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Epidemic models are widely used in financial risk prediction. The problems of nonlinear changes in infection rates and limited data samples in financial risk remain to be addressed. To this end, this paper proposes a nonlinear grey SIRS (abbreviated as GSIRS) model based on short-term data. This model employs a time-varying function to capture the nonlinear dynamics of infection rates. and integrates the system grey prediction model to analyze short-term data. Parameter optimization is achieved through the least square method and the whale optimization algorithm. The GSIRS model shows good prediction accuracy across three financial crisis datasets, with MAPE ranging from 3.379% to 4.981% for training sets and 2.913% to 3.212% for test sets. These values are significantly better than those of competition models. In addition, the CWC values ofthe interval prediction under the 95% confidence level ofthe model are 0.13,0.14 and 0.33, respectively. The combination of excellent RMSE and STD metrics furtlier proves the stable forecasting ability. Meanwhile, the sensitivity analysis shows that changes of infection rate have a 1-2 period lagged effect on the infected individual density. [ABSTRACT FROM AUTHOR]

For the grey GM(1,N) models, due to accumulation and other reasons, multicollinearity can arise between variables, which can cause instability in the model and result in erroneous predictions. Studying this ill-posed problem has important practical significance for improving the prediction accuracy of the GM(1,N) model. Firstly, to diagnose the multicollinearity in the GM(1,N) model, this paper uses the grey relational degree to measure the linear correlation between multiple variables for the GM(1,N) model's less informative characteristics. In addition, the eigenvalue method is used to measure the degree of multicollinearity. Then, in order to address the problem of multicollinearity in the GM(1,N) model, the principal component-ridge regression method (PCRE) is introduced into the GM(1,N) model. The admissibility and superiority of the PCRE method are studied under the balance loss function. Finally, an empirical analysis verified the superiority of the PCRE method in addressing the multicollinearity of the GM(1,N) model. [ABSTRACT FROM AUTHOR]

To predict urban road traffic flow more efficiently and rationally, we established a nonlinear fractional order grey model that integrates historical trends and residual items and provides a least squares parameter estimation formula and an analytical solution. The historical traffic flow data have been analyzed to predict the traffic flow on urban roads through the proposed model. Finally, we tested the traffic flow information fusion of fractional order grey model using the data of Yingpan/Ziwei Road in Changsha City. The results show that the traffic flow prediction model is highly accurate and practical. [ABSTRACT FROM AUTHOR]

The minimum order and extremal graph of a connected m-Kn-residual graph were first proposed by Erdös, Harary and Klawe, in addition to two important conjectures related to the graph. They addressed said conjectures solely from the perspective of Kn-residual graphs, and did not study the m - Kn-residual graphs m > 1. In this study, we found that with n > 2m + 2, the minimum order of connected m-Kn-residual graph was (m+ n)(m+ 1) and the unique extremal graph was Km+n ×Km+1. This conclusion agreed with the conjectures proposed by Erdös, Harary and Klawe. Moreover, with n = 2m + 2, we identified at least two non isomorphic m - Kn-residual graphs; this did not correspond with the conjecture. The m - Kn-residual graph was determined only by m; n and the maximum connected branch r. The relationship among m; n and r was similar to that among the parameters of Hill cryptosystem implementation steps. According to these observations and principle knowledge regarding Hill cryptosystem implementation, the novel binary cryptosystem related m-Kn-residual graphs was established. We also built a Hill password encryption algorithm that ensures the binary cryptosystem is effective. The complexity of the minimum order and extremal graphs of connected m-Kn-residual graphs make the ciphertext, plaintext, and relationship between the keys highly complex and give the binary cryptosystem favorable performance. [ABSTRACT FROM AUTHOR]

Under the development mode of low carbon economy, selecting the best low carbon supplier is the basis and prerequisite for establishing low carbon supply chain, and is the inevitable choice to achieve sustainable development for enterprises. In this paper, we investigate the problem of low carbon supplier selection in the multi-source and multi-attribute procurement. Concretely, we establish a new evaluation index system of low carbon supplier selection based on cost, low carbon, quality and service capacity. Then we present a multi-attribute decision making method for low carbon supplier selection based on a linguistic 2-tuple VIKOR method. In this proposed decision method, the hybrid attribute values (the real numbers and linguistic fuzzy variables coexist) are transformed into linguistic 2-tuples, and a ranking method based on an extended VIKOR method is then presented to rank all alternative suppliers. We also give an application example to highlight the implementation, availability, and feasibility of the proposed decision making method. [ABSTRACT FROM AUTHOR]

