Grey Systems Analysis: Methods, Models and Applications

Description

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.   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