Non-homogenous Discrete Grey Model Research Articles

Effect of urban traffic-restriction policy on improving air quality based on system dynamics and a non-homogeneous discrete grey model.

With the acceleration of urbanization, traffic congestion and vehicle exhaust pollution are becoming increasingly serious problems. Focusing on the problem of urban pollution from vehicle exhaust, this study used system dynamics to establish an urban congestion mitigation and emission-reduction management model. Specifically, a nonlinear function that integrates system dynamics and a non-homogeneous discrete grey model (SD-NDGM) was used to construct an algorithm, which improved the accuracy of the model. Thereafter, the mid- and long-term effects of the restriction policy were explored. The main findings from dynamic model simulations were as follows: All types of restrictions alleviated traffic congestion to varying degrees, but “odd and even” restrictions had more obvious effects, with an average annual reduction rate of 43.53% in the number of motor vehicle trips. The driving-restriction policy had a time effect, significantly reducing the number of vehicle trips in the short term. However, it could have negative effects in the long term (e.g., agglomeration effect, emission-reduction paradox), and it does not fundamentally solve traffic and environmental problems. Thus, it could only be used as a phased policy, not a long-term measure. The purchase-restriction policy controlled excessive increases in the number of private cars, but it had little effect in terms of solving environmental problems. Compared with a single policy, the combination of public-transport development and driving-restriction policy not only reduced traffic congestion, air pollution, and air quality health indexes by 29.13%, 52.63%, and 54.63%, respectively, but also improved environmental carrying capacity by 294.26%. A combined approach can therefore be said to have certain benefits for society, health, and the environment.Graphical abstract Supplementary InformationThe online version contains supplementary material available at 10.1007/s10098-022-02319-9.

Two types of conformable fractional grey interval models and their applications in regional electricity consumption prediction

Taking the unbalance development inside a region into consideration, it will be better to express the regional electricity consumption (EC) value as an interval number to preserve more complete information. However, there are rare papers about this interesting topic. For the small amount of EC data, grey interval prediction model is employed in this paper. However, the existing models are almost all integer-order grey interval models and based on area coordinate conversion method. In order to fill this gap, and to obtain more accurate forecasting results, a conformable fractional non-homogenous discrete grey model (CFNDGM(1,1,α)) is proposed, and on the basis of CFNDGM model, two conformable fractional grey interval models are built. One is based on area coordinate conversion method (CFNDGM_AC), and the other is with information decomposition conversion method (CFNDGM_ID). The mathematical relationship of the two types of grey interval models is firstly given in this paper. It indicates that which type of model has better performance depends on the characteristics of original data. To assess the two fractional grey models, annal EC values in southern Jiangsu are taken as an example, and other four grey interval models are taken for comparison. Results show that CFNDGM_ID has the best performance among six models in both simulation and prediction. Then CFNDGM_ID is chosen to predict EC of southern Jiangsu in the next five years. To further improve forecasting accuracy, the optimal fitting size of CFNDGM_ID is selected. Forecasting results show that the EC in southern Jiangsu will increase in the next five years, but at a lower growth rate.

Cardiovascular disease (CVD): assessment, prediction and policy implications

BackgroundThe study aims to predict and assess cardiovascular disease (CVD) patterns in highly affected countries such as Pakistan, India, China, Kenya, the USA, and Sweden. The data for CVD deaths was gathered from 2005 to 2019.MethodsWe utilized non-homogenous discrete grey model (NDGM) to predict growth of cardiovascular deaths in selected countries. We take this process a step further by utilizing novel Synthetic Relative Growth Rate (RGR) and Synthetic Doubling Time (Dt) model to assess how many years it takes to reduce the cardiovascular deaths double in numbers.ResultsThe results reveal that the USA and China may lead in terms of raising its number of deaths caused by CVDs till 2027. However, doubling time model suggests that USA may require 2.3 years in reducing the cardiovascular deaths.ConclusionsThis study is significant for the policymakers and health practitioners to ensure the execution of CVD prevention measures to overcome the growing burden of CVD deaths.

