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The purpose of this paper is to introduce the elementary concepts and fundamental principles of grey systems and the main components of grey systems theory. Also to discuss the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science.

The characteristics of unascertained systems including incomplete information and inaccuracies in data are analysed and four uncertain theories: probability statistics, fuzzy mathematics, grey system and rough set theory are compared. The scientific principle of simplicity and how precise models suffer from inaccuracies are also shown.

The four uncertain theories, probability statistics, fuzzy mathematics, grey system and rough set theory are examined with different research objects, different basic sets, different methods and procedures, different data requirements, different emphasis, different objectives and different characteristics.

The scientific principle of simplicity and how precise models suffer from inaccuracies are shown. So, precise models are not necessarily an effective means to deal with complex matters, especially in the case that the available information is incomplete and the collected data inaccurate.

The elementary concepts and fundamental principles of grey systems and the main components of grey systems theory are introduced briefly. The reader is given a general picture of grey systems theory as a new method for studying problems where partial information is known, partial information is unknown; especially for uncertain systems with few data points and poor information.

Many factors affect the emergence and development of crop diseases and insect pests. Traditional methods for investigating this subject are often difficult to employ and produce limited data with considerable uncertainty. The purpose of this paper is to predict the annual degree of cotton spider mite infestations by employing grey theory.

The authors established a GM(1,1) model to forecast mite infestation degree based on the analysis of historical data. To improve the prediction accuracy, the authors modified the grey model using Markov chain and BP neural network analyses. The prediction accuracy of the GM(1,1), Grey-Markov chain, and Grey-BP neural network models was 84.31, 94.76, and 96.84 per cent, respectively.

Compared with the single grey forecast model, both the Grey-Markov chain model and the Grey-BP neural network model had higher forecast accuracy, and the accuracy of the latter was highest. The improved grey model can be used to predict the degree of cotton spider mite infestations with high accuracy and overcomes the shortcomings of traditional forecasting methods.

The two new models were used to estimate mite infestation degree in 2015 and 2016. The Grey-Markov chain model yielded respective values of 1.27 and 1.15, whereas the Grey-BP neural network model yielded values 1.4 and 1.68; the actual values were 1.5 and 1.8.

The improved grey model can be used for medium- and long-term predictions of the occurrence of cotton spider mites and overcomes problems caused by data singularity and fluctuation. This research method can provide a reference for the prediction of similar diseases.

Given the effects of natural and social factors, data on both the supply and demand sides of electricity will produce obvious seasonal fluctuations. The purpose of this article is to propose a new dynamic seasonal grey model based on PSO-SVR to forecast the production and consumption of electric energy.

In the model design, firstly, the parameters of the SVR are initially optimized by the PSO algorithm for the estimation of the dynamic seasonal operator. Then, the seasonal fluctuations in the electricity demand data are eliminated using the dynamic seasonal operator. After that, the time series after eliminating of the seasonal fluctuations are used as the training set of the DSGM(1, 1) model, and the corresponding fitted, and predicted values are calculated. Finally, the seasonal reduction is performed to obtain the final prediction results.

This study found that the electricity supply and demand data have obvious seasonal and nonlinear characteristics. The dynamic seasonal grey model based on PSO-SVR performs significantly better than the comparative model for hourly and monthly data as well as for different time durations, indicating that the model is more accurate and robust in seasonal electricity forecasting.

Considering the seasonal and nonlinear fluctuation characteristics of electricity data. In this paper, a dynamic seasonal grey model based on PSO-SVR is established to predict the consumption and production of electric energy.

The aim of this paper is to solve the problem of low accuracy of traditional fatigue crack growth (FCG) prediction methods.

The GMSVR model was proposed by combining the grey modeling (GM) and the support vector regression (SVR). Meanwhile, the GMSVR model parameter optimal selection method based on the artificial bee colony (ABC) algorithm was presented. The FCG prediction of 7075 aluminum alloy under different conditions were taken as the study objects, and the performance of the genetic algorithm, the particle swarm optimization algorithm, the n-fold cross validation and the ABC algorithm were compared and analyzed.

The results show that the speed of the ABC algorithm is the fastest and the accuracy of the ABC algorithm is the highest too. The prediction performances of the GM (1, 1) model, the SVR model and the GMSVR model were compared, the results show that the GMSVR model has the best prediction ability, it can improve the FCG prediction accuracy of 7075 aluminum alloy greatly.

A new prediction model is proposed for FCG combined the non-equidistant grey model and the SVR model. Aiming at the problem of the model parameters are difficult to select, the GMSVR model parameter optimization method based on the ABC algorithm was presented. the results show that the GMSVR model has better prediction ability, which increase the FCG prediction accuracy of 7075 aluminum alloy greatly.

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.

Prediction problems raised in uncertain environments require different solution approaches such as grey prediction models, which consider uncertainty in information and also enable the use of small data sets. The purpose of this paper is to investigate the comparative performances of grey prediction models (GM) and Markov chain integrated grey models in a demand prediction problem.

