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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.

We attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.

In order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.

The results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.

By employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

The purpose of this paper is to establish a maturity evaluation model for the application of construction steel structure welding robotics suitable for the actual situation and specific characteristics of engineering projects in China and then to assess the maturity level of the technology in the application of domestic engineering projects more scientifically.

The research follows a qualitative and quantitative analysis method. In the first stage, the structure of the maturity model is constructed and the evaluation index system is designed by using the ideas of the capability maturity model and WSR methodology for reference. In the second stage, the design of the evaluation process and the selection of evaluation methods (analytic hierarchy process method, multi-level gray comprehensive evaluation method). In the third stage, the data are collected and organized (preparation of questionnaires, distribution of questionnaires, questionnaire collection). In the fourth stage, the established maturity evaluation model is used to analyze the data.

The evaluation model established by using multi-level gray theory can effectively transform various complex indicators into an intuitive maturity level or score status. The conclusion shows that the application maturity of building steel structure welding robot technology in this project is at the development level as a whole. The maturity levels of “WuLi – ShiLi – RenLi” are respectively: development level, development level, between starting level and development level. Comparison of maturity evaluation values of five important factors (from high to low): environmental factors, technical factors, management factors, benefit factors, personnel and group factors.

In this paper, based on the existing research related to construction steel structure welding robot technology, a quantitative and holistic evaluation of the application of construction steel structure welding robot technology in domestic engineering projects is conducted for the first time from a project perspective by designing a maturity evaluation index system and establishing a maturity evaluation model. This research will help the project team to evaluate the application level (maturity) of the welding robot in the actual project, identify the shortcomings and defects of the application of this technology, then improve the weak links pertinently, and finally realize the gradual improvement of the overall application level of welding robot technology for building steel structure.

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.

Grey target decision-making serves as a pivotal analytical tool for addressing dynamic multi-attribute group decision-making amidst uncertain information. However, the setting of bull's eye is frequently subjective, and each stage is considered independent of the others. Interference effects between each stage can easily influence one another. To address these challenges effectively, this paper employs quantum probability theory to construct quantum-like Bayesian networks, addressing interference effects in dynamic multi-attribute group decision-making.

Firstly, the bull's eye matrix of the scheme stage is derived based on the principle of group negotiation and maximum satisfaction deviation. Secondly, a nonlinear programming model for stage weight is constructed by using an improved Orness measure constraint to determine the stage weight. Finally, the quantum-like Bayesian network is constructed to explore the interference effect between stages. In this process, the decision of each stage is regarded as a wave function which occurs synchronously, with mutual interference impacting the aggregate result. Finally, the effectiveness and rationality of the model are verified through a public health emergency.

The research shows that there are interference effects between each stage. Both the dynamic grey target group decision model and the dynamic multi-attribute group decision model based on quantum-like Bayesian network proposed in this paper are scientific and effective. They enhance the flexibility and stability of actual decision-making and provide significant practical value.

To address issues like stage interference effects, subjective bull's eye settings and the absence of participative behavior in decision-making groups, this paper develops a grey target decision model grounded in group negotiation and maximum satisfaction deviation. Furthermore, by integrating the quantum-like Bayesian network model, this paper offers a novel perspective for addressing information fusion and subjective cognitive biases during decision-making.

With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (ε_ij), relative degree of grey incidence (r_ij) or synthetic degree of grey incidence (ρ_ij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.

To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).

It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.

Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.

In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.

This paper aims to build an improved grey panel clustering evaluation model and evaluate the comprehensive development potential of industrial economy, society and ecological environment in the Yangtze River Economic Belt of China. The purpose of this study is to provide some theoretical basis and tool support for management departments and relevant researchers engaged in industrial sustainable development.

This study uses the driving force pressure state impact response analysis framework to build a comprehensive evaluation index system. Based on the center point triangle whitening weight function, it classifies the panel grey clustering of improvement time and index weight.

The results show that there are great differences in the level of industrial ecological development in different regions of the Yangtze River Economic Belt, which further illustrates the scientificity and rationality of the evaluation method proposed in this paper.

Due to the industrial ecological development is in a constantly changing state, and the information is uncertain. Whitening weight function is introduced to represent the complete information of relevant data. The industrial ecological evaluation involves a comprehensive complex system, which belongs to the panel data analysis problem. The improved grey panel clustering evaluation model is applied to grade the industrial ecological development level of the Yangtze River Economic Belt. The results have important guiding significance for the balanced development of industrial ecology in the region.

Due to the industrial ecological development is in a constantly changing state, and the information is uncertain. Whitening weight function is introduced to represent the complete information of relevant data. The industrial ecological evaluation involves a comprehensive complex system, which belongs to the panel data analysis problem. In order to improve the effectiveness of industrial ecological evaluation, the improved grey panel clustering evaluation model is applied to grade the industrial ecological development level of the Yangtze River Economic Belt. The results have important guiding significance for the balanced development of industrial ecology in the region.

the new model proposed in this paper complements and improves the grey clustering analysis theory of panel data, that is, aiming at the subjective limitation of using time degree to determine time weight in panel grey clustering, a comprehensive theoretical method for determining time weight is creatively proposed. Combining the DPSIR (Driving force-Pressure-State-Influence-Response) model model with ecological development, a comprehensive evaluation model is constructed to make the evaluation results more authentic and comprehensive.

Given the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.

First, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.

The study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.

Acknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.

The purpose of this paper is to establish a two-stage grey cloud clustering model under the panel data for the multi-attribute clustering problem with three-parameter interval grey number to evaluation of agricultural drought resistance grade of 18 cities in Henan Province.

The clustering process is divided into two stages. In the first stage: Combining variance and time degree, the time weight optimization model is established. Applying the prospect theory, the index weight optimization model is established. Then, with the help of grey possibility function, the first stage of grey cloud clustering evaluation is carried out. In the second stage: the weight vector group of kernel clustering is constructed, and the grey class of the object is determined. A two-stage grey cloud clustering model under the panel data for the multi-attribute clustering problem is proposed.

This paper indicates that 18 cities in Henan Province are divided into four categories. The drought capacity in Henan province is high in the east and low in the west, high in the south and low in the north and the central region is relatively stable. The drought is greatly affected by natural factors. And the rationality and validity of this model is illustrated by comparing with other methods.

This paper provides a practical method for drought resistance assessment, and provides theoretical support for farmers to grasp the drought information timely and improve the drought resistance ability.

The model in this paper solves the situation of ambiguity and randomness to some extent with the help of grey cloud possibility function. Moreover, the time weight of time degree and variance are used to reduce the volatility and the degree of subjective empowerment. Considering the risk attitude of the decision makers, the prospect theory is applied to make the index weight more objective. The rationality and validity of the model are illustrated by taking 18 cities in Henan Province as examples.