Grey Systems: Theory and Applications

Keith William Hipel (University of Waterloo, Waterloo, Canada and Centre for International Governance Innovation, Waterloo, Canada)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 20 October 2011



Hipel, K.W. (2011), "Grey Systems: Theory and Applications", Grey Systems: Theory and Application, Vol. 1 No. 3, pp. 274-275.



Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited

Professors Sifeng Liu and Yi Lin have written another pioneering book on the important topic of grey systems. In 2006, the same authors wrote the well‐received book entitled Grey Information: Theory and Practical Applications which was also published by Springer‐Verlag. I am pleased to say that their second book on Grey Systems constitutes a significant expansion and improvement of their previous fine book. Accordingly, if you already possess a copy of the 2006 book, you can make a worthwhile academic investment by obtaining a copy of their recent book in order to be cognizant of the latest ideas and advancements in the crucial field of grey systems.

The question that naturally arises is why grey systems are of such great import at this point in history. The answer is quite straightforward: many challenging problems facing society consist of interconnected complex systems of systems exhibiting high uncertainty and having few measurements. For example, in order to effectively combat climate change, one must understand as much as possible the complex interactions among natural systems such as atmospheric, oceanic, geological, and hydrological systems, with societal systems including energy production, industrial, agricultural, and city systems. The deep uncertainty involved with these interconnected systems of systems and their potential emergent behavior, coupled with a dearth of observations, mean that formal tools for handling this uncertainty are in high demand. Fortunately, an arsenal of mathematically based methodologies and techniques have been developed over the years: a rich variety of probabilistic‐based tools, fuzzy sets founded by Lotfi Zadeh, rough sets started by Z. Pawlak, information‐gap modeling perfected by Yakov Ben‐Haim, uncertainty theory developed by Baoding Liu, and grey systems established by Julong Deng in 1982. The foregoing and other approaches to describing uncertainty are based upon different axioms and are thereby highly complementary for tackling a wide variety of uncertain situations.

Grey systems are purposefully designed for modeling uncertain systems, or systems of systems, problems having small samples and low‐quality information. Grey systems are capable of dealing with partially known information through generating, excavating, and extracting useful information from what is available. How this is accomplished is explained in‐depth in the timely grey systems book of Professors Liu and Lin.

In their contemporary textbook, Liu and Lin systematically present the theory and practice of grey systems. In fact, the excellent ideas and applications contained in their book are based upon the authors' many years of developing theoretical concepts, applying their methods to real world applications, testing and refining their new techniques with actual data, carrying out stimulating research with their students and colleagues, teaching their students about their exciting work, and delivering research papers at international conferences around the globe. Their comprehensive book contains the latest theoretical and applied advances created by the authors and other scholars around the world in order to place the readers at the forefront of international research in grey systems.

The main body of their book contains ten well‐explained and interconnected chapters: “Introduction to grey systems theory”, “Basic building blocks”, “Grey incidence and evaluation”, “Grey systems modeling”, “Discrete grey prediction models”, “Combined grey models”, “Grey models for decision making”, “Grey game models”, “Grey control systems”, and “Introduction to grey systems modeling software”. Moreover, the book includes a computer software package developed for grey systems modeling to permit both researchers and practitioners to use the new methodologies. Their book concludes with three appendices. The first appendix compares grey systems theory and interval analysis while revealing the fact that interval analysis is a part of grey mathematics. The second presents an array of different approaches to studying uncertainties. Finally, the last appendix shows how uncertainties occur using a general systems approach.

The book contains a wealth of mathematical results, techniques and algorithms which are presented by the authors for the first time. These contributions include an axiomatic system of buffer operators and a series of weakening and strengthening operators; axioms for measuring the greyness of grey numbers; general grey incidences (grey absolute incidence, grey relative incidence, grey comprehensive incidence, grey analogy incidence, and grey nearness incidence); discrete grey models; fixed weight grey cluster evaluation; and grey evaluation methods based on triangular whitenization weight functions, multi‐attribute intelligent grey target decision models, applicable range of the G(1,1), grey econometrics (G‐E), grey Cobb‐Douglass (G‐C‐D), grey input‐output (G‐I‐O), and grey game models (G‐G).

In their well‐written book, Drs Liu and Lin do a thorough job in their presentation of many difficult technical concepts. The authors are able to convince the readers of their book regarding the power and usefulness of their new theory by presenting many interesting examples of practical applications to real‐life problems. The challenging practical problems addressed in their book include urban economic planning, downtown traffic design, natural disaster prediction, relative strength evaluation of a state, investment projection of a company, and employee performance evaluation.

The depth and scope of the advancements in grey systems covered in this book, in conjunction with clarity of explanation, make this seminal book attractive to researchers, students, teachers, and practitioners working in many different fields. These areas of endeavor include image processing, video processing, multimedia security, computer vision, machinery, control, agriculture, water resources, medicine, astronomy, earth science, economics, and management. I personally found grey systems useful for accurately forecasting wastewater time series for which there is a scarcity of data. I intend to keep a copy of this valuable book easily accessible in my university office and purchase more copies of the book for use by my students.

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