Forecasting annual foreign tourist arrivals to China by incorporating firefly algorithm into fractional non-homogenous discrete Grey model

PurposeAccurate foreign tourist arrivals forecasting can help public and private sectors to formulate scientific tourism planning and improve the allocation efficiency of tourism resources. This paper aims to address the problem of low prediction accuracy of Chinese inbound tourism demand caused by the lack of valid historical data.Design/methodology/approachA novel hybrid Chinese inbound tourism demand forecasting model combining fractional non-homogenous discrete grey model and firefly algorithm is constructed. In the proposed model, all adjustable parameters of the fractional non-homogenous discrete grey model are optimized simultaneously by the firefly algorithm.FindingsThe data sets of annual foreign tourist arrivals to China are used to verify the validity of the proposed model. Experimental results show that the proposed method is effective and can be used as a useful predictor for the prediction of Chinese inbound tourism demand.Originality/valueThe method proposed in this paper is effective and can be used as a feasible approach for forecasting the development trend of Chinese inbound tourism.

Predictive analysis of quarterly electricity consumption via a novel seasonal fractional nonhomogeneous discrete grey model: A case of Hubei in China

Accurate electricity consumption forecasting plays a crucial role in electric power systems and is a challenging task due to its complicated mechanism induced by multiple influential factors. To address this problem, this paper develops a novel nonhomogeneous discrete grey model that considers seasonality by introducing a seasonal index into the fractional accumulation generation operator, which is abbreviated as SFNDGM. In addition, the introduction of a one-step ahead rolling mechanism can further improve its prediction performance. To enhance the efficacy, the particle swarm optimization (PSO) algorithm is employed to determine the fractional accumulation order. Subsequently, to demonstrate the effectiveness and superiority of the rolling SFNDGM model, this model is applied to simulate and predict Hubei’s quarterly electricity consumption from 2010Q4 to 2019Q3. The numerical results show that the proposed rolling model has a better performance than the other benchmark models. Therefore, the optimal model is utilized to predict Hubei’s quarterly electricity consumption by 2021, inferring that electricity consumption will continue to increase in the coming years. Based on the attained forecasts, several suggestions are put forward to promote the sustainable development of Hubei’s electricity consumption.

Assessment and prediction of environmental sustainability: novel grey models comparative analysis of China vs. the USA.

Emission forecasting is vital for policy-making and emission reduction goals globally. This research aimed to perform an accurate model for forecasting and assessing CO2 emissions and the production of renewable electricity for the top two countries contributing to these emissions, the USA and China. In this study, we employed three novel advanced mathematical grey models: optimized discrete grey model (ODGM), nonhomogeneous discrete grey model (NDGM), and variable speed and adaptive structure grey model (VSSGM) to estimate the future trends of CO2 emissions and renewable electricity production. These breakthrough models added value in this field of research by reducing uncertainty surrounding ambiguity and numerical ranges and improving accuracy in assessments by using small samples and imperfect information. The findings showed that, by 2026, China's electricity production based on renewable sources would be higher than that of the USA. We find CO2 emissions in a downward trend, with more significant reductions in the USA than in China by the year 2026. The contributions of this study are the application of novel VSSGM and the use of synthetic relative growth rate modeling for predicting the overall growth of CO2 emissions and the production of renewable electricity in analyzed countries. The originality of this study lies in proposing a novel synthetic doubling time model to compute how long it will take, for China and the USA, to reduce their CO2 emissions and doubling their increase in renewable electricity production.

Growing green? Sectoral-based prediction of GHG emission in Pakistan: a novel NDGM and doubling time model approach

Greenhouse gases (GHGs) are one of the leading causes of global warming. Therefore, accuracy estimates for greenhouse gases (GHGs) emissions are a key element in defining the best strategies for reducing GHG emissions from various source sectors of the economy. In the present study, an initial attempt has been made to estimate and forecast the GHG emissions in Pakistan from five major sectors, such as energy, industrial, agriculture, waste, and land-use change and forestry. The data were taken from the official website of the Pakistan climate database from 1990 to 2016. We employed advanced mathematical modeling, namely a non-homogenous discrete grey model (NDGM), to predict sector-wise GHGs emissions. Moreover, the present study is a milestone in the GHGs growth analysis by utilizing the synthetic relative growth rate (SRGR) and synthetic doubling time model (SDTM). The results reveal that the industry and land-use change and forestry contribute more in terms of increasing GHGs emissions till 2024, whereas agriculture and waste required comparatively less time to reduce GHGs emissions double in number among five sectors. All five sectors show an increasing trend in forecasting GHGs emissions between 1990 and 2016. However, the results indicate that land-use change and forestry and industrial sectors are more likely to be a reason for the increase in GHGs emissions in the future, followed by the agriculture, energy, and waste sectors. The land-use change and forestry was found prone to increase emission in the future, and the doubling time ( $${D}_{\mathrm{t}}$$ ) suggests less time expected to reduce GHGs. Finally, the study has suggested some policies for the policymakers, government, and decision-makers to reduce GHGs emissions and achieve sustainable development.

