Grey Systems Analysis
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Grey Systems Analysis
This open access book is the 2nd edition involving the update on data, methods and models of Grey Systems. It covers up-to-date theoretical and applied advances in grey systems 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 author, including kernel, degree of greyness of grey number, simplified form of grey number, general grey number and the operation system; the axiomatic system of buffer operators and a series of weakening and strengthening buffer operators; a series of grey relational analysis models, including grey absolute, relative, synthetic, similarity, closeness, negative, three dimension, and grey relational analysis model for cross-sequences, 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 weighted intelligent grey target decision models, kernel weight vector group and the weighted comprehensive clustering coefficient vector, and spectrum analysis of sequence operators, etc. The revision includes: (1) Added new achievements made in recent years, such as the moving average denoise operator, a series of negative grey relational models, grey relational model for cross-sequences, standard uncertainty numbers and their operations, adaptive Grey Prediction Models and so on; (2) Important data related to the development of grey system theory has been updated; (3) Research reviews have been added to each chapter, and a large number of references have been added; (4)Updated application examples of commonly used models and methods. This book will be appropriate as a reference and/or textbook for courses of grey system theory for graduate students or high level undergraduate students, majoring in various fields of natural sciences, social sciences and engineering technology. It can also be utilized by researchers and technicians in research institutions, business entities, and government agencies.
Grey Systems
Due to inherent limitations in human sensing organs, most data collected for various purposes contain uncertainties. Even at the rare occasions when accurate data are available, the truthful predictions derived on the data tend to create chaotic consequences. So, to effectively process and make sense out of available data, we need methods to deal with uncertainty inherently existing inside the data. The intent of this monograph is to explore the fundamental theory, methods, and techniques of practical application of grey systems theory, initiated by Professor Deng Julong in 1982. This volume presents most of the recent advances of the theory accomplished by scholars from around the world. From studying this book, the reader will not only acquire an overall knowledge of this new theory but also be able to follow the most current research activities. All examples presented are based on practical applications of the theory when urgent real-life problems had to be addressed. Last but not the least, this book concludes with three appendices. The first one compares grey systems theory and interval analysis while revealing the fact that interval analysis is a part of grey mathematics. The second appendix presents an array of different approaches of studying uncertainties. And, the last appendix shows how uncertainties appear using general systems approach.
Grey Data Analysis
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