New Progress of Grey System Theory in The New Millennium

Purpose – The purpose of this paper is to summarize the progress in grey system research during 2000- 2015, so as to present some important new concepts, models, methods and a new framework of grey system theory. Design/methodology/approach –The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “Kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of GM(1,1), such as Even Grey Model(EGM), Original Difference Grey Model(ODGM), Even Difference Grey Model(EDGM), Discrete Grey Model(DGM) and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well. Findings –The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper. Practical implications – A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science, and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate. Originality/value –The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section. Keywords Grey systems theory, Operations of grey numbers, Buffer operators, Grey forecasting models, Grey incidence analysis models, Grey cluster evaluation models, Grey decision models, Combined grey models, Grey contro

4th International Probabilistic Workshop: 12th-13th October 2006, Berlin, BAM (Federal Institute for Materials Research and Testing)

Die heutige Welt der Menschen wird durch große Dynamik geprägt. Eine Vielzahl verschiedener Prozesse entfaltet sich parallel und teilweise auf unsichtbare Weise miteinander verbunden. Nimmt man z.B. den Prozess der Globalisierung: Hier erleben wir ein exponentielles Wachstum der internationalen Verknüpfungen von der Ebene einzelner Menschen und bis zur Ebene der Kulturen. Solche Verknüpfungen führen uns zum Begriff der Komplexität. Diese wird oft als Produkt der Anzahl der Elemente eines Systems mal Umfang der Verknüpfungen im System verstanden. In anderen Worten, die Welt wird zunehmend komplexer, denn die Verknüpfungen nehmen zu. Komplexität wiederum ist ein Begriff für etwas unverstandenes, unkontrollierbares, etwas unbestimmtes. Genau wie bei einem Menschen: Aus einer Zelle wächst ein Mensch, dessen Verhalten wir im Detail nur schwer vorhersagen können. Immerhin besitzt sein Gehirn 1011 Elemente (Zellen). Wenn also diese dynamischen sozialen Prozesse zu höherer Komplexität führen, müssen wir auch mehr Unbestimmtheit erwarten. Es bleibt zu Hoffen, dass die Unbestimmtheit nicht existenzielle Grundlagen betrifft. Was die Komplexität der Technik angeht, so versucht man hier im Gegensatz zu den gesellschaftlichen Unsicherheiten die Unsicherheiten zu erfassen und gezielt mit ihnen umzugehen. Das gilt für alle Bereiche, ob nun Naturgefahrenmanagement, beim Bau und Betrieb von Kernkraftwerken, im Bauwesen oder in der Schifffahrt. Und so verschieden diese Fachgebiete auch scheinen mögen, die an diesem Symposium teilnehmen: Sie haben erkannt, das verantwortungsvoller Umgang mit Technik einer Berücksichtigung der Unbestimmtheit bedarf. Soweit sind wir in gesellschaftlichen Prozessen noch nicht. Wünschenswert wäre, dass in einigen Jahren nicht nur Bauingenieure, Maschinenbauer, Mathematiker oder Schiffsbauer an einem solchen Probabilistik- Symposium teilnehmen, sondern auch Soziologen, Politiker oder Manager... (aus dem Vorwort) --- HINWEIS: Das Volltextdokument besteht aus einzelnen Beiträgen mit separater Seitenzählung.PREFACE: The world today is shaped by high dynamics. Multitude of processes evolves parallel and partly connected invisible. For example, the globalisation is such a process. Here one can observe the exponential growing of connections form the level of single humans to the level of cultures. Such connections guide as to the term complexity. Complexity is often understood as product of the number of elements and the amount of connections in the system. In other words, the world is going more complex, if the connections increase. Complexity itself is a term for a system, which is not fully understood, which is partly uncontrollable and indeterminated: exactly as humans. Growing from a single cell, the humans will show latter a behaviour, which we can not predict in detail. After all, the human brain consists of 1011 elements (cells). If the social dynamical processes yield to more complexity, we have to accept more indetermination. Well, one has to hope, that such an indetermination does not affect the basic of human existence. If we look at the field of technology, we can detect, that here indetermination or uncertainty is often be dealt with explicitly. This is valid for natural risk management, for nuclear engineering, civil engineering or for the design of ships. And so different the fields are which contribute to this symposium for all is valid: People working in this field have realised, that a responsible usage of technology requires consideration of indetermination and uncertainty. This level is not yet reached in the social sciences. It is the wish of the organisers of this symposium, that not only civil engineers, mechanical engineers, mathematicians, ship builders take part in this symposium, but also sociologists, managers and even politicians. Therefore there is still a great opportunity to grow for this symposium. Indetermination does not have to be negative: it can also be seen as chance