Predicting monthly natural gas production in China using a novel grey seasonal model with particle swarm optimization

Accurate prediction of short and medium-term monthly natural gas production in a country is the basis for understanding the supply capacity of natural gas in different months, and for the timely adjustment of natural gas production and import strategies. In China the monthly production of natural gas has obvious seasonal and cyclical variations, thus the use of a traditional grey prediction model is not very effective. As a result, a novel grey seasonal model is proposed in this paper. This is the Particle swarm optimized Fractional-order-accumulation non-homogenous discrete grey Seasonal Model (PFSM(1,1) model). This model enhances the adaptability to seasonal fluctuation data in two ways: the seasonal adjustment of the original data, and improvement of model self-adaptability. We use monthly natural gas production data of China for the period 2013–2018 as samples to predict those for the period 2019–2023. To demonstrate the PFSM(1,1) model does indeed exhibit better predictive capability, we also use the Holt–Winters model and a seasonal GM(1,1) model to predict monthly natural gas production, and compare the results with the model proposed here. The prediction results show that monthly natural gas production in China will continue to increase throughout the 2019–2023 period, that the peak-to-valley differences in monthly production values will also increase, and that the seasonal variations in production will become increasingly pronounced. Moreover, although Chinese production of natural gas is increasing, it will still be difficult to meet future demand, and hence the gap between supply and demand will increase year by year. We conclude that China needs to develop a more complete import plan for gas to meet expected natural gas consumption.

Forecasting cocoa production of six major producers through ARIMA and grey models

PurposeIn the current study, two grey prediction models, Even GM (1, 1) and Non-homogeneous discrete grey model (NDGM), and ARIMA models are deployed to forecast cocoa bean production of the six major cocoa-producing countries. Furthermore, relying on Relative Growth Rate (RGR) and Doubling Time (Dt), production growth is analyzed.Design/methodology/approachThe secondary data were extracted from the United Nations Food and Agricultural Organization (FAO) database. Grey forecasting models are applied using the data covering 2008 to 2017 as their performance on the small sample size is well-recognized. The models' performance was estimated through MAPE, MAE and RMSE.FindingsResults show the two grey models fell below 10% of MAPE confirming their high accuracy and forecasting performance against that of the ARIMA. Therefore, the suitability of grey models for the cocoa production forecast is established. Findings also revealed that cocoa production in Côte d'Ivoire, Cameroon, Ghana and Brazil is likely to experience a rise with a growth rate of 2.52, 2.49, 2.45 and 2.72% by 2030, respectively. However, Nigeria and Indonesia are likely to experience a decrease with a growth rate of 2.25 and 2.21%, respectively.Practical implicationsFor a sustainable cocoa industry, stakeholders should investigate the decline in production despite the implementation of advanced agricultural mechanization in cocoa farming, which goes further to put food security at risk.Originality/valueThe study presents a pioneering attempt of using grey forecasting models to predict cocoa production.

Future of quality management system (ISO 9001) certification: novel grey forecasting approach

Regarded as one of the most effective tools to guide quality systems management, ISO 9001 is a valuable certification. Yet, the growth observed throughout the world by this standard provides a strong polarisation of interest in this practice by the companies. Our research goals are to analyze and forecast trends involving ISO 9001 certification of six countries, China, Italy, Germany, Japan, the United Kingdom, and India. We gathered ISO 9001 countrywide certification data over nine years from 2018 to 2026. The methods used in this study include Even GM (1, 1), Discrete GM (1, 1) and Non-homogeneous discrete grey model (NDGM) with an accompanying synthetic growth rate and synthetic doubling time grey models to investigate the comparison among these countries. The result reveals that Germany will likely continue to lead ISO 9001 certifications at a country level through 2026. We also find that Japan and UK required more time for ISO 9001 certification to double than other countries. Our forecasting of the uptake of the ISO 9001 standard is significant for the certification bodies to understand market diffusion and trends. Implications include this study providing valuable policy guidelines for decision-makers, and new opportunities for further research for scholars.

