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Greenhouse gas emissions have brought a serious challenge to the global environment and climate. Efficient and accurate prediction of carbon emissions is essential for the decision-making sectors to control growth and formulate policies. Firstly, considering the economic, demographic, and energy factors, a novel nonlinear multivariate grey model (ENGM(1,4)) based on environmental Kuznets curve (EKC) is proposed with respect to the data characteristics of the incomplete information of carbon emission of transportation sector. The model integrates the IPAT ("Influence = Population, Affluence, Technology") equation and the extended atochastic impacts by regression on population, affluence, and technology model (STIRPAT). Secondly, the derivation method is used to solve the time response equation of the model and the quantum particle swarm optimization algorithm (QPSO) is designed to optimize the model parameters. Then, 18 years of carbon emission data from China, the USA, and Japan are selected as the validation set. Comparative analysis indicates that the prediction accuracy of the statistical models and the intelligent models depends on sufficient samples and complex variables, and has certain limitations in limited sample prediction. The calculation results show that the new model outperforms other models in various evaluation indicators, indicating that its prediction accuracy is higher. Finally, the projections show that in 2019-2025, the average increase in carbon emissions from the transport sector in China and the USA was 2.837% and 2.394%, respectively, while Japan shows a downward trend with an average decline rate of 1.2231%. The analyzed prediction results are consistent with current situation of the three countries and the transport sectors, demonstrating the high accuracy and reliability of the new model.

Precious metal recovery is the main economic power of electronic waste (e-waste) 1 recovery. The prediction of e-waste and its precious metal content is of great significance to the realisation of China’s circular economy. In this work, the generation mechanism of e-waste is firstly deduced to determine model characteristics suitable for its prediction. Fractional derivative grey models base on a weak singular power kernel function (PFGM(q,1)) and a non-singular exponential kernel function (EFGM(q,1)) are established. Compared with the PFGM(q,1), the EFGM(q,1) has the advantages of simpler solution, lower calculation complexity and wider scope of application. Next, some data are selected to verify the validity. The EFGM(q,1) is used to predict mobile phone, laptop, desktop and television waste, and the weight of printed circuit boards (PCBs) in the waste and content of precious metals in these PCBs are calculated. Finally, the trend of e-waste and its precious metal contents are analysed and discussed based on the calculation results.

Structural prediction and analysis of sub-industrial energy consumption with economic data across three industrial sectors are an important basis for reflecting the coordinated development relationship between energy consumption and industrial development. Empirically, the sub-industrial energy consumption and economic structure have numerous compositional data. The multivariate compositional data’s fractional gray multivariate model on the basis of the Simplex space and its algebraic system is proposed in this study aiming at the multi-dimensional small sample size with high uncertainties. First, the fractional accumulative generation operation sequence of multivariate compositional data is defined according to Aitchison geometry. Then, the novel model with the form of the compositional data vector is obtained. Second, the least square parameter estimation of the model is studied. A derived model is deduced and selected as the time-response expression of the model solution. Moreover, the gray wolf optimizer is introduced and designed to determine the optimal value of the fractional order. Detailed modeling procedures, including the computational steps and the intelligent optimization algorithm, have been clearly presented. Furthermore, 10-year economic structural data of 14 provinces in China are used to validate the effectiveness of the proposed model. The validation presents that the proposed model performs better in fitting, prediction, stability, and applicability, in comparison with the two other models in the Simplex space. Last, from the updated real-time datasets from 2008 to 2018, the proposed model is applied to analyze and forecast the sub-industrial energy consumption structure and industrial structure of Beijing. Results show that the proposed model presents high accuracy and is efficient in addressing the multivariate compositional data in some structural energy and economic issues.

The Mahalanobis–Taguchi system (MTS) is a multivariate data diagnosis and prediction technology, which is widely used to optimize large sample data or unbalanced data, but it is rarely used for high-dimensional small sample data. In this paper, the optimized MTS for the classification of high-dimensional small sample data is discussed from two aspects, namely, the inverse matrix instability of the covariance matrix and the instability of feature selection. Firstly, based on regularization and smoothing techniques, this paper proposes a modified Mahalanobis metric to calculate the Mahalanobis distance, which is aimed at reducing the influence of the inverse matrix instability under small sample conditions. Secondly, the minimum redundancy-maximum relevance (mRMR) algorithm is introduced into the MTS for the instability problem of feature selection. By using the mRMR algorithm and signal-to-noise ratio (SNR), a two-stage feature selection method is proposed: the mRMR algorithm is first used to remove noise and redundant variables; the orthogonal table and SNR are then used to screen the combination of variables that make great contribution to classification. Then, the feasibility and simplicity of the optimized MTS are shown in five datasets from the UCI database. The Mahalanobis distance based on regularization and smoothing techniques (RS-MD) is more robust than the traditional Mahalanobis distance. The two-stage feature selection method improves the effectiveness of feature selection for MTS. Finally, the optimized MTS is applied to email classification of the Spambase dataset. The results show that the optimized MTS outperforms the classical MTS and the other 3 machine learning algorithms.

