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The effective prediction of crude oil futures prices can provide a reference for relevant enterprises to make production plans and investment decisions. To the nonlinearity, high volatility and uncertainty of the crude oil futures price, a matrixed nonlinear exponential grey Bernoulli model combined with an exponential accumulation generating operator (MNEGBM(1,1)) is proposed in this paper.

First, the original sequence is processed by the exponential accumulation generating operator to weaken its volatility. The nonlinear grey Bernoulli and exponential function models are combined to fit the preprocessed sequence. Then, the parameters in MNEGBM(1,1) are matrixed, so the ternary interval number sequence can be modeled directly. Marine Predators Algorithm (MPA) is chosen to optimize the nonlinear parameters. Finally, the Cramer rule is used to derive the time recursive formula.

The predictive effectiveness of the proposed model is verified by comparing it with five comparison models. Crude oil futures prices in Cushing, OK are predicted and analyzed from 2023/07 to 2023/12. The prediction results show it will gradually decrease over the next six months.

Crude oil futures prices are highly volatile in the short term. The use of grey model for short-term prediction is valuable for research. For the data characteristics of crude oil futures price, this study first proposes an improved model for interval number prediction of crude oil futures prices.

In order to make full use of the generalized greyness of interval grey number, this paper analyzes the properties and its applications of generalized greyness.

Firstly, the static properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain are analyzed. Then, this paper gives the dynamic properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain and explains the dialectical principle contained in it. Finally, the generalized greyness is used to judge the effectiveness of interval grey number transformation.

The results show that the generalized greyness of interval grey number has relativity, normativity, unity, eternity and conservation. The static and dynamic properties of generalized greyness are the same in the infinite and infinitesimal background domain, while they are different in the bounded background domain. The generalized greyness can be used as an index to judge whether the grey number transformation is greyness or information preservation.

The research shows that the generalized greyness can be used as an index to judge the validity of the grey number transformation and also can be applied in grey evaluation, grey decision-making and grey prediction and so on.

The paper succeeds in realizing the mathematical principle of “white is black”, the “greyness clock-slow effect” of the value domain of interval grey number and the generalized greyness conservation principle, which provides a theoretical basis for the rational use of generalized greyness of interval grey number.

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 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.

Tourism demand forecasting is vital for the airline industry and tourism sector. Combination forecasting has the advantage of fusing several forecasts to reduce the risk of inappropriate model selection for analyzing decisions. This paper investigated the effects of a time-varying weighting strategy on the performance of linear and nonlinear forecast combinations in the context of tourism.

This study used grey prediction models, which did not require that the available data satisfy statistical assumptions, to generate forecasts. A quality-control technique was applied to determine when to change the combination weights to generate combined forecasts by using linear and nonlinear methods.

The empirical results showed that except for when the Choquet fuzzy integral was used, forecast combination with time-varying weights did not significantly outperform that with fixed weights. The Choquet integral with time-varying weights significantly outperformed that with fixed weights for all model combinations, and had a superior forecasting accuracy to those of other combination methods.

The tourism sector can benefit from the use of the Choquet integral with time-varying weights, by using it to formulate suitable strategies for tourist destinations.

Combining forecasts with time-varying weights may improve the accuracy of the predictions. This study investigated incorporating a time-varying weighting strategy into combination forecasting by using CUSUM. The results verified the effectiveness of the time-varying Choquet integral for tourism forecast combination.

Financial performance has been paid attention at an unprecedented level, which can be confirmed as a fact that the quantitative expansion of financial performance evaluation work. The purpose of this study is to propose a more appropriate model for financial performance evaluation under the unbalanced development.

This paper introduces the differentiation criteria to eliminate the deviation caused by the same principle for multiple performance evaluation objects whose development are unbalanced; Then the generalized grey number is adopted to describe the value of performance evaluation index; and the information entropy weight is used to obtain the index weight to reduce the artificial judgment error; Finally, the generalized grey information entropy weight TOPSIS evaluation model is constructed.

Empirical research shows that in the new evaluation model, the differentiated possibility function effectively eliminates the deviation caused by the same principle, the application of information entropy weight reduces the human judgment error, and the value of generalized grey number further enhances the closeness of the results. Moreover, it is also found that in different scenarios, an adaptive performance evaluation model should be selected to match scientifically reasonable results.

The proposed model offers a solution for financial performance evaluation considering unbalanced development among cities. It can be realized by determining the differentiation possibility function matrix, and then the information entropy weight TOPSIS evaluation model can be constructed. This model reflects the actual situation, improves the performance evaluation accuracy, and can be used under similar conditions.

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.

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.

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.

With the rise in wine consumption, accurate wine price forecasts have significantly impacted restaurant and hotel purchasing decisions and inventory management. This study aims to develop a precise and effective wine price point and interval forecasting model.

The proposed forecast model uses an improved hybrid kernel extreme learning machine with an attention mechanism and a multi-objective swarm intelligent optimization algorithm to produce more accurate price estimates. To the best of the authors’ knowledge, this is the first attempt at applying artificial intelligence techniques to improve wine price prediction. Additionally, an effective method for predicting price intervals was constructed by leveraging the characteristics of the error distribution. This approach facilitates quantifying the uncertainty of wine price fluctuations, thus rendering decision-making by relevant practitioners more reliable and controllable.

The empirical findings indicated that the proposed forecast model provides accurate wine price predictions and reliable uncertainty analysis results. Compared with the benchmark models, the proposed model exhibited superiority in both one-step- and multi-step-ahead forecasts. Meanwhile, the model provides new evidence from artificial intelligence to explain wine prices and understand their driving factors.

This study is a pioneering attempt to evaluate the applicability and effectiveness of advanced artificial intelligence techniques in wine price forecasts. The proposed forecast model not only provides useful options for wine price forecasting but also introduces an innovative addition to existing forecasting research methods and literature.