An Improved Nonhomogeneous Discrete Grey Model and Its Application

In recent years, the nonhomogeneous grey model has received much attention owing to its flexibility and applicability of forecasting small samples. To improve further the prediction accuracy of the nonhomogeneous grey model, this paper is to introduce a new whitening equation with variable coefficient into the original nonhomogeneous grey model, which is abbreviated as ONGM1,1,k,c. First of all, the detailed computational steps of the time response function of the novel model and the restored values of the raw data sequence are deduced through grey modelling techniques. Secondly, two empirical examples from the previous literature are conducted to prove the validity of the novel model. Finally, the novel model is applied to forecast natural gas demand of China, and the results show that the novel model has a better prediction performance compared with other commonly used grey models, including GM1,1, DGM1,1, NGM1,1,k,c, and NGBM1,1.

Forecasting Nitrous Oxide emissions based on grey system models.

Accurate forecasting is required to measure future national energy performance levels in order to establish clear policies for both monitoring and reducing Nitrous Oxide and other harmful emissions. Using the well-established and accepted measures, we predict the Nitrous Oxide emissions for the year 2030 based on actual data from the years 2000 to 2016 for six countries responsible for 61% of global emissions (China, Indonesia, India, Japan, Russia and the USA). Three advanced mathematical grey predictions models were employed, namely the Even Grey Model (1, 1), the Discrete Grey Model (1, 1) and the Non-homogeneous Discrete Grey Model, which is capable of working with poor or limited data. Results showed that the Non-homogeneous Discrete Grey Model was a better fit and proved more effective in forecasting Nitrous Oxide emissions because it produced the lowest mean absolute percentage error for all countries when compared to the Even Grey Model (1, 1) and the Discrete Grey Model (1, 1). The mean absolute percentage error of the Even Grey Model (1, 1) was 2.4%, that of the Discrete Grey Model (1, 1) was 2.16%, and that of the Non-homogeneous Discrete Grey Model was 1.9%. Furthermore, the results show that China has the highest Nitrous Oxide emissions during the years studied (China 20,578,144, Russia 1,705,110, India 7,806,137, Indonesia 3,405,389, USA 8,891,219 and Japan 780,118). This study also suggests some implications for both academicians and practitioners in respect of reducing Nitrous Oxide emission levels.

Forecasting number of ISO 14001 certifications of selected countries: application of even GM (1,1), DGM, and NDGM models.

The adaptability of ISO 14001 is considered as one of the most useful tools for environmental sustainability and worldwide competitive advantage; however, the future of ISO 14001 certification faces some uncertainties because of its uneven acceptance in various countries. These uncertainties, if not properly managed, can hinder the implementation of business management systems in these countries. In order to guide policymakers in better management of ISO 14001 in future with certainty, this study aims to forecast the ISO 14001 certifications for 10years for China, India, the USA, Italy, Japan, and Germany, the top six certified countries, through advanced mathematical modeling, namely grey models, even GM (1,1), discrete GM (1,1), and non-homogenous discrete grey model (NDGM). The benefits of mentioned models are ensured accuracy in assessment using small samples and poor information. Moreover, current research is a pioneer in the certifications growth analysis using the Synthetic Relative Growth Rate and Synthetic Doubling Time models. Finally, the empirical analysis indicated that China is constantly leading in terms of its ISO 14001 certifications till 2026 and the performance of developing countries was spectacular. Furthermore, the article has proposed some suggestions for the policymakers to make the environment more sustainable.