The modeling process of grey models is initially described, and then an integrated model called the Grey-Markov model is presented for the convenience of applications. The analyses are conducted on a monthly demand prediction problem to demonstrate the modeling accuracies of the GM (1,1), GM (2,1), GM (1,1)-Markov, and GM (2,1)-Markov models.

Numerical results reveal that the Grey-Markov model based on GM (2,1) achieves better prediction performance than the other models.

It is thought that the methodology and the findings of the study will be a significant reference for both academics and executives who struggle with similar demand prediction problems in their fields of interest.

The novelty of this study comes from the fact that the GM (2,1)-Markov model has been first used for demand prediction. Furthermore, the GM (2,1)-Markov model represents a relatively new approach, and this is the second paper that addresses the GM (2,1)-Markov model in any area.

The rise in malaria deaths discloses a decline of global malaria eradication that shows that control measures and fund distribution have missed its right of way. Therefore, the purpose of this paper is to study and evaluate the impact and control of malaria on the independent states of the Sub-Saharan African (SSA) region over the time period of 2010–2017 using Deng’s Grey incidence analysis, absolute degree GIA and second synthetic degree GIA model.

The purposive data sampling is a secondary data from World Developmental Indicators indicating the incidence of new malaria cases (per 1,000 population at risk) for 45 independent states in SSA. GIA models were applied on array sequences into a single relational grade for ranking to be obtained and analyzed to evaluate trend over a predicted period.

Grey relational analysis classifies West Africa as the highly infectious region of malaria incidence having Burkina Faso, Sierra Leone, Ghana, Benin, Liberia and Gambia suffering severely. Also, results indicate Southern Africa to be the least of all affected in the African belt that includes Eswatini, Namibia, Botswana, South Africa and Mozambique. But, predictions revealed that the infection rate is expected to fall in West Africa, whereas the least vulnerable countries will experience a rise in malaria incidence through to the next ten years. Therefore, this study draws the attention of all stakeholders and interest groups to adopt effective policies to fight malaria.

The study is a pioneer to unravel the most vulnerable countries in the SSA region as far as the incidence of new malaria cases is a concern through the use of second synthetic GIA model. The outcome of the study is substantial to direct research funds to control and eliminate malaria.

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 understand the trend and forecast the number of tourists from different regions of the world to Mauritius.

The paper adopts two grey system models, the even model GM(1,1) and the non-homogeneous discrete grey model (NDGM), to forecast the total number of international tourism to Mauritius and its structure from different regions tourist arrivals to Mauritius for the next three years. Grey system theory models were used to account for uncertainties and the dynamism of the tourism sector environment. The two models were applied as a comparison to obtain more reliable forecasting figures.

The results demonstrate that both of the grey system models can be successfully applied with high accuracy for Mauritian tourism prediction, and also the number of tourist arrivals to Mauritius shows a continued augmentation for the upcoming years.

Forecasting is meaningful since the Government of Mauritius, private companies or any concerned authority can adopt the forecasting methods exposed in this paper for the development of the tourism sector through managerial and economic decision making.

Mauritius is a charming travel destination. Through this paper, it can be seen that future tourism travel to Mauritius has been successfully predicted based on previous data. Moreover, it seems that the grey system theory models have not been utilised yet as forecasting tools for the tourism sector of Mauritius as opposed to other countries such as China and Taiwan.

The purpose of this paper is to propose a new method based on nonlinear least squares (NLS) for solving the parameters of nonlinear grey Bernoulli model (NGBM(1,1)) and to verify the proposed model using the case of employee demand prediction of high-tech enterprises in China.

First of all, minimising the square sum of fitting error of grey differential equation of NGBM(1,1) is taken as the optimisation target and the parameters of classic grey model (GM(1,1)) are set as the initial value of parameter vector. Afterwards, the structural parameters and power exponents are solved by using the Gauss-Newton iteration algorithm so as to calculate the parameters of NGBM(1,1) under given rules for ceasing the algorithm. Finally, by taking the employee demand of high-tech enterprises in the state-level high-tech industrial development zone in China as examples, the validity of the new method is verified.

The results show that the parameter estimation algorithm based on the NLS method can effectively identify the power exponents of NGBM(1,1) and therefore can favourably adapt to the nonlinear fluctuations of sequences. In addition, the algorithm is superior to the GM(1,1) model, grey Verhulst model, and Quadratic-Exponential smoothing algorithm in terms of the simulation and prediction accuracy.

Under the framework of solving parameters based on NLS, various aspects of NGBM(1,1) remain to be further investigated including background value, initial condition and variable structural modelling methods.

The parameter estimation algorithm based on NLS can effectively identify the power exponent of NGBM(1,1) and therefore it can favourably adapt to the nonlinear fluctuation of sequences.

According to the basic principle of NLS, a new method for solving the parameters of NGBM(1,1) is proposed by using the Gauss-Newton iteration algorithm. Moreover, by conducting the modelling case about employees demand in high-tech enterprises in China, the effectiveness and superiority of the new method are verified.