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The purpose of this paper is to combine the interval grey number algorithm with a project scheduling model, so as to solve the interval grey number based project scheduling problem.

According to the grey system theory, if we could not clearly collect the right value of an activity while obtaining the upper and lower boundaries of the activity duration time, we can find activity duration time as interval grey number. This paper tries to combine interval grey number with project scheduling problem. The general definition of interval grey number was given. And then the linear operations of independent interval grey number and non-independent interval grey number were further defined. Interval grey number based project scheduling model and its algorithm were further proposed. Finally, a numerical case was adopted to test the effectiveness of the proposed method.

The results show that grey project scheduling and grey critical path method could be established under interval grey number measured activities.

Scheduling problem was widely used in project planning and control. This manuscript attempted to combine interval grey number with project scheduling so as to explain the flexible deadline in a special project. It is truly in accordance with the requirements for real applications.

This paper proposed linear operations of independent and non-independent interval grey numbers, and proposed a interval grey number based project scheduling model. Valuable contribution is to combine interval grey numbers with project scheduling and it is meaningful to make a useful strategy in a flexible condition of project scheduling.

The purpose of this paper is to summarize the different types of grey information, explain the mechanism of grey system modeling and reconstruct the framework of grey system theory (GST).

GST has been developed for more than three decades; however, the framework of GST is still in an evolutionary process. This manuscript first explains grey information in detail, and then summarizes a series of grey system models under limited data and poor information. Figures and general steps for different types of grey system models are provided in this paper.

The findings in this paper clearly differentiate between grey information and other uncertainty information. The differences between grey system models and other uncertainty models are clearly explained. In addition, general steps for different grey system models are given which demonstrate the orientation of grey system modeling.

Theoretical framework is very important for developing a new theory. This paper clarified grey information and grey system-based modeling mechanism. It is very useful to understand and explain the systematic framework of GST and it contributes undoubtedly to make GST perfect.

Grey information is explained in terms of limited data and two types of grey numbers. Accordingly, all of the grey system models were divided into limited data-based grey system models and grey number-based grey system models.

This paper aims to investigate the grey scheduling, which is the combination of grey system theory and scheduling problems with uncertain processing time. Based on the interval grey number and its related definitions, properties, and theorems, the single machine scheduling with uncertain processing time and its general forms are studied as the research object. Then several single machine scheduling models are reconstructed, and an actual production case is developed to illustrate the rationality of the research.

In this paper, the authors first summarize the definitions and properties related to interval grey numbers, especially the transitivity of the partial order of interval grey numbers, and give an example to illustrate that the transitivity has a positive effect on the computational time complexity of multiple interval grey number comparisons. Second, the authors redefine the general form of the single machine scheduling problem with uncertain processing time according to the definitions and theorems of interval grey numbers. The authors then reconstruct three single machine scheduling models with uncertain processing time, give the corresponding heuristic algorithms based on the interval grey numbers and prove them. Finally, the authors develop a case study based on the engine test shop of K Company, the results show that the proposed single machine scheduling models and algorithms with uncertain processing time can provide effective guidance for actual production in an uncertain environment.

The main findings of this paper are as follows: (1) summarize the definitions and theorems related to interval grey numbers and prove the transitivity of the partial order of interval grey numbers; (2) define the general form of the single machine scheduling problem with interval grey processing time; (3) reconstruct three single machine scheduling models with uncertain processing time and give the corresponding heuristic algorithms; (4) develop a case study to illustrate the rationality of the research.

In the further research, the authors will continue to summarize more advanced general forms of grey scheduling, improve the theory of grey scheduling and prove it, and further explore the application of grey scheduling in the real world. In general, grey scheduling needs to be further combined with grey system theory to form a complete theoretical system.

It is a fundamental work to define the general form of single machine scheduling with uncertain processing time used the interval grey number. However, it can be seen as an important theoretical basis for the grey scheduling, and it is also beneficial to expand the application of grey system theory in real world.

The purpose of this paper is to summarize progress of grey forecasting modelling, explain mechanism of grey forecasting modelling and classify exist grey forecasting models.

General modelling process and mechanism of grey forecasting modelling is summarized and classification of grey forecasting models is done according to their differential equation structure. Grey forecasting models with linear structure are divided into continuous single variable grey forecasting models, discrete single variable grey forecasting models, continuous multiple variable grey forecasting models and discrete multiple variable grey forecasting models. The mechanism and traceability of these models are discussed. In addition, grey forecasting models with nonlinear structure, grey forecasting models with grey number sequences and grey forecasting models with multi-input and multi-output variables are further discussed.

It is clearly to explain differences between grey forecasting models with other forecasting models. Accumulation generation operation is the main difference between grey forecasting models and other models, and it is helpful to mining system developing law with limited data. A great majority of grey forecasting models are linear structure while grey forecasting models with nonlinear structure should be further studied.

Mechanism and classification of grey forecasting models are very helpful to combine with suitable real applications.

The main contributions of this paper are to classify models according to models' structure are linear or nonlinear, to analyse relationships and differences of models in same class and to deconstruct mechanism of grey forecasting models.

The year 2022 marks the 40th anniversary of the establishment of the grey system theory (GST), which has been widely applied in the engineering field. This paper aims to systematically identify the achievements, hotspots, knowledge structure and emerging trends in this field.

A bibliometrics analysis was conducted on relevant publications retrieved from Web of Science (WoS) using CiteSpace and MapEquation. A statistical analysis of the collected 3,384 papers was completed. Three networks, including a co-occurrence network, cooperation network and co-citation network, were obtained to draw knowledge structure, hotspots and research frontiers.

