,1)
7.2.1 The Basic Forms of Model GM(1,1)
7.2.2 Properties and Characteristics of the Basic Model
7.3 Suitable Ranges of Different GM(1,1)
7.3.1 Suitable Sequences of Different GM(1,1)
7.3.2 Applicable Ranges of EGM
7.4 Remnant GM(1,1) Model
7.5 Group of GM(1,1) Models
7.6 The Fractional Grey Model
7.7 The Models of GM(r,h)
7.7.1 The Model of GM(0,N)
7.7.2 The Model of GM(1, N)
7.7.3 The Grey Verhulst Model
7.7.4 The Self-memory Grey Model
7.7.5 The Models of GM(r,h)
7.8 Practical Applications
References
8 Combined Grey Models
8.1 Grey Econometrics Models
8.1.1 Determination of Variables Using the Grey Relational Principles
8.1.2 Grey Econometrics Models
8.2 Combined Grey Linear Regression Models
8.3 Grey Cobb–Douglas Model
8.4 Grey Artificial Neural Network Models
8.4.1 BP Artificial Neural Model and Computational Schemes
8.4.2 Steps in Grey BP Neural Network Modeling
8.5 Grey Markov Model
8.5.1 Grey Moving Probability Markov Model
8.5.2 Grey State Markov Model
8.6 Combined Grey-Rough Model
8.6.1 Rough Membership, Grey Membership and Grey Numbers
8.6.2 Grey Rough Approximation
8.6.3 Combined Grey Clustering and Rough Set Model
8.7 Practical Applications
References
9 Techniques for Grey Systems Forecasting
9.1 Introduction
9.2 Interval Forecasting
9.3 Grey Distortion Forecasting
9.4 Wave Form Forecasting
9.5 System Forecasting
9.5.1 The Five-Step Modeling Process
9.5.2 System Models for Prediction
9.6 Practical Applications
References
10 Grey Models for Decision-Making
10.1 Introduction
10.2 Grey Target Decisions
10.3 Other Approaches to Grey Decision
10.3.1 Grey Relational Decision
10.3.2 Grey Development Decision
10.3.3 Grey Clustering Decision
10.4 Multi-attribute Intelligent Grey Target Decision Model
10.4.1 The Uniform Effect Measure
10.4.2 The Weighted Synthetic Effect Measure
10.5 On Paradox of Rule of Maximum Value and Its Solution
10.5.1 The Weight Vector Group with Kernel
10.5.2 The Weighted Comprehensive Clustering Coefficient Vector
10.5.3 Several Functional Weight Vector Groups with Kernel
10.6 Practical Applications
References
11 Grey Control Systems
11.1 Introduction
11.2 Controllability and Observability of Grey System
11.3 Transfer Functions of Grey System
11.3.1 Grey Transfer Function
11.3.2 Transfer Functions of Typical Links
11.3.3 Matrices of Grey Transfer Functions
11.4 Robust Stability of Grey System
11.4.1 Robust Stability of Grey Linear Systems
11.4.2 Robust Stability of Grey Linear Time-Delay Systems
11.4.3 Robust Stability of Grey Stochastic Linear Time-Delay System
11.5 Several Typical Grey Control Models
11.5.1 Control of Redundancy Removal
11.5.2 Grey Relational Control
11.5.3 Control of Grey Prediction
References
12 Spectrum Analysis of Sequence Operators
12.1 Introduction
12.2 Spectrum Analysis of Time Series Data
12.3 Filtering Effect of Mean Operator and Accumulation Operator
12.3.1 Filtering Effect of Mean Operator
12.3.2 Filtering Effect of Accumulation Operator
12.3.3 Filtering Effect of Series Operator
12.4 Spectrum Analysis of Buffer Operator
References
Appendix Introduction to Grey Systems Modeling Software
A.1 Introduction
A.2 Software Features and Functions
A.3 Main Components
A.4 Operation Guide
A.4.1 The Confirmation System
A.4.2 Using the Software Package
Memorabilia of the Establishment and Development of Grey System Theory (1982–2021)
Farewell to Our Tutor
Bibliography
Index
