Grey Data Analysis (eBook)

Methods, Models and Applications

Jeffrey Forrest, Sifeng Liu, Yingjie Yang (Autoren)

eBook Download: PDF

2016 | 1st ed. 2017
XXIX, 333 Seiten
Springer Singapore (Verlag)
978-981-10-1841-1 (ISBN)

Infos

This book inclusively and systematically presents the fundamental methods, models and techniques of practical application of grey data analysis, bringing together the authors' many years of theoretical exploration, real-life application, and teaching. It also reflects the majority of recent theoretical and applied advances in the theory achieved by scholars from across the world, providing readers a vivid overall picture of this new theory and its pioneering research activities. 

The book includes 12 chapters, covering the introduction to grey systems, a novel framework of grey system theory, grey numbers and their operations, sequence operators and grey data mining, grey incidence analysis models, grey clustering evaluation models, series of GM models, combined grey models, techniques for grey systems forecasting, grey models for decision-making, techniques for grey control, etc. It also includes a software package that allows practitioners to conveniently and practically employ the theory and methods presented in this book. All methods and models presented here were chosen for their practical applicability and have been widely employed in various research works.

I still remember 1983, when I first participated in a course on Grey System Theory. The mimeographed teaching materials had a blue cover and were presented as a book. It was like finding a treasure: This fascinating book really inspired me as a young intellectual going through a period of confusion and lack of academic direction. It shone with pearls of wisdom and offered a beacon in the mist for a man trying to find his way in academic research. This book became the guiding light in my life journey, inspiring me to forge an indissoluble bond with Grey System Theory.

--Sifeng Liu

Professor Sifeng Liu, PhD., SM IEEE, is an Honorary Fellow of the WOSC, and Senior Fellow of the Marie Curie International Incoming Fellowships of the 7th Research Framework Programme of the European Commission. Sifeng Liu received PhD in systems engineering from Huazhong University of Science and Technology, China, in 1998. Dr. Liu is currently a distinguished professor at Nanjing University of Aeronautics and Astronautics, and a research professor at De Montfort University. He is the founding director of the Institute for Grey Systems Studies, the founding chair of TC of IEEE SMC on Grey Systems, and the founding president of the Grey Systems Society of China.

Professor Yingjie Yang is currently a full Professor of Computational Intelligence at the Centre for Computational Intelligence of De Montfort University, Leicester, UK. He received his BSc (Hons.), MSc and PhD degrees in engineering from Northeastern University, Shenyang, China, in 1987, 1990, and 1994, respectively. He was awarded his PhD degree in computer science at Loughborough University, Loughborough, UK, in 2008. Before joining De Montfort University in 2002, Dr. Yang had worked at Beijing Jiaotong University, Nottingham Trent University and Loughborough University in connection with various research projects.  

Professor Jeffrey Forrest earned his educational degrees in pure mathematics. His PhD degree was granted in 1988 by Auburn University, Alabama; and he did one year of post-doctoral research in statistics at Carnegie Mellon University, Pittsburgh, from 1990 to 1991. Dr. Forrest is currently a specially appointed professor of economics, finance, and systems science at Nanjing University of Aeronautics and Astronautics, a specially appointed professor of mathematics and systems science at National University of Defense Technology, China, and a tenured professor of mathematics at Slippery Rock University of Pennsylvania. Dr. Forrest is a founder and the current president of the International Institute for General Systems Studies (IIGSS), a non-profit organization registered in PA in the mid-1990s. 

