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This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey matrix and grey linear programming plays an important role in establishing a grey computational system.

Starting from the fact that missing information often appears in complex systems, and therefore that true values of elements are uncertain when the authors construct a matrix, as well as calculate its inverse. However, the authors can get their ranges, which are called the number-covered sets, by using grey computational rules. How to get the matrix-covered set of inverse grey matrix became a typical approach. In this paper, grey linear programming was explained in detail, for the point of grey meaning and the methodology to calculate the inverse grey matrix can successfully solve grey linear programming.

The results show that the ranges of grey value of inverse grey matrix and grey linear programming can be obtained by using the computational rules.

Because the matrix and the linear programming have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey matrix and grey linear programming may have great potential application in real world. The methodology realizes the feasibility to control the complex system under uncertain situations.

The paper successfully obtained the ranges of uncertain inverse matrix and linear programming by using grey system theory, when the elements of matrix and the coefficients of linear programming are intervals and the results enrich the contents of grey mathematics.

This paper attempts to establish the conceptional and computational systems of grey determinant and apply it to solve n grey equations with n grey linear equations, which can be viewed as the important parts of grey mathematics.

Starting from the fact that missing information often appears in complex systems, the true values of elements when constructing a determinant and of coefficients when solving n equations with n linear equations cannot be obtained, so they are uncertain. However, their ranges can be obtained by using correct investigation methods. The uncertain elements and coefficients are grey and their ranges are number‐covered sets. On the basis of the results of Li and Wang, the paper systematically proposes the definition system of grey determinant and n grey linear equations, and utilizes the computational rules of grey determinant to solve the n grey equations with n grey linear equations. Some numerical examples are computed to illustrate the results in this paper.

The results show that the ranges of grey value of grey determinant and grey solutions of grey equations with n grey linear equations can be obtained by using computational rules proposed.

Because the determinant and the linear equations have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey determinant and grey linear equations may have great potential application in the real world. The method realizes the feasibility of system analysis under uncertain situations.

The paper succeeds in providing systematic results of computation of uncertain determinant and n linear equations by using grey systems theory and enriches the contents of grey mathematics.

The purpose of this paper is to simplify the computation of parameter estimation in the grey linear regression model and solve the problem that the development coefficient could not be computed in some sequence data, such as short‐term traffic flow.

Starting from the limitation that can be identified in the equation and analyzing the range using the method to estimate parameters, this paper researches the modelling mechanism and the other forms which are equivalent with the original form. At the same time, this paper gives an estimation method and gets the relationship in various forms and the relationship between the model and GM(1,1) model.

For the grey linear regression model, there exists a new method of parameter identification and three other forms as follows: the original form, the Whitenization equation and the connotation form.

The method of parameter identification exposed in the paper expanded the scope of the application of the grey linear regression model, and it can be used to model and forecast the urban road short‐time traffic flow.

This paper has solved some complicated problems such as the parameter estimation computation in the grey linear regression model. In addition, three kinds of representation forms of the model and its relationship between the model and GM(1,1) have also been presented. Finally, its application of the model in a short‐term traffic flow prediction has shown its superiority.

This paper describes the use of grey system theory in mathematical programming problems. In particular, the linear programming problem, which is one of the most widely used mathematical programming problems, with grey interval and grey forecasting are developed. The adaptability of both these linear programming problems is rather satisfactory.

The purpose of this paper is to address and overcome the problem that a single prediction model cannot accurately fit a data sequence with large fluctuations.

Initially, the grey linear regression combination model was put forward. The Discrete Grey Model (DGM)(1,1) model and the multiple linear regression model were then combined using the entropy weight method. The grain yield from 2010 to 2015 was forecasted using DGM(1,1), a multiple linear regression model, the combined model and a GM(1,N) model. The predicted values were then compared against the actual values.

The results reveal that the combination model used in this paper offers greater simulation precision. The combination model can be applied to the series with fluctuations and the weights of influencing factors in the model can be objectively evaluated. The simulation accuracy of GM(1,N) model fluctuates greatly in this prediction.

The combined model adopted in this paper can be applied to grain forecasting to improve the accuracy of grain prediction. This is important as data on grain yield are typically characterised by large fluctuation and some information is often missed.

This paper puts the grey linear regression combination model which combines the DGM(1,1) model and the multiple linear regression model using the entropy weight method to determine the results weighting of the two models. It is intended that prediction accuracy can be improved through the combination of models used within this paper.

The proposed model was capable of being used in both promoting safety performance level and evaluating and ranking safety units. The paper aims to discuss these issues.

Managers must be able to determine positive impacts of safety programmes on the organisation and level of goal achievement and information access about performance of safety units. Since uncertain judgements of decision makers can be hardly estimated by numerical values, in this paper, based on grey system theory, a method was proposed for evaluating performance of safety units which was done using qualitative criteria of safety performance in an uncertain environment by one of the newest developed theory. This method used concept of grey theory to convert verbal variables into interval grey numbers; in the quantitative method, degree of grey possibility was imported.

The results showed that the most important performance indicator in the field of safety in inter-urban transportation management included specialized safety training, safety auditing, hazard identification and risk evaluation, employees’ health monitoring, solid waste management and management review.

This model could be extended for the whole safety issues and can be used as a simple and efficient method to evaluate performance of safety units in metro company of all the cities in order to determine their weaknesses and introduce the applied control strategies.

The paper aims to analyze some properties of GM(1,1,β) model based on the principle that the grey GM(1,1) model parameters are grey and adjustable.

At first, according to the principle that grey GM(1,1) model parameters are grey and adjustable, and the GM(1,1,β) model with parameter packet is put forward. Second, some properties of the GM(1,1,β) model are discussed, and the applicable region of the GM(1,1,β) model is given based on the grey differential equation of the GM(1,1,β) model. At last, the background value coefficient's calculation formula and optimization algorithm of the GM(1,1,β) model are also given. A numeric example is also computed in the last part of the paper.

The result of the study shows that the application scope of the GM(1,1,β) model is (−8,+8).

The GM(1,1,β) model provides the theoretical basis for the GM(1,1) model's optimization and can hence forecast its precision.

The paper succeeds in realizing the GM(1,1) model's application scope (−2,+2) is broadened to (−8,+8).

The purpose of this paper is to extend an approach to solve linear programming problems with grey data and variables, based on a developed multi‐objective programming approach.

The proposed approach to generally solve the grey linear programming problems is based on the notion of order relation between interval grey numbers. This notion is applied to cascade the grey objective function to a bi‐objective problem based on the objective function of the original problem. The same approach is taken to transform grey constraints to a set of corresponding linear constraints. Finally, the obtained multi‐objective model can be solved by any existing methods in the literature.

One of the shortcomings of previous approaches to solve grey linear programming problems was that they required the grey coefficients of objective function to be both side negative or positive. The approach proposed here does not have such a requirement and guarantees the feasibility of solutions.

A different approach is developed in the paper that can be used to solve grey linear programming problems in general form. The method relaxes the limitation of existing approaches.

The purpose of this paper is to build a linear time-varying discrete Verhulst model (LTDVM), to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations.

The methodology of the paper is by the light of discrete thoughts and countdown to the original data sequence.

The research of this model manifests that LTDVM is unbiased on the “s” sequential simulation.

The example analysis shows that LTDVM embodies simulation and prediction with high precision.

This paper is to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations. Meanwhile, the research of this model manifests that LTDVM is unbiased on the “s” sequential simulation.