1、Grey Theory,付兴民,Necessary introduction,邓聚龙，湖南涟源人,华中科技大学控制科学与工程系教授，博士生导师。兼任英国灰色系统期刊 （JOURNAL OF GREY SYSTEM）主编，荷兰国际期刊（Fuzzy Seys & Systems）以及罗马尼亚、德国等国期刊编委。60年代提出“去余控制”理论，1982年提出灰色系统理论。出版专著10部，其中灰色控制系统1988年获国家科技专著二等奖，1995年被中国科技图书总公司评为畅销书。1998年获湖北省科技进步一等奖。至2001年共发表论文216篇。SCI连续三年（1991至1993年）检索。据“中国科学引文数
2、据库”的统计，1996年至1998年邓聚龙教授的灰色系统理论被引用533次，居全国之先。其论文多次SCI、SA、MR、EI、ISPT检索（其中SCI37次）。在科研方面：80年代先后完成了国家经委、国家计委、山西榆次市、湖北省老河口市等有关灰色系统的多项课题。80至90年代完成国家自然科学基金、“八五”科技攻关及国家教委博士点基金项目共4项。 1986至1998年获省部级以上奖励7次。先后赴法国（宇航中心）、美国（马里兰大学）、台湾（中央大学、大同工学院）进行讲学。“灰色系统”已收入中国大百科全书、系统科学辞典。灰色系统理论及方法已广泛应用于工业、 农业、环境、经济、社会、管理、军事地震、交通
3、、石油等领域。近年来应用灰色系统理论取得了突出的成效。其中黄河三角洲地形灰色预测可获效益30亿元，河北病虫害预报15亿元。,Necessary introduction,刘思峰，男，1955年7月生，河南人。1998年毕业于华中理工大学系统工程专业，获博士学位。担任职务：现任南京航空航天大学经济与管理学院院长、教授、博导。主要从事“灰色系统理论”和“数量经济学”等领域的教学和研究工作。主持、参加国家、省部级课题和国际合作项目50多项；在国际国内学术界期刊发表论文200多篇，其中英文论文60余篇；出版著作16部，其中英文著作2部，分别由美国IIGSS学术出版社和德国Springer-Verlag
4、出版公司出版；论文被SCI,EI,ISTP等国际重要文摘机构收录80余次，论著被国内外学者引用4000余次。获省部级科技成果奖12项，其中一等奖2项，二等奖5项，三等奖5项。2002年获得系统与控制世界组织奖。主持的灰色系统理论和预测方法与技术课程被评为江苏省精品课程，主编的预测方法与技术和应用统计学教材入选国家“十一五”规划教材。他采用灰色系统理论的思想方法和模型技术，消除索洛“余值”中的非技术进步因素，建立了一种新的技术进步测度模型G-C-D模型，在一定程度上解决了技术进步测度中一个长期悬而未决的问题。,THE SCIENTIFIC BACKGROUND FOR APPEARANCE OF
5、 GREY SYSTEMS THEORY,At the end of the 1940s, there appeared general systems theory,information theory, cybernetics and operations research.During the 1950s and the 1960s, systems dynamics and thetheory of dissipative structures have been put forwarded.During the 1970s, there appeared one by one suc
6、h new transfield and interfiled theories of systems science as thesynergetics, catastrophe theory, hypercycle theory, geneticalgorithms, chaos theory and fractal theory, etc.When people investigating a systems, due to both theexistence of internal and external disturbances and the limitation of our
7、understanding, the available information tendsto contain various kinds of uncertainty and noises. Along with the development of science and technology and the progress of the mankind, our understanding of uncertainties of systems has been gradually deepened and the research of uncertain systems has
8、reached at a new height. During the second half of the 20th century, in the areas of systems science and systems engineering, the seemingly non-stoppable emergence of various theories and methodologies of unascertained systems has been a great scene. For instance, L. A. Zadeh established fuzzy mathe
9、matics in the 19 60s, Julong Deng developed grey systems theory and,THE SCIENTIFIC BACKGROUND FOR APPEARANCE OF GREY SYSTEMS THEORY,Z. Pawlak advanced rough set theory in the 1980s, etc. All these works represent some of the most important efforts in the research of uncertain systems of this time pe
10、riod. From different angles, these works provide the theories and methodologies for describing and dealing with uncertain information.The grey systems theory, established by Julong Deng in1982, is a new methodology that focuses on the study of problems involving small samples and poor informaion. It
11、 deals with uncertain systems with partially known information through generating, excavating, and extracting useful information from what is available. So, systems operational behaviors and their laws of evolution can be correctly described and effectively monitored. In the natural world, uncertain
12、 systems with small samples and poor information exist commonly. That fact determines the wide range of applicability of grey systems theory.,THE DEVELOPMENT HISTORY AND CURRENT STATE OF GREY SYSTEMS THEORY,In 1982, Systems & Control Letters, an international journal by North-Holland, published the
13、first paper in grey systems theory, “The Control Problems of Grey Systems,“ by Julong Deng. In the same year, the Journal of Huazhong University of Science and Technology published the first paper, also by Julong Deng, on grey systems theory in Chinese language. The publication of these papers signa
14、led the official appearance of the cross disciplinary grey systems theory. As soon as these works appeared, they immediately caught the attention of many scholars and scientific practitioners from across the world. Numerous well-known scientists strongly supported the validity and livelihood of such
15、 research. Many young scholars actively participated in the investigation of grey systems theory. With great enthusiasm these young men and women carried thetheoretical aspects of the theory to new heights and employed their exciting results to various fields of application. In particular, successfu
16、l applications in great many fields have won the attention of the international world of learning. Currently, a great number of scholars from China, United States, England, Romania, South Africa, Germany, Japan, Australia, Canada, Poland, Spain, Cuba, Korea, Russia, Turkey, the Netherlands, Iran, an
17、d,THE DEVELOPMENT HISTORY AND CURRENT STATE OF GREY SYSTEMS THEORY,others, have been involved in the research and application of grey systems theory. In 1989, the British journal, The Journal of Grey System, was launched. Currently, this publication is indexed by INSPEC (formerly Science Abstracts)