This study aims to reflect the information coverage grey number and the interaction between attributes in grey relational decision making. Therefore, a multi-attribute decision method based on the grey information coverage interaction relational degree (GIRD) is proposed. Firstly, this paper defines the information coverage grey number, and establishes the GIRD model by using the Choquet fuzzy integral and grey relational principle. It proves that the proposed model not only is the general and unified form of the point relational degree, interval relational degree, mixed relational degree and grey fuzzy integral relational degree, but also can effectively deal with the interaction between attributes. Further, a decision making example of evaluating the industrial operation quality for 14 cities in Hunan province of China is provided to high-light the implementation, availability, and feasibility of the proposed decision model.

Constructing scientific evaluation system and evaluation methods to make timely quantitative evaluation for regional industrial operation quality is of great practical significance for expediting the new industrialization process and promoting the improvement of national economic operation quality. Aiming at the problem of evaluating the industrial operation quality, this paper constructs a new evaluation system from the perspective of industrial operation performance and industrial development potential, and then proposes a multi-source heterogeneous multi-attribute decision-making method based on the linguistic 2-tuple model to evaluate the industrial operation quality. In this method, the original multi-source heterogeneous data whereby real numbers, interval numbers, and linguistic fuzzy numbers coexist are all transformed into linguistic 2-tuples, then a new ranking method based on grey relational degree of linguistic 2-tuple matrix is presented to rank the level of industrial operation quality for the given cities. Further, a decision-making example of evaluating the industrial operation quality for 14 cities in Hunan Province of China is provided to highlight the implementation, availability, and feasibility of the proposed evaluation model.

A traffic flow system is a complex dynamic system. Traffic flows data are the product of the velocity and density, and its data have dynamic and fluctuation characteristics. Therefore, three new inertia grey discrete models (IDGMs) were proposed and used to estimate short-term traffic flow based on traffic flow data mechanics and characteristics and traffic-state characteristics. The modelling process of the traditional grey DGM using the least square method may lead to a large parameter estimation deviation and a low model precision. The new model uses the mechanical characteristics of the data and applies the evolutionary process of the mechanical decomposition of the data to the modelling process. It has a more reasonable modelling process and a more stable structure and solves the shortcomings of the traditional grey DGM parameter estimation. Moreover, it uses matrix analysis to study the important characteristics of the IDGM, and it simplifies the forms of the parameter model and structural model. Then, the traffic flow of the Whitemud Drive City Expressway in Canada is analysed empirically, and the effect of the new model and the judgment of three-phase traffic flow state are analysed.

The two-stage controlled rolling and cooling at 0.5–50 °C/s of low-carbon Mo–V–Ti steels with the increasing nitrogen content from 0.0032 to 0.0081 and 0.0123 wt.% were simulated through a Gleeble 3500 system. The continuous cooling transition (CCT) of γ→α in each steel was estimated via microstructure characterization and CCT diagram. The results indicated that CCT diagram for each steel was divided into three regions of γ→ferrite, γ→pearlite and γ→bainite, and the increasing N content elevated all the starting temperatures for γ→α. Consequently, the polygonal ferrite (PF) and pearlite formed in each steel cooled at 1 °C/s and, however, the increasing N content led to slightly coarser ferrite grain and pearlite colony. With the increased cooling rate to 10 and 30 °C/s, a mixed microstructure of acicular ferrite (AF), granular bainite (GB) and lath bainite (LB) formed in 32N steel and in contrast, the mixture of PF+AF+GB in 81N and 123N steels. The increasing N content promoted (Ti,V)(C,N) precipitation, enhanced the intragranular PF/AF nucleation, increased martensite/austenite constituent and depressed LB. In addition, the mechanisms dominating the effect of increasing N on this CCT of γ→α were discussed.

Accurate real-time prediction of urban traffic flows is one of the most important problems in traffic management and control optimization research. Short-term traffic flow has complex stochastic and nonlinear characteristics, and it shows a similar seasonality within intraday and weekly trends. Based on these properties, we propose an improved binding cycle truncation accumulated generating operation seasonal grey rolling forecasting model. In the new model, the traffic flow sequence of seasonal fluctuation is converted to a flat sequence using the cycle truncation accumulated generating operation. Then, grey modeling of the cycle truncation accumulated generating operation sequence weakens the stochastic disturbances and highlights the intrinsic grey exponential law after the sequence is accumulated. Finally, rolling forecasts of the limited data reflect the new information priority and timeliness of the grey prediction. Two numerical traffic flow examples from China and Canada, including four groups at different time intervals (1 h, 15 min, 10 min, and 5 min), are used to verify the performance of the new model under different traffic flow conditions. The prediction results show that the model has good adaptability and stability and can effectively predict the seasonal variations in traffic flow. In 15 or 10 min traffic flow forecasts, the proposed model shows better performance than the autoregressive moving average model, wavelet neural network model and seasonal discrete grey forecasting model.