The GM(1,1) model identifies the parameters by utilizing the least squares and builds its model by the function which aims at minimizing the error sum of squares of the original sequences. The least squares are established under the assumption that the error term is homoscedastic, while generalized least squares are more applicable when the heteroscedasticity of the error term occur. In this paper we first distinguish the heteroscedasticity of the GM(1,1) model by Goldfeld-Quandt testing and establish the GM (1,1) model under the significance of the generalized least squares, then provide the optimized matrix and expansion form according to the parameters of [a,b]T simultaneously. Subsequent analysis proves that multiple transformation does not change the precision of the heteroscedastic GM(1,1) model while it can reduce its morbidity. At the end of this paper, when the heteroscedasticity of the error terms occur, the case studies indicate that the effects of the heteroscedastic GM(1,1) model are more favorable than that of the GM(1,1) model. [ABSTRACT FROM AUTHOR]

This paper studies the grey coupled prediction problem of traffic data with panel data characteristics. Traffic flow data collected continuously at the same site typically has panel data characteristics. The longitudinal data (daily flow) is time-series data, which show an obvious intra-day trend and can be predicted using the autoregressive integrated moving average (ARIMA) model. The cross-sectional data is composed of observations at the same time intervals on different days and shows weekly seasonality and limited data characteristics; this data can be predicted using the rolling seasonal grey model (RSDGM(1,1)). The length of the rolling sequence is determined using matrix perturbation analysis. Then, a coupled model is established based on the ARIMA and RSDGM(1,1) models; the coupled prediction is achieved at the intersection of the time-series data and cross-sectional data, and the weights are determined using grey relational analysis. Finally, numerical experiments on 16 groups of cross-sectional data show that the RSDGM(1,1) model has good adaptability and stability and can effectively predict changes in traffic flow. The performance of the coupled model is also better than that of the benchmark model, the coupled model with equal weights and the Bayesian combination model. [ABSTRACT FROM AUTHOR]

New product diffusion is influenced by both external and internal factors in the market. To address the promotion style of new products and the characteristics of a small sample, this paper proposes a grey diffusion model based on grey system theory. We describe the modeling process and the method of parameter estimation, resolve the model to obtain the time-response formula and discuss the model solutions properties. Finally, this model is used to analyze the proliferation problem of "dating site" membership. The results show that a grey diffusion model can obtain satisfactory results with insufficient data. [ABSTRACT FROM AUTHOR]

This paper studies theoretically the relative error between the discrete grey forecasting model abbreviated as DGM and the GM(1,1) model. Firstly, in the two applicable ranges (-2,0] and [0,2) of the developing coefficient a, the upper bound of each relative error at time k between DGM and GM(1,1) is calculated. Then, by using the properties of a bivariate differentiable function, we study the relevant properties of the relative error upper bounds r1 (a, k, n) and r2 (a, k, n). Further, we derive the quantitative relation between the relative error and the developing coefficient a. The results show that when a is within the range [-0.2, 1] the relative error between DGM and GM(1,1) at time k is less than 5.21%, and hence DGM and GM(1,1) can substitute appositely each other; However, when a is in the range (-2,-0.4] or [1,2) the relative error may exceed 12.46%. Therefore, this work provides a quantitative criterion for whether DGM and GM(1,1) model can reasonably substitute each other. [ABSTRACT FROM AUTHOR]

This paper applies multiple and rotation transformation of vectors to discuss the morbidity problem of GM(2,1) model in the parameter identification processing. Firstly, we analyze the factors which affect the condition number of special matrix, and get the result that the condition number relate to the ratio of length and the included angle of column vector. So we can adjust the special matrix to be a well-conditioned one by multiple transformations for the ratio of length and by rotation transformation for the included angle respectively. Then, we study the morbidity problem of GM(2,I) model by vectors transformation. We convert a 3-order matrix to a 2-order matrix by using equalization to convert a 3-order matrix into a block diagonal matrix. To a 2-order matrix, we do multiple transformations of vectors for its ratio of length and do rotation transformation of vectors for its included angle. Finally, the calculation steps of the parameters is given and a numerical results show that this method can perfectly solve the morbidity problem of GM(2,1) model. [ABSTRACT FROM AUTHOR]