Inhalt

Foreword I 6
Foreword II 8
Foreword III 11
Foreword IV 13
Preface 15
Acknowledgements 17
Contents 19
About the Authors 24
Abstract 27
1 Introduction to Grey Systems Research 28
1.1 Appearance and Growth of Grey Systems Research 28
1.2 Development History and Current State 29
1.3 Characteristics of Uncertain System 32
1.3.1 Incomplete Information 32
1.3.2 Inaccuracies in Data 33
1.3.3 The Scientific Principle of Simplicity 34
1.3.4 Precise Models Suffer from Inaccuracies 35
1.4 Comparison of Several Studies of Uncertain Systems 37
1.5 Most Actively Studied Uncertain Systems Theories 38
1.6 Elementary Concepts of Grey System 40
1.7 Fundamental Principles of Grey Systems 41
2 The Grey Systems Theory Framework 44
2.1 Grey Models and Framework 44
2.2 The Thinking, Models and Framework of Grey Systems Theory 45
2.2.1 Grey Numbers and Its Operations 45
2.2.2 The Grey Sequence Operator 46
2.2.3 The Grey Prediction Models 47
2.2.4 Grey Incidence Analysis Models 48
2.2.5 Grey Clustering Evaluation Models 49
2.2.6 Grey Decision-Making Models 51
2.2.7 Combined Grey Models 52
2.2.8 Grey Control Models 52
2.3 The New Framework and Main Components of Grey Systems Theory 53
3 Grey Numbers and Their Operations 56
3.1 Grey Numbers 56
3.2 The Whitenization of a Grey Number and Degree of Greyness 57
3.3 Degree of Greyness Defined by Axioms 60
3.4 The Operations of Interval Grey Numbers 62
3.5 General Grey Numbers and Their Operations 64
3.5.1 Reduced Form of Interval Grey Numbers 64
3.5.2 General Grey Numbers and Their Reduced Form 65
3.5.3 Synthesis of Degree of Greyness and Operations of General Grey Numbers 67
4 Sequence Operators and Grey Data Mining 71
4.1 Introduction 71
4.2 Systems Under Shocking Disturbances and Buffer Operators 73
4.2.1 The Trap for Shocking Disturbed System Forecasting 73
4.2.2 Axioms that Define Buffer Operators 74
4.2.3 Properties of Buffer Operators 75
4.3 Construction of Practically Useful Buffer Operators 76
4.3.1 Weakening Buffer Operators 76
4.3.2 Strengthening Buffer Operators 80
4.3.3 The General Form of Buffer Operator 81
4.4 Average Operator 83
4.5 The Quasi-Smooth Sequence and Stepwise Ratio Operator 84
4.6 Accumulating and Inverse Accumulating Operators 86
4.7 Exponentiality of Accumulating Generation 88
5 Grey Incidence Analysis Models 92
5.1 Introduction 92
5.2 Grey Incidence Factors and Set of Grey Incidence Operators 94
5.3 Degrees of Grey Incidences Model 97
5.4 Absolute Degree of Grey Incidence Model 101
5.4.1 Relative and Synthetic Degree of Grey Incidence Models 106
5.4.1.1 Relative Degree of Grey Incidence Model 106
5.4.1.2 Synthetic Degree of Grey Incidence Model 109
5.4.2 Similarity, Closeness and Three-Dimensional Degree of Grey Incidence Models 110
5.4.2.1 Grey Incidence Models Based on Similarity and Closeness 110
5.4.2.2 Three-Dimension Degree of Grey Incidence Models 114
5.5 Superiority Analysis 117
5.5.1 Practical Application 124
6 Grey Clustering Evaluation Models 129
6.1 Introduction 129
6.2 Grey Incidence Clustering Model 131
6.3 Variable Weight Grey Clustering Model 134
6.4 Fixed Weight Grey Clustering Model 141
6.5 Grey Clustering Evaluation Models Based on Mixed Possibility Functions 145
6.5.1 Grey Clustering Evaluation Model Based on End-Point Mixed Possibility Functions 145
6.5.2 Grey Clustering Evaluation Model Based on Center-Point Mixed Possibility Functions 151
6.6 Practical Applications 155
7 Series of GM Models 164
7.1 Introduction 164
7.2 The Four Basic Forms of GM (1, 1) 165
7.2.1 The Basic Forms of Model GM (1, 1) 165
7.2.2 Properties and Characteristics of the Basic Model 168
7.3 Suitable Ranges of Different GM (1, 1) 172
