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The purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.

Firstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.

The model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.

Due to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.

The main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.

The statistical report published by the Iranian Social Security Organization in 2012 showed that, of all industries, the construction industry is associated with the highest number of work-related accidents. Furthermore, as this sector contains a large human workforce, identification of the factors contributing to the occurrence of such accidents is vital. The paper aims to discuss these issues.

Furthermore, as this sector contains a large human workforce, identification of the factors contributing to the occurrence of such accidents is vital. In the present study, such factors were initially identified, after which the most important of these, managerial factors, were selected. Subsequently, the identification of the causes of the managerial factors was carried out with the use of the fault tree analysis (FTA) method and application of OR and AND entries.

Since it is difficult to determine the probability of occurrence of events in this industry with certainty, and because gray numbers (numbers of which the exact value is unknown, and which represent uncertain information) have a strong relationship with human expressions, the probability of occurrence of the main undesired events was also evaluated using the gray numbers as input entries, in addition to ranking the probability of occurrence of intermediate events.

The findings revealed that FTA using gray numbers is a useful and effective tool in risk assessment.

The purpose of this paper is to determine the project completion time and cost under non-deterministic conditions using interval gray numbers (IGNs).

The earned value management (EVM) method based on the IGN has been developed.

The EVM method based on the IGN has been verified by a numerical example that can be applied to construction projects.

The EVM method, based on the gray numbers, reduces the budget and time shortage risk. Also, using this method, the managers would not be restricted to provide very exact values in their progress reports in the non-deterministic conditions.

One notable and significant point in all projects during the execution process is to estimate the project completion time and cost. However, non-deterministic conditions for both planned and actual physical completion percentage of projects have not been considered for predicting the project completion time and cost in the literature. Therefore, the novelty of this paper is the prediction of project completion time and cost under non-deterministic conditions using IGN.

The purpose of this paper is to research attribute reduction and decision making by gray dual‐information, taking into account the attribute reduction of attribute decision unknown for the interval gray numbers.

The authors obtain the attribute weights considering the consistency of experts’ judgment matrixes and the decision matrixes with gray information. They propose some experts’ attribute reduction ideas based on interval gray numbers of rough set. With the help of experts’ decision information, they consider attribute uncertainty ratio and attribute value ratio to reduce attribute. Finally, a numerical example shows its feasibility.

Some experts’ attribute reduction ideas are proposed based on interval gray numbers of rough set. With the help of experts’ decision information, attribute uncertainty ratio and attribute value ratio to reduce attribute can be considered.

Attribute reduction is keeping classified information systems under the same conditions and deleting redundant and irrelevant or unimportant attributes in order to solve the problem of decision making. This paper considers the attribute reduction based on gray dual‐information.

In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods.

This paper establishes a new gray model (GM) (1,N) prediction model based on the new kernel and degree of grayness sequences under the case that the interval gray number distribution information is known. First, the new kernel and degree of grayness sequences of the interval gray number sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval gray number sequence. Finally, the upper and lower bounds of the interval gray number are deduced based on the calculation formulas of the kernel and degree of grayness.

To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction model established in this paper has better prediction effect and accuracy.

This paper improves the traditional GM(1,N) prediction model and establishes a new GM(1,N) prediction model in the case of the known distribution information of the interval gray number of the smog pollutants concentrations data.

Gray code is a code with the property that there is one and only one bit‐change between any two neighboring numbers. An algorithm for generating gray codes is presented. It turns out that there are other codes which have the same characteristics as gray codes. We call this class of codes generalized gray code (GGC). More precisely, a GGC is a code which has both the reflective property and the unit distance property. Algorithms for generating n‐bit GGC from the (n – 1)‐bit GGC are presented with illustrative examples. It is found that the number of n‐bit GGC is equal to 2n times the number of (n – 1)‐bit GGC. GGC generation trees are used to find GGC. Shows that GGC may be used in the two cases: where 1: gray code cannot be used, and as 2: member of the GGC is better suited than the gray code. Deduces that through the use of GGC, we have more choices than using just gray codes, and that we may obtain better results in terms of fan‐in, fan‐out, propagation delays, power consumption, or other related constraints in designing digital systems. The results obtained in this paper may also have useful applications in implementing special logic functions such as fuzzy threshold functions or fuzzy symmetric functions.

The classification of aircraft failures has been a significant part of functional hazard analysis (FHA). Aiming at the shortcomings of the traditional FHA method in the evaluation of aircraft risk, the purpose of this paper is to put forward a new approach by combining the gray comprehensive relation calculation method in the gray system theory with the traditional FHA in order to deal with the problem of “little data, poor information.”

