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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.

The purpose of this study is to advance a novel evaluation index system and evaluation approach for ability of older adults in China.

This study constructed a comprehensive older adult ability evaluation index system with 4 primary indicators and 17 secondary indicators. Grey clustering analysis and entropy weight method are combined into a robust evaluation model for the ability of older adults.

The result demonstrates that the proposed grey clustering model is readily available to calculate the disability level of elderly individuals. The constructed index system more comprehensively considers all aspects of the disability of the elderly.

This study provides a quantitative method and a more reasonable index system for the determination of the disability level of the elderly.

The purpose of this work is to construct a grey entropy comprehensive evaluation model to measure the regional green innovation vitality (GIV) of 31 provinces in China.

The traditional grey relational proximity and grey relational similarity degree are integrated into the novel comprehensive grey evaluation framework. The evaluation system of regional green innovation vitality is constructed from three dimensions: economic development vitality, innovative transformation power and environmental protection efficacy. The weights of each indicator are obtained by the entropy weight method. The GIV of 31 provinces in China is measured based on provincial panel data from 2016 to 2020. The ward clustering and K-nearest-neighbor (KNN) algorithms are utilized to explore the regional green innovation discrepancies and promotion paths.

The novel grey evaluation method exhibits stronger ability to capture intrinsic patterns compared with two separate traditional grey relational models. Green innovation vitality shows obvious regional discrepancies. The Matthew effect of China's regional GIV is obvious, showing a basic trend of strong in the eastern but weak in the western areas. The comprehensive innovation vitality of economically developed provinces exhibits steady increasing trend year by year, while the innovation vitality of less developed regions shows an overall steady state of no fluctuation.

The grey entropy comprehensive relational model in this study is applied for the measurement and evaluation of regional GIV, which improves the one-sidedness of traditional grey relational analysis on the proximity or similarity among sequences. In addition, a three-dimensional evaluation system of regional GIV is constructed, which provides the practical guidance for the research of regional development strategic planning as well as promotion paths.

A comprehensive grey entropy relational model based on traditional grey incidence analysis (GIA) in terms of proximity and similarity is proposed. The three-dimensional evaluation system of China's regional GIV is constructed, which provides a new research perspective for regional innovation evaluation and expands the application scope of grey system theory.

The purpose of this paper is to establish a more reasonable evaluation system and model for the development level of rural tourism, and provides a method for quantifying the development level of regional rural tourism.

This paper provides a method for evaluating the development level of rural tourism, constructs an evaluation index system according to the connotation of rural tourism, then calculates the index weight by entropy method, and makes a comprehensive evaluation by grey relational analysis. Taking the development of rural tourism in 11 cities in Jiangxi Province as the research object, the ranking results of 11 cities were obtained by using grey relational analysis.

The overall development level of rural tourism in Jiangxi Province is positive, but the spatial distribution is uneven, showing the characteristics of “low-level aggregation and high-level dispersion”. The barrier model diagnoses that the degree of financial input is the biggest constraint to the development level of rural tourism in Jiangxi Province.

This study puts forward an evaluation model based on entropy weight and grey relational analysis, which is an important supplement to the grey relational analysis method system and has a positive role in promoting the quantitative evaluation of regional rural tourism level.

This study aims to predict China's carbon emission intensity and put forward a set of policy recommendations for further development of a low-carbon economy in China.

In this paper, the Interaction Effect Grey Power Model of N Variables (IEGPM(1,N)) is developed, and the Dragonfly algorithm (DA) is used to select the best power index for the model. Specific model construction methods and rigorous mathematical proofs are given. In order to verify the applicability and validity, this paper compares the model with the traditional grey model and simulates the carbon emission intensity of China from 2014 to 2021. In addition, the new model is used to predict the carbon emission intensity of China from 2022 to 2025, which can provide a reference for the 14th Five-Year Plan to develop a scientific emission reduction path.

The results show that if the Chinese government does not take effective policy measures in the future, carbon emission intensity will not achieve the set goals. The IEGPM(1,N) model also provides reliable results and works well in simulation and prediction.

The paper considers the nonlinear and interactive effect of input variables in the system's behavior and proposes an improved grey multivariable model, which fills the gap in previous studies.

This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

The possibility function-based grey clustering model has evolved into a complete approach for dealing with uncertainty evaluation problems. Existing models still have problems with the choice dilemma of the maximum criteria and instances when the possibility function may not accurately capture the data's randomness. This study aims to propose a multi-stage skewed grey cloud clustering model that blends grey and randomness to overcome these problems.

First, the skewed grey cloud possibility (SGCP) function is defined, and its digital characteristics demonstrate that a normal cloud is a particular instance of a skewed cloud. Second, the border of the decision paradox of the maximum criterion is established. Third, using the skewed grey cloud kernel weight (SGCKW) transformation as a tool, the multi-stage skewed grey cloud clustering coefficient (SGCCC) vector is calculated and research items are clustered according to this multi-stage SGCCC vector with overall features. Finally, the multi-stage skewed grey cloud clustering model's solution steps are then provided.

The results of applying the model to the assessment of college students' capacity for innovation and entrepreneurship revealed that, in comparison to the traditional grey clustering model and the two-stage grey cloud clustering evaluation model, the proposed model's clustering results have higher identification and stability, which partially resolves the decision paradox of the maximum criterion.

Compared with current models, the proposed model in this study can dynamically depict the clustering process through multi-stage clustering, ensuring the stability and integrity of the clustering results and advancing grey system theory.

The purpose of this research is to provide a theoretical framework for complex equipment quality risk evaluation. The primary aim of the framework is to enhance the ability to identify risks and improve risk control efficiency during the development phase.

A novel framework for quality risk evaluation in complex equipment is proposed, which integrates probabilistic hesitant fuzzy set-quality function deployment (PHFS-QFD) and grey clustering. PHFS-QFD is applied to identify the quality risk factors, and grey clustering is used to evaluate quality risks in cases of poor quality information during the development stage. The unfolding function of QFD is applied to simplify complex evaluation problems.

The methodology presents an innovative approach to quality risk evaluation for complex equipment development. The case analysis demonstrates that this method can efficiently evaluate the quality risks for aircraft development and systematically trace back the risk factors through hierarchical relationships. In comparison to traditional failure mode and effects analysis methods for quality risk assessment, this approach exhibits superior effectiveness and reliability in managing quality risks for complex equipment development.

This study contributes to the field by introducing a novel theoretical framework that combines PHFS-QFD and grey clustering. The integration of these approaches significantly improves the quality risk evaluation process for complex equipment development, overcoming challenges related to data scarcity and simplifying the assessment of intricate systems.

In this study, a new neural differential grey model is proposed for the purpose of accurately excavating the evolution of real systems.

For this, the proposed model introduces a new image equation that is solved by the Runge-Kutta fourth order method, which makes it possible to optimize the sequence prediction function. The novel model can then capture the characteristics of the input data and completely excavate the system's evolution law through a learning procedure.

The new model has a broader applicability range as a result of this technique, as opposed to grey models, which have fixed structures and are sometimes over specified by too strong assumptions. For experimental purposes, the neural differential grey model is implemented on two real samples, namely: production of crude and consumption of Cameroonian petroleum products. For validation of the new model, results are compared with those obtained by competing models. It appears that the precisions of the new neural differential grey model for prediction of petroleum products consumption and production of Cameroonian crude are respectively 16 and 25% higher than competing models, both for simulation and validation samples.

This article also takes an in-depth look at the mechanics of the new model, thereby shedding light on the intrinsic differences between the new model and grey competing models.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.