The top four applied engineering fields are engineering electrical electronics, computer science artificial intelligence, engineering multi-disciplinary and automation control system. In total, 65 countries have engaged in this field, and China has occupied a leading position, with the largest number of articles published and the widest cooperation with other countries. The USA, United Kingdom (UK) and China Taiwan also contribute a lot. The Nanjing University of Aeronautics and Astronautics and Professor Liu Sifeng have a core position in the cooperation network. More hotspots appear in the last ten years. Regarding the emerging trends, the combination of theoretical models and practical engineering problems has attracted more attention. Besides, the application of GST in environment protection and the integration of the GST and intelligent algorithm became more popular.

The comprehensive bibliometrics analysis and visualization demonstration were conducted, presenting the interdisciplinary characteristics, major research topics and research frontiers in this field.

This paper aims to analyze general development trend of China’s population and to forecast China’s total population under the change of China’s family planning policy so as to measure shock disturbance effects on China’s population development.

China has been the most populous country for hundreds of years. And this state will be sustained in the forthcoming decade. Obviously, China is confronted with greater pressure on controlling total scale of population than any other country. Meanwhile, controlling population will be beneficial for not only China but also the whole world. This paper first analyzes general development trend of China’s population total amount, sex ratio and aging ratio. The mechanism for measurement of the impact effect of a policy shock disturbance is proposed. Linear regression model, exponential curve model and grey Verhulst model are adopted to test accuracy of simulation of China’s total population. Then considering the policy shock disturbance on population, discrete grey model, DGM (1, 1), and grey Verhulst model were adopted to measure how China’s one-child policy affected its total population between 1978 and 2015. And similarly, the grey Verhulst model and scenario analysis of economic developing level were further used to forecast the effect of adjustment from China’s one-child policy to two-child policy.

Results show that China has made an outstanding contribution toward controlling population; it was estimated that China prevented nearly 470 million births since the late 1970s to 2015. However, according to the forecast, with the adjustment of the one-child policy, the birth rate will be a little higher, China’s total population was estimated to reach 1,485.59 million in 2025. Although the scale of population will keep increasing, but it is tolerable for China and sex ratio and trend of aging will be relieved obviously.

The approach constructed in the paper can be used to measure the effect of population change under the policy shock disturbance. It can be used for other policy effect measurement problems under shock events’ disturbance.

The paper succeeded in studying the mechanism for the measurement of the post-impact effect of a policy and the effect of changes in China’s population following the revision of the one-child policy. The mechanism is useful for solving system forecasting problems and can contribute toward improving the grey decision-making models.

purpose of this paper is providing a solution for flexible flow shop scheduling problem with uncertain processing time in aeronautical composite lay-up workshop.

A flexible flow scheduling model and algorithm with interval grey processing time is established. First, according to actual needs of composite laminate shop scheduling process, interval grey number is used to represent uncertain processing time, and interval grey processing time measurement method, grey number calculation and comparison rules, grey Gantt chart, and other methods are further applied. Then a flexible flow shop scheduling model with interval grey processing time (G-FFSP) is established, and an artificial bee colony algorithm based on an adaptive neighbourhood search strategy is designed to solve the model. Finally, six examples are generated for simulation scheduling, and the efficiency and performance of the model and algorithm are evaluated by comparing the results.

Results show that flexible flow shop scheduling model and algorithm with interval grey processing time can provide an optimal solution for composite lay-up shop scheduling problems and other similar flow shop scheduling problems.

Uncertain processing time is common in flexible workshop manufacturing, and manual scheduling greatly restricts the production efficiency of workshop. In this paper, combined with grey system theory, an intelligent algorithm is used to solve flexible flow shop scheduling problem to promote intelligent and efficient production of enterprises.

This paper applies and perfects interval grey processing time measurement method, grey number calculation and comparison rules, grey Gantt chart and other methods. A flexible flow shop scheduling model with interval grey processing time is established, and an artificial bee colony algorithm with an adaptive domain search strategy is designed. It provides a comprehensive solution for flexible flow shop scheduling with uncertain processing time.

The cumulative sum (Cusum) operator, also referred to as accumulating generation operator, is the fundamental of grey system models and proves to be successful in various real-world applications. This paper aims to uncover the advantages of the Cusum operator from a parameter estimation perspective, i.e. comparing integral matching with classical gradient matching.

Grey system models are represented as a state space form to investigate the effect of measurement errors on estimation performance; subsequently, gradient matching and integral matching are respectively formulated to estimate parameters from noisy observations and, then, their quantitative relationships are established by using matrix computation tricks.

Extensive simulations, which are conducted on both linear and non-linear models under different sample size and noise level combinations, show that integral matching is superior to gradient matching, and, also the former is less sensitive to measurement error.

This paper explains why the Cusum operator is widely utilized in grey system models, thereby further solidifying the mathematical fundamentals of grey system models.

The purpose of this paper is to propose an uncertainty representation and information measurement method for characterizing grey numbers, estimating their internal laws and solving how to generate them based on available information data in the real world.

This paper attempts to present a new mathematical methodology in the field of grey numbers. The generalized grey number is defined at first with the concept of information elements and information samples. Then, the probability function of a grey number is proposed to describe the internal law of the grey number. By finding the feasible information elements from information samples, the probability calculation method for the true value of a grey number is presented. Finally, some numerical examples and comparisons are carried out to assess the efficiency and performance.

The results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.

Uncertain information is widespread in practical applications. In this manuscript, the grey number is represented and its information is measured through some existing data in discrete or interval forms, which provides a grey information concept that utilizes information elements to represent uncertainty in the real world.

The proposal presents a novel data-driven method to generate a grey number representation from available data rather than the classical whitening weight function constructed from experience, and the dynamic evolution process of a grey number is measured by the increase of information samples.