A Multimode Dynamic Short‐Term Traffic Flow Grey Prediction Model of High‐Dimension Tensors

Short‐term traffic flow prediction is an important theoretical basis for intelligent transportation systems, and traffic flow data contain abundant multimode features and exhibit characteristic spatiotemporal correlations and dynamics. To predict the traffic flow state, it is necessary to design a model that can adapt to changing traffic flow characteristics. Thus, a dynamic tensor rolling nonhomogeneous discrete grey model (DTRNDGM) is proposed. This model achieves rolling prediction by introducing a cycle truncation accumulated generating operation; furthermore, the proposed model is unbiased, and it can perfectly fit nonhomogeneous exponential sequences. In addition, based on the multimode characteristics of traffic flow data tensors and the relationship between the cycle truncation accumulated generating operation and matrix perturbation to determine the cycle of dynamic prediction, the proposed model compensates for the periodic verification of the RSDGM and SGM grey prediction models. Finally, traffic flow data from the main route of Shaoshan Road, Changsha, Hunan, China, are used as an example. The experimental results show that the simulation and prediction results of DTRNDGM are good.

Predicting the research output/growth of selected countries: application of Even GM (1, 1) and NDGM models

The study aims to forecast the research output of four selected countries (USA, China, India and Pakistan) using two models of Grey System Theory—Even Model GM (1, 1) and Nonhomogeneous Discrete Grey Model (NDGM). The study also conducts publication growth analysis using relative growth rate (RGR) and the doubling time (D t). The linear and exponential regression analyses were also performed for comparison. The study also proposes and successfully tests two novel synthetic models for RGR and D t that facilities the comparison of the countries’ performance when actual data and forecasted data produce different sequences of performance in the given period of time. The data of documents published by the four countries from 2005 to 2016 was collected from SJR/Scopus website. Performance criterion was Mean Absolute Percentage Error. The study confirms that NDGM is a better model for forecasting research output as its accuracy level is higher than that of the Even Model GM (1, 1) and statistical regression models. The results revealed that USA is likely to continue leading in research output at least till 2025 however the research output difference between USA and China is likely to reduce. The study reveals that the less developed countries tend to possess higher relative growth rate in publications whereas the more developed countries tend to possess lower relative growth rate. Further, the more developed countries need more time for publications to double in numbers for a given relative growth rate and less developed countries need less time to do so. The study is original in term of its analysis of the problem using the models involved in the study. The study suggests that the strategies of USA and China to enhance the research output of their respective countries seem productive for the time being however in long run less developed countries have greater competitive advantage over the more developed countries because of their publication growth rate and time required to double the number of publications. The study reported nearly linear trend of growth in research output among the countries. The study is primarily important for the academic policy makers and encourages them to take corrective measures if the growth rate of their academic/publishing sector is not reasonable.

Grey-based model for forecasting Mauritius international tourism from different regions

PurposeThe purpose of this paper is to understand the trend and forecast the number of tourists from different regions of the world to Mauritius.Design/methodology/approachThe 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.FindingsThe 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.Practical implicationsForecasting 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.Originality/valueMauritius 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.

Electricity consumption forecasting for Turkey with nonhomogeneous discrete grey model

ABSTRACTThe accuracy of forecasting is an essential issue for decision makers in terms of energy planning. During the recent years, several techniques have been used for electricity consumption forecasting in order to accurately predict the future demand. Although there are several forecasting techniques, selection of the most appropriate one is of paramount importance. In this study, three different grey forecasting models are built and used for modeling and predicting yearly net electricity consumption in Turkey. Additionally, these three models are compared to find the best model by using performance criteria. The best approach, Nonhomogeneous Discrete Grey Model (NDGM), is employed to forecast electricity consumption from 2014 to 2030. In addition, a comparison is made with recent studies proving the grey model (GM) proposed by this study delivers better forecasting performance.

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGMp/q) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGMp/q and the NDGMp/q can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGMp/q was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGMp/q and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGMp/q was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional non-homogenous discrete grey forecasting model (NDGM), the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence (MAPEM) and mean percent of interval sequence simulating value set covered (MPSVSC), are defined and, the procedure of the interval grey number sequence based the NDGM (IG-NDGM) is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM(1,1) model and GM(1,1) model.

Expansion modelling of discrete grey model based on multi-factor information aggregation

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model (GM (1, h)), always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method (abbreviated as FDGM (1, h)), is proposed accordingly. Then the feedback control equation and the parameters' solution of the FDGM (1, h) model are given. Finally, a real application is used to test the modelling accuracy of the FDGM (1, h) model. Results show that the FDGM (1, h) model is much better than the non-homogeneous discrete grey forecasting model (NDGM) and the GM (1, h) model.