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The purpose of this paper is to develop some grey models to analyze and control the poor information systems, or grey systems.

The grey system theory has been a more widespread application in recent years and the authors have solved many forecast problems of incomplete information with it. However, the establishment of gray control models still needs certain prerequisites.

Based on incomplete information or poor information, by using the viewpoint of the grey system theory and the integral generation operation in this paper, six kinds of grey control models have been established.

The paper offers very useful advice for incomplete (or poor) information control.

The paper is aimed at control engineers and offers a new approach to the optimal choice of information control models.

Classical control theory and modern control theory satisfy the Galilean principle of relativity. If the velocity v of controlled systems is high that is to say, v approaches the velocity of light in vacuo, then the existing control theories must be transformed into relativistic form, i.e. based on relativistic physics, we must reform relativistic control theory, making it satisfy Einstein’s principle of relativity. Based on this, some properties of relativistic control theory are discussed in this paper.

The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.

Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively.

The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space.

The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc.

The purpose of this paper is to explore a new approach to solve the problem of positive and negative offset in the calculation process of integral elements, then propose a series of new grey relational degree model for cross sequences.

The definitions of cross sequences and area elements have been proposed at first. Then the concept of difference degree between sequences has been put forward. Based on the definition of difference degree between sequences, various modified grey relational degree models for cross sequences have been proposed to solve the measurement problem of cross sequence correlation relationships.

(1) The new definition of cross sequences; (2) The area element; (3) Various modified grey relational degree models for cross sequences based on the definition of difference degree between sequences.

The grey relational analysis model of cross sequences is a difficult problem in grey relational analysis. The new model proposed in this article can effectively avoid the calculation deviation of grey relational analysis model for cross sequences, and reasonably measure the correlation between cross sequences. The new model was used to analyse the food consumer price index in Shaanxi Province, clarifying the relationship between different types of food consumer price indices, some interesting results that are not completely consistent with general economic theory were obtained.

The new definition of cross sequences, the area element and various modified grey relational degree models for cross sequences were proposed.

The purpose of this paper is to construct some negative grey relational analysis models to measure the relationship between reverse sequences.

The definition of reverse sequence has been given at first based on analysis of relative position and change trend of sequences. Then, several different negative grey relational analysis models, such as the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model have been put forward based on the corresponding common grey relational analysis models. The properties of the new models have been studied.

The negative grey relational analysis models proposed in this paper can solve the problem of relationship measurement of reverse sequences effectively. All the new negative grey relational degree satisfying the requirements of normalization and reversibility.

The proposed negative grey relational analysis models can be used to measure the relationship between reverse sequences. As a living example, the reverse incentive effect of winning Fields Medal on the research output of winners is measured based on the research output data of the medalists and the contenders using the proposed negative grey relational analysis model.

The definition of reverse sequence and the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model are first proposed in this paper.

The purpose of this paper is to propose a second relational grade based on the general grey relational grade and analyze several of its properties.

Grey system theory. The paper proposes and studies second grey relational grade, establishes second grey relational formula, and studies several characteristics of second grey relational formula.

Proposing a second relational grade proved it could solve the problem of the parallelism partly and weaken relativity of space position.

Until now, the problem of the consistency could not be solved, nor could the problem of the effect which keeps the sequence the same.

The precision of the grey forecasting model could be strengthened if used in the forecasting model.

The general relational grade only thinks over the relation between two sequences but does not involve the relation in one sequence. The second relational grade considers these two, so if the forecasting model is established with it, the model should be more exact.

The purpose of this paper is to present a method to accurately forecast the tendency of the gross amount of energy sources consumption of the country and construct a new kind of algorithm for forecasting that synthesizes the advantages of the grey model, Markov chains, and least square method.

With the application of this new algorithm, this paper have forecasted the trend of the gross amount of energy sources consumption of the country and come to the conclusions that the new algorithm is more precise than the grey model. It is proved that the improved grey‐Markov chain algorithm is effective and can be used by authorities to make decision.

It was found that combining the grey model, Markov chains, and least square method, can be a new algorithm for forecasting the trendency of the gross amount of energy sources consumption.

The new algorithm is only suitable for the short‐term forecast.

The grey forecasting method reflects the overall tendency of primitive data sequence of the gross amount of energy source, and the Markov chain forecasting method reflects the effect of the random fluctuation. The least square method reflects the tendency of increase. The new algorithm is more precise than the grey model.