7.3.1 Suitable Sequences of Different GM (1, 1) 172
7.3.2 Applicable Ranges of EGM 180
7.4 Remnant GM (1,1) Model 183
7.5 Group of GM (1, 1) Models 188
7.6 The Models of GM (r, h) 192
7.6.1 The Model of GM (0, N) 192
7.6.2 The Model of GM (1, N) 194
7.6.3 The Grey Verhulst Model 196
7.6.4 The Models of GM (r, h) 199
7.7 Practical Applications 201
8 Combined Grey Models 205
8.1 Grey Econometrics Models 205
8.1.1 Determination of Variables Using the Principles of Grey Incidence 205
8.1.2 Grey Econometrics Models 206
8.2 Combined Grey Linear Regression Models 209
8.3 Grey Cobb-Douglas Model 212
8.4 Grey Artificial Neural Network Models 213
8.4.1 BP Artificial Neural Model and Computational Schemes 213
8.4.2 Steps in Grey BP Neural Network Modeling 214
8.5 Grey Markov Model 216
8.5.1 Grey Moving Probability Markov Model 216
8.5.2 Grey State Markov Model 217
8.6 Combined Grey-Rough Model 219
8.6.1 Rough Membership, Grey Membership and Grey Numbers 219
8.6.2 Grey Rough Approximation 221
8.6.3 Combined Grey Clustering and Rough Set Model 224
8.7 Practical Applications 225
9 Techniques for Grey Systems Forecasting 230
9.1 Introduction 230
9.2 Interval Forecasting 232
9.3 Grey Disaster Forecasting 236
9.4 Wave Form Forecasting 240
9.5 System Forecasting 242
9.5.1 The Five-Step Modeling Process 242
9.5.2 System Models for Prediction 243
9.6 Practical Applications 244
10 Grey Models for Decision-Making 248
10.1 Introduction 248
10.2 Grey Target Decisions 250
10.3 Other Approaches to Grey Decision 255
10.3.1 Grey Incidence Decision 255
10.3.2 Grey Development Decision 260
10.3.3 Grey Clustering Decision 262
10.4 Multi-attribute Intelligent Grey Target Decision Model 262
10.4.1 The Uniform Effect Measure 263
10.4.2 The Weighted Synthetic Effect Measure 265
10.5 The Paradox of Rule of Maximum Value and Its Solution 269
10.5.1 The Weight Vector Group of Kernel Clustering 270
10.5.2 The Weighted Coefficient Vector of Kernel Clustering for Decision-Making 271
10.5.3 Several Functional Weight Vector Groups of Kernel Clustering 273
10.6 Practical Applications 274
11 Grey Control Systems 277
11.1 Introduction 277
11.2 Controllability and Observability of Grey System 278
11.3 Transfer Functions of Grey System 280
11.3.1 Grey Transfer Function 280
11.3.2 Transfer Functions of Typical Links 281
11.3.3 Matrices of Grey Transfer Functions 285
11.4 Robust Stability of Grey System 286
11.4.1 Robust Stability of Grey Linear Systems 286
11.4.2 Robust Stability of Grey Linear Time-Delay Systems 289
11.4.3 Robust Stability of Grey Stochastic Linear Time-Delay System 291
11.5 Typical Grey Controls 296
11.5.1 Control with Abandonment 296
11.5.2 Control of Grey Incidence 297
11.5.3 Control of Grey Prediction 298
12 Introduction to Grey Systems Modeling Software 304
12.1 Introduction 304
12.2 Software Features and Functions 305
12.3 Main Components 307
12.4 Operation Guide 309
12.4.1 The Confirmation System 309
12.4.2 Using the Software Package 310
Farewell to Our Tutor 319
References 321
Index 345

Produkt-Details

• Erscheint lt. Verlag: 1.9.2016
• Reihe/Serie: Computational Risk Management
• Zusatzinfo: XXIX, 333 p. 59 illus., 19 illus. in color.
• Verlagsort: Singapore
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Datenbanken
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Unternehmensführung / Management
• Schlagworte: buffer operator • General Grey Number • grey cluster evaluation • Grey Control • grey decision-making • Grey Forecasting • grey incidence analysis • Grey system
• ISBN-10: 981-10-1841-3 / 9811018413
• ISBN-13: 978-981-10-1841-1 / 9789811018411