In this paper, a new generating method of the Generalized Accumulated Generating Operation (GAGO) is proposed based on the traditional AGO. Then the generating space of GAGO is constructed, and the frame of AGO generating space is discussed. These outcomes can widen the application range of AGO and enrich the foundation of grey generating theory. [ABSTRACT FROM AUTHOR]

Discussed in this paper are the difference information for the transformation series of power function x-α in grey forecast modeling, and the applied condition of α which should be satisfied in high precision GM(1,1) modeling. Then the data processing mechanism of this function is given. Therefore, it widens the range of grey transformation methods, and provides the feasibility guarantee for practical application of the grey forecasting model. The per capita income forecasting of urban households is cited as an example, and it has obtained a satisfactory result. [ABSTRACT FROM AUTHOR]

This paper researches the difference information on the transformation series of logarithm-power function in grey forecast modeling. The condition of parameter T in this function transformation which should be satisfied in high precision GM(1,1) modeling is discussed, then the data processing mechanism of this function transformation is given. So these results widen the range of grey transformation methods, and provide feasibility guarantee for gery modeling. [ABSTRACT FROM AUTHOR]

Forced merge behavior on freeway merging areas is a major cause of traffic conflicts. Intelligent transportation systems can provide the possibility of information interaction and collaborative control, and optimized trajectory planning methods for merging vehicles in a vehicle-to-infrastructure (V2I) environment can improve the safety and efficiency of freeway merging areas. However, it is difficult for vehicles to determine suitable gaps for merging from the ramp to the mainline. Although some researchers have developed models to determine the appropriate insertable gap, they usually assume that the vehicles are driving at the same speed and acceleration, and there is no corresponding selection strategy for different traffic density scenarios. This study develops a trajectory planning method for merging vehicles according to characteristics of different mainline densities in a V2I environment, which can be applied in for the development of dynamic merging assistance systems to distribute control signals to drivers. The trajectory planning problem is transformed into a nonlinear optimal control problem, and the goal is to optimize the insertion gap, energy consumption, and passenger comfort. The decision variables include the time-varying longitudinal acceleration of a group of vehicles and the optimal insertable gap; the optimization problem is then solved by a heuristic algorithm. To verify the applicability and safety of the proposed method, numerical simulation experiments are carried out in different density traffic flow scenarios, and the safety of the experimental results was evaluated from the individual vehicle level and traffic flow level. Results show that the proposed method is suitable for different mainline densities and can effectively improve merge safety. Simulation examples are included to compare the performance of the proposed model to a baseline model with results showing significant improvements in both travel time and safety. [ABSTRACT FROM AUTHOR]

As extremely complex interactions exist in the process of economic research and development, a novel grey multivariable coupling model called CFGM(1,N) is proposed to evaluate the coordination degree between China's technology and economy with limited information. This proposed model improves the aggregation in GM(1,N) model through the Choquet integral among λ-fuzzy measure, which can reflect interactions among factor indexes. Meanwhile, it can estimate the coordinate parameters via the whale optimization algorithm and obtains the coupling coordination degree combining with grey comentropy. To verify the proposed model, a case study using a dataset from China's technology and the economic system is conducted. The CFGM(1,N) model has a better performance in the convergence and interpretability, as compared to the three heuristic algorithm and two classical approaches. Our finding suggests that China's technology and the economic system is still relatively coordinated. Results also reveal that there exists strong negative cooperation between the comprehensive human input and the comprehensive capital investment in this system. [ABSTRACT FROM AUTHOR]

Based on four forms of a grey hazy set, this paper defines the topological system of grey information space containing grey information level space and grey information treated space. Then, the grey information measure problem is researched, and we use Shannon entropy to characterize in grey level space and propose four concepts (grey original kennel, grey original information measure, grey transfer kennel, grey transfer information measure) and their calculation formulas and rules of the grey information element. [ABSTRACT FROM AUTHOR]