18、of England, Mathematical Review of the United States, Science Citation Index, and other important indexing agencies from around the world. In 1997, a Chinese publication, named Journal of Grey System, is launched in Taiwan. It is later in 2004 that this publication becomes all English. In 2011, a ne
19、w journal, named Grey Systems: Theory and application, edited by the faculty of Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, launched by Emerald of England. There are currently thousands of different professional journals in the world that have accepted and
20、 published papers in grey systems theory. As of this writing, a journal of the Association for Computing Machinery (USA), Communications in Fuzzy Mathematics (Taiwan), Kybernetes: The International Journal of Systems & Cybernetics, have published special issues on grey systems theory respectively.,C
21、HARACTERISTICS OF UNASCERTAINED SYSTEMS,The fundamental characteristic of uncertain systems is the incompleteness and inadequacy in their information. Due to the dynamics of system evolutions, the biological limitations of the human sensing organs, and the constraints of relevant economic conditions
22、 and technological availabilities, uncertain systems exist commonly. A. Incomplete Information Incompleteness in information is one of the fundamental characteristics of uncertain systems. The situation involving incomplete system information can have the following four cases: The information about
23、the elements (parameters) is incomplete; The information about the structure of the system is incomplete; The information about the boundary of the system is incomplete; The information on the systems behaviors is incomplete.,CHARACTERISTICS OF UNASCERTAINED SYSTEMS,B. Inaccuracies in DataAnother fu
24、ndamental characteristic of uncertain systems is the inaccuracy naturally existing in the available data. The meanings of uncertain and inaccurate are roughly the same. They both stand for errors or deviations from the actual data values. From the essence of how uncertainties are caused, they can be
25、 categorized into three types: the conceptual, level, andprediction types. The Conceptual TypeInaccuracies of the conceptual type item from the expression about a certain event, object, concept, or wish. For instance, all such frequently used concepts as “large,“ “small,“ “many,“ “few,“ “high,“ “low
26、,“ “fat,“ thin, “good,“ “bad,“ young, “beautiful,“ etc., are inaccurate due to the lack of clear defmition. It is very difficult to use exact quantities to express these concepts. As a second example, suppose that a job seeker with an MBA degree wishes to get an offer of an annual salary of no less
27、than $150,000. A manufacturing firm plans to control its rate of deficient products to be less than 0.01%. These are all cases of inaccurate wishes.,CHARACTERISTICS OF UNASCERTAINED SYSTEMS,2) The Level TypeThis kind of inaccuracy of data is caused by a change in the level of research or observation
28、. The available data, when seen on the level of the system of concern, that is the macroscopic level, or on the level of the whole, or in broad outline level of cognitive, might be accurate. However, when they are seen on a lower level, that is a microscopic level or a partial localized level of the
29、 system, they generally become inaccurate. For example, the height of a person can be measured accurately to the unit of centimeters or millimeters. However, if the measurement has to be accurate to the level of one ten-thousandth micron, the earlier accurate reading will become extremely inaccurate
30、. 3) The Prediction Type (The Estimation Type) Because it is difficult to completely understand the laws of evolution, prediction of the future tends to be inaccurate. For instance, it is estimated that two years from now, the GDP of a certain specified area will surpass $10 billion; it is estimated
31、 that,CHARACTERISTICS OF UNASCERTAINED SYSTEMS,a certain bank will attract as much savings from individual residents in an amount between $70 billion to $90 billion for the year in 2015; it is predicted that in the coming years the temperature in Nanjing during the month of October will not go beyon
32、d 30 C; etc. All these examples provide the uncertain numbers of the prediction type. In statistics, it is often the case that samples are collected to estimate the whole. So, many statistical data are inaccurate. As a matter of fact, no matter what method is used, it is very difficult for anyone to
33、 obtain the absolutely accurate (estimated) value. When we draw out plans for the future and make decisions about what course of action to take, we in general have to rely on predictions and estimates which are not completely accurate.,ELEMENTARY CONCEPTS AND FUNDAMENTAL PRINCIPLES OF GREY SYSTEMS,A
