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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.

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 grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM 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.

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.

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.

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.

The purpose of this paper is to advance new rules about operations of grey numbers.

The paper first puts forward the definitions of basic element of grey number and general grey number. The operation axiom, operation rules of general grey numbers and a new algebraic system for general grey numbers are built based on the “kernel” and the degree of greyness of grey numbers.

Up to now, the operation of general grey numbers has been transformed to operation of real numbers; thus, the difficult problem for set up operation of general grey numbers has been solved to a certain degree.

The method exposed in the paper can be used to integrate information from a different source. The operation of general grey numbers could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers. The operation system of general grey numbers also opened a new passageway for research on grey input‐output and grey programming, etc.

The new conception of a basic element of grey number and general grey number was given for the first time in this paper. The novel operation rules of general grey numbers were also constructed.

The purpose of this paper is to present the terms of grey numbers and its operations.

The definitions of elementary terms about grey numbers and its operations are presented one by one.

The reader could know the basic explanation about the important terms about grey numbers and its operations from this paper.

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

This paper aims to present a new model of marketing analysis that is capable of using the embedded knowledge that sits untapped in the history of marketing thought to solve contemporary marketing problems – the conceptual-historical analytical research model (CHARM).

This paper outlines the evolution of historical analysis methods (HAM), along with critiques and enhancements of the prior processes offered by Savitt (1980), Nevett (1991) and Golder (2000). From these foundations, the paper outlines the components of the model of historical analysis, detailing the development of the analytical template design. It also details the four-step process of engaging structured revisits of past knowledge for contemporary problem-solving.

The CHARM for problem-solving in marketing is a knowledge-gathering system that informs marketing decisions addressing contemporary problems. This is achieved through the use of embedded knowledge from a corpus of historical texts.

This paper provides a method for future researchers to apply for replicable examination of historical texts and to assist intercoder reliability for multi-author history projects through the application of structured templates.

The CHARM for problem-solving in marketing is a knowledge-gathering system that informs marketing decisions addressing contemporary problems. This is achieved through the use of embedded knowledge from a corpus of historical texts.

The CHARM process applies a systematic protocol for engaging qualitative sources for historical analysis through preset data collection templates, structured analysis frameworks and definitional understanding templates for improved replicability. This paper presents a new model of approaching historical analysis through a problem-solving lens, whereby historical sources become the foundations for the solution to a problem, rather than just the literature review that identifies the presence of gap.

To consider aspects of a theory of systemic construction by discussing two concepts which will assist in our understanding of the surrounding world which it is considered is made of both systemic and non‐systemic entities.

Considers how these entities (metasystem, network, transitron etc.) can be conceived and defined. Systemic frames notions are presented and examples of systems given. Discusses the historic use of the word “system” and systemic thinking and its varieties.

Discovered that on the basis of these concepts, an understanding of the surrounding world can be achieved which is not homogeneous but made of both systemic and non‐systemic entities. These can change when certain systemic properties are reached as well as in their specific degrees in their limitations and paradoxes.

Introduces an original approach to the life support system by proposing concepts that are discussed and defined and that will provide cyberneticians and systemists with a revised view of systemic thinking.

There has been considerable discussion recently about business schools’ shortcomings and how their curriculum should be changed. Many presume discipline-wide agreement that managing is a rational and model-able decision-making practice. But practitioners are not convinced and often suggest rationality-dominated business schools are teaching impractical ideas. The purpose of this paper is to look at this discussion's micro foundations and offers a novel approach that presumes managerial judgment is crucial to firms’ processes and, indeed, is the reason firms exist.

The paper combines discussion of the conceptual nature of firms and managing them with data about business schools’ growth and curriculum evolution.

If we presume firms are rational apparatus for achieving known goals, managing is little more than computing; and if Knightian uncertainty is taken seriously, managerial judgment becomes the core of the analysis. But schools that attempt to train students’ judgment are extraordinarily difficult to manage, especially in the current academic environment.

While many are aware of Knight's influential thinking, it has not yet been brought into a theory of the firm or of managing. The paper works toward a novel theory of the managed firm (TMF) in which management's uncertainty-resolving judgments are key.

Presents the scientific methodology from the enlarged cybernetical perspective that recognizes the anisotropy of time, the probabilistic character of natural laws, and the entry that the incomplete determinism in Nature opens to the occurrence of innovation, growth, organization, teleology communication, control, contest and freedom. The new tier to the methodological edifice that cybernetics provides stands on the earlier tiers, which go back to the Ionians (c. 500 BC). However, the new insights reveal flaws in the earlier tiers, and their removal strengthens the entire edifice. The new concepts of teleological activity and contest allow the clear demarcation of the military sciences as those whose subject matter is teleological activity involving contest. The paramount question “what ought to be done”, outside the empirical realm, is embraced by the scientific methodology. It also embraces the cognitive sciences that ask how the human mind is able to discover, and how the sequence of discoveries might converge to a true description of reality.

The distinction between essence and existence cannot be a distinction in God: in the actual infinite, essence and existence coincide and are one. In it, maximum and minimum coincide. Coincidentia oppositorum is a Latin phrase meaning coincidence of opposites. It is a neo-Platonic term, attributed to the fifteenth-century German scholar Nicholas of Cusa in his essay, Docta Ignorantia. God (coincidentia oppositorum) is the synthesis of opposites in a unique and absolutely infinite being. God transcends all distinctions and oppositions that are found in creatures. The purpose of this paper is to study Cusanus’s thought in respect to infinity (actual and potential), Spinoza’s relationship with Cusanus, and present a mathematical theory of coincidentia oppositorum based on complex numbers.

Mathematical development of a dialectical logic is carried out with truth values in a complex field.

The conclusion is the same as has been made by thinkers and mystics throughout time: the inability to know and understand the idea of God.

The history of the Infinite thus reveals in both mathematics and philosophy a development of increasingly subtle thought in the form of a dialectical dance around the ineffable and incomprehensible Infinite. First, the authors step toward it, reaching with their intuition beyond the limits of rationality and thought into the realm of the paradoxical. Then, they step back, struggling to express their insight within the limited scope of reason. But the Absolute Infinite remains, at the border of comprehensibility, inviting them with its paradoxes, to once again step forward and transcend the apparent division between finite and Infinite.

This piece takes issue with the deployment of Trotsky’s idea of uneven and combined development (UCD) in the Anglophone discipline of International Relations (IR). It argues that this strand of thought makes a theory out of what is really a theorem (a deduction from an axiom), whilst forgetting about the original, actual theory of which it was part, Leon Trotsky’s theory of permanent revolution. IR U&CD, marketed in the discipline as International Historical Sociology (IHS), posits ‘the international’ as the field to which ‘the theory’ must be applied in order to open it up to social theorisation. This is analogous to the late-19th-century subjective turn in social science in which reality is presented as unfathomable, and rationality is merely subjective, an attribute of individual ‘actors’. ‘The international’ in this sense may be compared to ‘the market’ in neoclassical economics. Although it presents itself as Marxist, the U&CD/IHS project was part of a regressive conjuncture in Anglo-American, mainstream IR, as transpires from its attempt to position itself close to the ‘English School’ in IR. I conclude with a variation on Trotsky’s original theory, applying it to the ‘permanent counterrevolution’, of which the current war on terror is the latest stage.