A.Kǒtzig had studied Hamilton decomposition, he had proved that cartesian product of two cycles decomposable into hamiltonian cycles. Bermond J.C. came up with some conjectures in [1], the conjectu...

Supplier selection for a type of divisible goods was investigated.We design a two-stage compound mechanism of selecting suppliers.This mechanism considers both the risk attributes and commercial attributes.The first stage can effectively motivate suppliers to report true information.Method of grey correlation degree of mixed sequence is proposed to rank supplier(s). The quality of the supplier base affects the competitiveness of firms and the attendant supply chain. The supplier selection decision is key to effective supply chain management. This paper investigates the problem of supplier selection under multi-source procurement for a type of divisible goods (such as coal, oil, and natural gas). By considering both the risk attributes and the attributes under a commercial criterion, we design a new two-stage compound mechanism for supplier selection based on multi-attribute auction and supply chain risk management. In the first stage, a multi-auction mechanism is established to determine the shortlist among all qualified suppliers based on four attributes (quality, price, quantity flexibility, and delivery time reliability) under a commercial criterion. In the second stage, seven risk attributes against the shortlisted suppliers are further considered, and a new ranking method based on grey correlation degree of mixed sequence is proposed to rank the finalists and to select the final winners. Moreover, the implementation, availability, and feasibility of the two-stage compound mechanism are highlighted by using an example of the multi-source procurement of electricity coal. This presented compound mechanism may well improve the procurement efficiency of divisible goods and greatly reduce the procurement risk.

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.

Studying the rear-end early warning methods of connected automated vehicles (CAVs) is useful for issuing early warnings and reducing traffic accidents. Establishing a corresponding driving model according to CAV characteristics is necessary when designing intelligent decision and control systems, especially for the safety speed threshold. However, since traffic systems are stochastic, there are random factors that influence car-following behavior. Therefore, this study proposes a rear-end collision warning method for CAVs based on a stochastic local multivehicle optimal speed (SLMOV) car-following model. First, the SLMOV model is proposed to characterize the car-following behavior of CAVs. Simultaneously, a stability analysis and parameter estimation method are discussed. Second, the safety distance between the CAVs changes with time because the speed of the rear vehicles satisfies the SLMOV model, which is used to calculate the safety probability of rear-end CAV collisions through an analysis of the driving process. The speed threshold is assessed by controlling the rear-end collision probability. Third, next-generation simulation (NGSIM) data are used in an empirical analysis of a rear-end collision warning method on the basis of a parameter estimation of the SLMOV model. The results present the speed thresholds of vehicles under different braking deceleration levels. Finally, the merits and demerits of fixed-speed and variable-speed adjustment time intervals are compared by considering driving safety and comfort as evaluation indexes. A reasonable CAV adjustment time interval of 0.4 s is determined. This result can be used to help develop a vehicle loading rear-end collision warning system.

To fully display the modeling mechanism of the novel fractional order grey model (FGM (q,1)), this paper decomposes the data matrix of the model into the mean generation matrix, the accumulative generation matrix and the raw data matrix, which are consistent with the fractional order accumulative grey model (FAGM (1,1)). Following this, this paper decomposes the accumulative data difference matrix into the accumulative generation matrix, the q-order reductive accumulative matrix and the raw data matrix, and then combines the least square method, finding that the differential order affects the model parameters only by affecting the formation of differential sequences. This paper then summarizes matrix decomposition of some special sequences, such as the sequence generated by the strengthening and weakening operators, the jumping sequence, and the non-equidistance sequence. Finally, this paper expresses the influences of the raw data transformation, the accumulation sequence transformation, and the differential matrix transformation on the model parameters as matrices, and takes the non-equidistance sequence as an example to show the modeling mechanism.

Of the grey models proposed for making predictions based on small sample data, the GM(1,1) model is the most important because of its low demands of data distribution, simple operation, and calculation requirements. However, the classical GM(1,1) model has two disadvantages: it cannot reflect the new information priority principle, and, if it is necessary to obtain the ideal effect of modeling, the original data must meet the class ratio test. This paper presents a new fractional grey model, FGM(q, 1), which is an extension of the GM(1,1) model in that first-order differential equations are transformed into fractional differential equations. Decomposition of the data matrix parameters during the process of solution shows that the new model follows the new information priority principle. For modeling, the mean absolute percentage error (MAPE) is established as the objective function of the optimization model, and a particle swarm algorithm is used to calculate the accumulation number and the order of the differential equation that can minimize the MAPE. Finally, the results from three groups of data modeling show that, compared with other classical grey models, FGM(q, 1) has higher modeling precision, can overcome the GM(1,1) model class ratio test restrictions and has a wider adaptability.