34、. Elementary Concepts of Grey SystemsMany social, economic, agricultural, industrial, ecological,biological, etc., systems are named by considering the features of classes of the research objects, while grey systems are labeled using the color of the systems of concern.In the theory of control, peop
35、le often make use of colors to describe the degree of clearness of the available information.For instance, Ashby refers the objects with unknown internal information to as black boxes. This terminology has been widely accepted in the scientific community. For example, as a society moves toward democ
36、racy, the citizens gradually demand more information regarding the formation of policies and more in depth meaning of the policies. That is, the citizens want to have an increased degree of transparency. We use “black“ to indicate unknown information, “white“ the completely known information, and “g
37、rey“ the partially known and partially unknown information. Accordingly, the systems with completely known information will be regarded as white, those systems with completely unknown information black, and the systems with partially known information and partially unknown information will be seen a
38、s grey.,ELEMENTARY CONCEPTS AND FUNDAMENTAL PRINCIPLES OF GREY SYSTEMS,At this junction, we need to pay attention to the difference between “systems“ and “boxes.“ Usually, “boxes“ are used when one does not pay much attention on or does not attempt to utilize the information regarding the interior w
39、hile focusing on the external characteristics. In this case, the researcher generally investigates the properties and characteristics of the object through analyzing the input-output relation. Other the other hand, “systems“ are employed to indicate the study of the objects structure and functions t
40、hrough analyzing the existing organic connections between the object, relevant factors, and its environment and the related laws of change.The research objects of grey systems theory consist of such uncertain systems that they are known only partially with small samples and poor information. The the
41、ory focuses on the generation and excavation of the partially known information to materialize the accurate description and understanding of the material world.Incompleteness in information is the fundamental meaning of being “grey.“ From different angles and in varied situations, the meaning of “gr
42、ey“ can be expanded or stretched. For this end, see the details in Table I.,TABLE I. EXTENSIONS OF THE CONCEPT OF “GREY“,ELEMENTARY CONCEPTS AND FUNDAMENTAL PRINCIPLES OF GREY SYSTEMS,B. Fundamental Principles o/Grey SystemsIn the process of establishing the grey systems theory, Professor Julong Den
43、g discovered and extracted the following fundamental principles of grey systems. It is readily for the reader to see that these principles contain intrinsic philosophical intensions. Axiom 1 (Principle of informational differences).“Difference“ implies the existence of information. Each piece of inf
44、ormation must carry some kind of “difference“. Axiom 2 (Principle of Non-Uniqueness). The solution to any problem with incomplete and indeterminate information is not unique. Axiom 3 (Principle of Minimal Information). One characteristic of grey systems theory is that it makes the most and best use
45、of the available “minimal amount of information.“ Axiom 4 (Principle of Recognition Base). Information is the foundation on which people recognize and understand (nature). Axiom 5 (Principle of New Information Priority). The function of new pieces of information is greater than that of old pieces of
46、 information. Axiom 6 (Principle of Absolute Greyness).“Incompleteness“ of information is absolute.,MAIN COMPONENTS OF GREY SYSTEMS THEORY,Through nearly thirty years of development, grey systems theory has been built up as a newly emerging scientific discipline with its very own theoretical structu
47、re consisting of systems analysis, evaluation, modeling, prediction, decision-making, control, and techniques of optimization. Its main contents contain Grey numbers and algebraic system, grey matrices, grey equations, etc., constitute the foundation of grey systems theory. In terms of the theoretic
48、al beauty and completeness of the theory, there are still a lot of problems left open in this area. The sequence operators mainly include buffer operators (weakening buffer operators, strengthening operators), mean generation operators, stepwise ratio generators, accumulating generators, inverse acc
49、umulating generators, etc. Grey incidence analysis refers such materials as grey incidence axioms, degree of grey incidence, generalized degree of grey incidence (absolute degree, relative degree, synthetic degree), the degrees of grey incidence based on either similar visual angles or nearness visu
50、al angles, grey incidence order, superiority analysis, and others. Grey cluster evaluation focuses on such contents as grey variable weight clustering, grey fixed weight clustering, cluster evaluations based on (center-point or end-point) triangular whitenization weight functions, and other related materials.,
