Xinping Xiao

Grey Coupled Prediction Model for Traffic Flow with Panel Data Characteristics

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.

Study on the combination weighting method of hybrid multiple attribute decision-making

Because attribute weights may affect the ranking results of alternatives, one important problem in hybrid multiple attribute decision-making is to determine attribute weights of different types of data. To obtain the mixed entropy weight, we define the entropy values of precise number, interval number and fuzzy number. Then we get the grey relational weight based on ideal solution. Next we combine two weights above by using the relative entropy model. The combined weight not only reflects the difference of attribute values, but also reflects the closeness to the ideal solution. Finally, an example is proposed to prove that the new method is rational and effective.

A novel algorithm of image denoising based on the grey absolute relational analysis

The paper presents a novel image denoising algorithm based on grey absolute relational analysis of grey system theory. The time of applying grey system theory into noise reduction is not very long, and there are some imperfections left to be Improved We analyze the classic filter based on the grey relational analysis, and propose a novel approach to design the reference sequence, which may be much closer to the true value of the central pixel in the window. Note that there is noise whose value is not very little existing in the filter window around the central pixel, and we improve the decision-making method of grey absolute relational coefficients which are the weights of each pixel in the window. The final procedure of measures we have taken is to adopt the continuity in time and direction or position among the image pixels between the last filter window and the next one, which can decrease noise in the neighborhoods of the filter window. Compared with other popular filters, such as the traditional mean filter, the median filter, and the adaptive added-weigh mean filter based on the grey relational degree, the experimental results show that our method is more effective and feasible as it can keep the details of images while eliminating the noise.

Grey multi-variables GM(1,N/τ,r) model with delay and its application

Based on the complicated and nonlinear grey system of multi-variables, this paper proposes grey multi-variables GM(1,N/^τ,r) model with delay, and discusses parameter space of the model, then analyses the impacts of multiple transformation for parameters of GM(1,N/^τ,r), as well as iteration of this model. Finally we build GM(1,N/^τ,r) on reverse logistics network of scrap steel for forecasting flux of scrap steel at collected point which can be transformed to a optimized problem of the average comparative error about ^τ and ^r, results indicate that the precision of GM(1,N/^τ,r) is superior to GM(1,N). Therefore, GM(1,N/^τ,r) has important academic and practical significance.

Modeling mechanism of a novel fractional grey model based on matrix analysis

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.

Grey decision rules for interval MADA based on rough set theory

Based on rough set theory, a new decision rule for information system with interval numbers is proposed. First the interval values are discretized through an improved rough clustering algorithm. Then the redundant set of attributes is obtained by constituting homogenous matrix. Then, after a part of decision rules have been generated, we propose grey decision rules that are useful in inducing rules after referring to preference-classified data tables based on grey relational analysis. To obtain weights of attribute, the reciprocal matrix which can avoid the influence of subjective factors, is constituted according to the definition of relative significance between two attributes, and then an optimal model connected with the reciprocal matrix is solved by genetic algorithm. Through contrastive analysis with back propagation (BP) neural network on stapling training planes, it is shown that the grey decision rules are more efficient than BP neural network.

Stochastic multi-attribute decision-making model based on grey matrix relational analysis and its application

In this paper, a method based on grey matrix relational analysis is proposed for stochastic multi-attribute decision-making (SMADM) problem which features incomplete information on attributes weights and attribute values in terms of random variables which obey normal distribution. Firstly, on the basis of analyzing the related property of normal distribution, we design an index-preference probability matrix to distinguish different alternatives. A single objective programming model based on the deviation maximization theory among attributes is developed to determine the optimal weight vector. Secondly, according to grey matrix relational degree, alternatives are ranked and the complete order is obtained. Finally, a practical example is used to show the feasibility and validity of this method.

Maximum likelihood estimation of McKean-Vlasov stochastic differential equation and its application

McKean-Vlasov stochastic differential equation is a class of complicated and special equation since the drift term is a function of stochastic process and its distribution. This paper discusses the maximum likelihood estimation of parameters in the drift term through transforming McKean-Vlasov stochastic process into homogeneous one and estimates parameters of the latter to discuss that of McKean-Vlasov equation. Then we build a McKean-Vlasov stochastic model for ion diffusion since ions moved by liquid viscous force and also by coulomb interaction related with ion charged distribution, and simulate the changing trajectory of the ion motion through numerical calculation. Results manifest that the ion motion shows strong random property and has the same tendency for different time intervals, however, the smaller of time lag, the more distinct of wave trajectory observed.

A modeling method for GM(1,1) and its application based on a particular data feature

By leading in the concept of quasi-central symmetry data sequence, this paper presented and proved a sufficient condition for the parameter identification value of the development coefficient to equal zero, and discussed the impact of truncation errors in the floating-point calculation on the development coefficient. Then, an additional test step was added to the traditional grey modeling procedure, and an improved GM(1,1) modeling method was proposed. The actual numerical examples show that this new modeling method is conducive for constructing grey models with higher prediction accuracy. Finally, using the proposed modeling method this paper demonstrated an actual application in forecasting gasoline prices and the result indicates high prediction precision.

Grey linear regression model and its application

The parameter estimation computation in grey linear regression model is relatively complicated, the development coefficient is decided by its simple average and its vulnerable with the aberrant value and logarithmic neck may be negative. Aiming at those problems, in this paper, we present a new estimation method and three kinds of representations of the model including the Range form, Connotation form and Differential form, then, we obtain the relationship between Connotation form and Differential form, and also get the relationship between the model and GM(1,1) model. Finally an application of short-term traffic flow prediction based on the model is given and some good effects have been achieved.