Liu / Yang / Forrest Grey Data Analysis

Methods, Models and Applications
1. Auflage 2017
ISBN: 978-981-10-1841-1
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 351 Seiten

Reihe: Computational Risk Management

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. 

Autoren/Hrsg.

Liu, Sifeng

Yang, Yingjie

Forrest, Jeffrey

Inhaltsverzeichnis

1;Foreword I;6
2;Foreword II;8
3;Foreword III;11
4;Foreword IV;13
5;Preface;15
6;Acknowledgements;17
7;Contents;19
8;About the Authors;24
9;Abstract;27
10;1 Introduction to Grey Systems Research;28
10.1;1.1 Appearance and Growth of Grey Systems Research;28
10.2;1.2 Development History and Current State;29
10.3;1.3 Characteristics of Uncertain System;32
10.3.1;1.3.1 Incomplete Information;32
10.3.2;1.3.2 Inaccuracies in Data;33
10.3.3;1.3.3 The Scientific Principle of Simplicity;34
10.3.4;1.3.4 Precise Models Suffer from Inaccuracies;35
10.4;1.4 Comparison of Several Studies of Uncertain Systems;37
10.5;1.5 Most Actively Studied Uncertain Systems Theories;38
10.6;1.6 Elementary Concepts of Grey System;40
10.7;1.7 Fundamental Principles of Grey Systems;41
11;2 The Grey Systems Theory Framework;44
11.1;2.1 Grey Models and Framework;44
11.2;2.2 The Thinking, Models and Framework of Grey Systems Theory;45
11.2.1;2.2.1 Grey Numbers and Its Operations;45
11.2.2;2.2.2 The Grey Sequence Operator;46
11.2.3;2.2.3 The Grey Prediction Models;47
11.2.4;2.2.4 Grey Incidence Analysis Models;48
11.2.5;2.2.5 Grey Clustering Evaluation Models;49
11.2.6;2.2.6 Grey Decision-Making Models;51
11.2.7;2.2.7 Combined Grey Models;52
11.2.8;2.2.8 Grey Control Models;52
11.3;2.3 The New Framework and Main Components of Grey Systems Theory;53
12;3 Grey Numbers and Their Operations;56
12.1;3.1 Grey Numbers;56
12.2;3.2 The Whitenization of a Grey Number and Degree of Greyness;57
12.3;3.3 Degree of Greyness Defined by Axioms;60
12.4;3.4 The Operations of Interval Grey Numbers;62
12.5;3.5 General Grey Numbers and Their Operations;64
12.5.1;3.5.1 Reduced Form of Interval Grey Numbers;64
12.5.2;3.5.2 General Grey Numbers and Their Reduced Form;65
12.5.3;3.5.3 Synthesis of Degree of Greyness and Operations of General Grey Numbers;67
13;4 Sequence Operators and Grey Data Mining;71
13.1;4.1 Introduction;71
13.2;4.2 Systems Under Shocking Disturbances and Buffer Operators;73
13.2.1;4.2.1 The Trap for Shocking Disturbed System Forecasting;73
13.2.2;4.2.2 Axioms that Define Buffer Operators;74
13.2.3;4.2.3 Properties of Buffer Operators;75
13.3;4.3 Construction of Practically Useful Buffer Operators;76
13.3.1;4.3.1 Weakening Buffer Operators;76
13.3.2;4.3.2 Strengthening Buffer Operators;80
13.3.3;4.3.3 The General Form of Buffer Operator;81
13.4;4.4 Average Operator;83
13.5;4.5 The Quasi-Smooth Sequence and Stepwise Ratio Operator;84
13.6;4.6 Accumulating and Inverse Accumulating Operators;86
13.7;4.7 Exponentiality of Accumulating Generation;88
14;5 Grey Incidence Analysis Models;92
14.1;5.1 Introduction;92
14.2;5.2 Grey Incidence Factors and Set of Grey Incidence Operators;94
14.3;5.3 Degrees of Grey Incidences Model;97
14.4;5.4 Absolute Degree of Grey Incidence Model;101
14.4.1;5.4.1 Relative and Synthetic Degree of Grey Incidence Models;106
14.4.1.1;5.4.1.1 Relative Degree of Grey Incidence Model;106
14.4.1.2;5.4.1.2 Synthetic Degree of Grey Incidence Model;109
14.4.2;5.4.2 Similarity, Closeness and Three-Dimensional Degree of Grey Incidence Models;110
14.4.2.1;5.4.2.1 Grey Incidence Models Based on Similarity and Closeness;110
14.4.2.2;5.4.2.2 Three-Dimension Degree of Grey Incidence Models;114
14.5;5.5 Superiority Analysis;117
14.5.1;5.5.1 Practical Application;124
15;6 Grey Clustering Evaluation Models;129
15.1;6.1 Introduction;129
15.2;6.2 Grey Incidence Clustering Model;131
15.3;6.3 Variable Weight Grey Clustering Model;134
15.4;6.4 Fixed Weight Grey Clustering Model;141
15.5;6.5 Grey Clustering Evaluation Models Based on Mixed Possibility Functions;145