This paper combines FHA, 1–9-scale method and gray relation analysis. At first, aircraft failure scenarios are chosen and data from experts are collected; then gray system theory is applied to find the relevance of such scenarios. Finally, the classification according to relevance is determined.

In the past, “little data, poor information” made it difficult for researchers to implement FHA. In this paper, the authors manage to deal with the problem of “poor information” and provide an approach to find the seriousness of aircraft failure.

Due to the use of expert-evaluating methods, the classification of failures is still a little subjective and can be improved in this area. In the future, the method can be improved from the perspective of combining FMEA to analyze more complex indicators or using multisource heterogeneous solutions to solve fuzzy numbers, probabilities, gray numbers and indicators that cannot be assigned.

The paper uses FHA to divide the failure state and establishes a gray evaluation model of the aircraft failure state classification to verify the relevant method. Some aircraft safety design requirements are used to check the safety hazards of the aircraft during the design process, and to provide rational recommendations for the functional design of the aircraft.

Improving the safety of aircraft is undoubtedly of great practical significance and has become a top priority in the development of the civil aviation industry. In this paper, the FHA method and the failure state of the aircraft are studied. The original FHA method is innovated by using the gray system theory applicable to the poor information state. Therefore, to some extent, this study has significance for improving the safety of civil aircraft flight, ensuring people’s travel safety and enhancing the society’s trust in civil aviation.

The main innovation of this paper is integrating the FHA method and the gray system theory. This study calculates the comprehensive relation degree of each failure under different flight stages, and uses FHA to divide the failure state, and finally establishes a gray evaluation model of the aircraft failure state classification to analyze the different conditions of the landing gear brake system, so that it improves the present situation, and the problem with the character of “little data, poor information” can be addressed better.

The purpose of this paper is to propose a new MCDM method called ranking based on optimal points (RBOP).

By employing two abstract groups of alternatives as the optimum alternatives and an optimal alternative, in order to offer the most desirable alternative, RBOP imitates human behavior in the decision-making process. RBOP policy is to find the best alternative through measuring alternatives distances from optimum alternatives and optimal alternative, thus, the best alternative must be sitting on the closest distance to its optimum points and the closest distance to the optimal points simultaneously.

In this paper, the author introduced a ten-step gray form of RBOP which is applied in a case of buying running shoes and results compared to the existing MCDM methods. Results showed the considerable differences.

Generally, in order to select the best alternative(s), and to aid decision makers (DMs) to make better decisions for the real-world problems, MCDM methods evaluate a number of alternatives via a number of criteria through the proposed mathematical algorithms. Frequently, for the direct impact of the DMs on the decision-making process, MCDM methods have inflexible algorithms. They only allow DMs to make an impact on the criteria analysis. The inflexibility emerges as a problem when perfect information is available for DMs and MCDM final results are not desirable. The process of the new method completely depends on DMs’ decisions, their interpretation of the periphery and their personal impressions. Hence, the output of RBOP is not necessarily the best alternative, but it offers the most desirable alternative to DM.

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 Grey System Theory (GST) is an emerging area of research within artificial intelligence. Since its founding in 1982, it has seen a lot of multidisciplinary applications. In just a short period, it has garnered some considerable strengths. Based on the 1987–2021 data collected from the Web of Science (WoS), the current study reports the advancement of the GST.

Research papers utilizing the GST in the fields of economics and education were retrieved from the Web of Science (WoS) platform using a set of predetermined keywords. In the final stage of the process, the papers that underwent analysis were manually chosen, with selection criteria based on the information presented in the titles and abstracts.

The study identifies prominent authors, institutions, publications and journals closely associated with the subject. In terms of authors, two major clusters are identified around Liu SF and Wang ZX, while the institution with the highest number of publications is Nanjing University of Aeronautics and Astronautics. Moreover, significant keywords, trends and research directions have been extracted and analyzed. Additionally, the study highlights the regions where the theory holds substantial influence.

The study is subject to certain limitations stemming from factors such as the language employed in the chosen literature, the papers included within the Web of Science (WoS) database, the designation of works categorized as “articles” in the database, the specific selection of keywords and keyword combinations, and the meticulous manual process employed for paper selection. While the manual selection process itself is not inherently limiting, it demands a greater investment of time and meticulous attention, contributing to the overall limitations of the study.

The significance of the study extends not only to scholars and practitioners but also to readers who observe the development of emerging scientific disciplines.

The analysis of trends revealed a growing emphasis on the application of GST in diverse domains, including supply chain management, manufacturing and economic development. Notably, the emergence of COVID-19 as a new research focal point among GST scholars is evident. The heightened interest in COVID-19 can be attributed to its global impact across various academic disciplines. However, it is improbable that this interest will persist in the long term, as the pandemic is gradually brought under control.