15.5.1;6.5.1 Grey Clustering Evaluation Model Based on End-Point Mixed Possibility Functions;145
15.5.2;6.5.2 Grey Clustering Evaluation Model Based on Center-Point Mixed Possibility Functions;151
15.6;6.6 Practical Applications;155
16;7 Series of GM Models;164
16.1;7.1 Introduction;164
16.2;7.2 The Four Basic Forms of GM (1, 1);165
16.2.1;7.2.1 The Basic Forms of Model GM (1, 1);165
16.2.2;7.2.2 Properties and Characteristics of the Basic Model;168
16.3;7.3 Suitable Ranges of Different GM (1, 1);172
16.3.1;7.3.1 Suitable Sequences of Different GM (1, 1);172
16.3.2;7.3.2 Applicable Ranges of EGM;180
16.4;7.4 Remnant GM (1,1) Model;183
16.5;7.5 Group of GM (1, 1) Models;188
16.6;7.6 The Models of GM (r, h);192
16.6.1;7.6.1 The Model of GM (0, N);192
16.6.2;7.6.2 The Model of GM (1, N);194
16.6.3;7.6.3 The Grey Verhulst Model;196
16.6.4;7.6.4 The Models of GM (r, h);199
16.7;7.7 Practical Applications;201
17;8 Combined Grey Models;205
17.1;8.1 Grey Econometrics Models;205
17.1.1;8.1.1 Determination of Variables Using the Principles of Grey Incidence;205
17.1.2;8.1.2 Grey Econometrics Models;206
17.2;8.2 Combined Grey Linear Regression Models;209
17.3;8.3 Grey Cobb-Douglas Model;212
17.4;8.4 Grey Artificial Neural Network Models;213
17.4.1;8.4.1 BP Artificial Neural Model and Computational Schemes;213
17.4.2;8.4.2 Steps in Grey BP Neural Network Modeling;214
17.5;8.5 Grey Markov Model;216
17.5.1;8.5.1 Grey Moving Probability Markov Model;216
17.5.2;8.5.2 Grey State Markov Model;217
17.6;8.6 Combined Grey-Rough Model;219
17.6.1;8.6.1 Rough Membership, Grey Membership and Grey Numbers;219
17.6.2;8.6.2 Grey Rough Approximation;221
17.6.3;8.6.3 Combined Grey Clustering and Rough Set Model;224
17.7;8.7 Practical Applications;225
18;9 Techniques for Grey Systems Forecasting;230
18.1;9.1 Introduction;230
18.2;9.2 Interval Forecasting;232
18.3;9.3 Grey Disaster Forecasting;236
18.4;9.4 Wave Form Forecasting;240
18.5;9.5 System Forecasting;242
18.5.1;9.5.1 The Five-Step Modeling Process;242
18.5.2;9.5.2 System Models for Prediction;243
18.6;9.6 Practical Applications;244
19;10 Grey Models for Decision-Making;248
19.1;10.1 Introduction;248
19.2;10.2 Grey Target Decisions;250
19.3;10.3 Other Approaches to Grey Decision;255
19.3.1;10.3.1 Grey Incidence Decision;255
19.3.2;10.3.2 Grey Development Decision;260
19.3.3;10.3.3 Grey Clustering Decision;262
19.4;10.4 Multi-attribute Intelligent Grey Target Decision Model;262
19.4.1;10.4.1 The Uniform Effect Measure;263
19.4.2;10.4.2 The Weighted Synthetic Effect Measure;265
19.5;10.5 The Paradox of Rule of Maximum Value and Its Solution;269
19.5.1;10.5.1 The Weight Vector Group of Kernel Clustering;270
19.5.2;10.5.2 The Weighted Coefficient Vector of Kernel Clustering for Decision-Making;271
19.5.3;10.5.3 Several Functional Weight Vector Groups of Kernel Clustering;273
19.6;10.6 Practical Applications;274
20;11 Grey Control Systems;277
20.1;11.1 Introduction;277
20.2;11.2 Controllability and Observability of Grey System;278
20.3;11.3 Transfer Functions of Grey System;280
20.3.1;11.3.1 Grey Transfer Function;280
20.3.2;11.3.2 Transfer Functions of Typical Links;281
20.3.3;11.3.3 Matrices of Grey Transfer Functions;285
20.4;11.4 Robust Stability of Grey System;286
20.4.1;11.4.1 Robust Stability of Grey Linear Systems;286
20.4.2;11.4.2 Robust Stability of Grey Linear Time-Delay Systems;289
20.4.3;11.4.3 Robust Stability of Grey Stochastic Linear Time-Delay System;291
20.5;11.5 Typical Grey Controls;296
20.5.1;11.5.1 Control with Abandonment;296
20.5.2;11.5.2 Control of Grey Incidence;297
20.5.3;11.5.3 Control of Grey Prediction;298
21;12 Introduction to Grey Systems Modeling Software;304
21.1;12.1 Introduction;304
21.2;12.2 Software Features and Functions;305
21.3;12.3 Main Components;307
21.4;12.4 Operation Guide;309
21.4.1;12.4.1 The Confirmation System;309
21.4.2;12.4.2 Using the Software Package;310
22;Farewell to Our Tutor;319
23;References;321
24;Index;345