Study on distance measuring and sorting method of general grey number

Purpose The purpose of this paper is to study distance measuring and sorting method of general grey number. Design/methodology/approach First, the concept of generalised grey number based on grey system theory is given in this paper. Second, from the perspective of kernel and degree of greyness of general grey number, the method of measuring the distance of general grey number and its properties are given. At the same time, the concepts of the kernel expectation and the kernel variance of the general grey number are proposed. Findings Up to now, the method of measuring the distance and sorting of general grey number is established. Thus, the difficult problem for set up sorting of general grey number has been solved to a certain degree. Research limitations/implications The method exposed in this paper can be used to integrate information form a different source. Distance measuring and sorting method of general grey number could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers, etc. Originality/value The concepts of the kernel expectation and the kernel variance of the general grey number are proposed for the first time in this paper; the novel sorting rules of general grey numbers were also constructed.

Application of Grey Model GM(1, 1) to Ultra Short-Term Predictions of Universal Time

A mathematical model known as one-order one-variable grey differential equation model GM(1, 1) has been herein employed successfully for the ultra short-term (<10days) predictions of universal time (UT1-UTC). The results of predictions are analyzed and compared with those obtained by other methods. It is shown that the accuracy of the predictions is comparable with that obtained by other prediction methods. The proposed method is able to yield an exact prediction even though only a few observations are provided. Hence it is very valuable in the case of a small size dataset since traditional methods, e.g., least-squares (LS) extrapolation, require longer data span to make a good forecast. In addition, these results can be obtained without making any assumption about an original dataset, and thus is of high reliability. Another advantage is that the developed method is easy to use. All these reveal a great potential of the GM(1, 1) model for UT1-UTC predictions.

A GM(1,N)-based economic cybernetics model for the high-tech industries in China

Purpose – The purpose of this paper is to propose an economic cybernetics model based on the grey differential equation GM(1,N) for China's high-tech industries and provide the necessary support to assist high-tech industries management departments with their policy making. Design/methodology/approach – Based on the principle of grey differential equation GM(1,N), the grey differential equations of five high-tech industries in China are established using the net fixed assets, labor quantity and patent application quantity as cybernetics variables. After the discretization and first-order subtraction reduction to the simultaneous equation of the five grey models, a linear cybernetics model is resulted in. The structure parameters in the cybernetics system show explicit economic significance and can be identified through least square principle. At last, the actual data in 2004-2010 are introduced to empirically analyze the high-tech industrial system in China. Findings – The cybernetics system for China's high-tech industries are stable, observable, and controllable. On the whole, China's high-tech industries show higher output coefficients of the patent application quantity than those of net fixed assets and labor quantity. This suggests that China's industry development mainly depends on technological innovation rather than capital or labor inputs. It is expected that the total output value of China's high-tech industries will grow at an average annual rate of 15 percent in 2011-2015, with contributions of pharmaceuticals, aircraft and spacecraft, electronic and telecommunication equipments, computers and office equipments, medical equipments and meters by 21, 16, 13, 10, and 28 percent, respectively. In addition, pharmaceuticals, as well as medical equipments and meters, present upward proportions in the gross of Chinese high-tech industries significantly. Electronic and telecommunication equipments, plus computers and office equipments exhibit an obvious decreasing proportion. The proportion of the output value of aircraft and spacecraft is basically stable. Practical implications – Empirical analysis results are helpful for related management departments to formulate reasonable industrial policies to keep the sustained and stable development of the high-tech industries in China. Originality/value – Based on the grey differential equation GM(1,N), this research puts forward an economic cybernetics model for the high-tech industries in China. This model is applicable to the economic system with small sample data set.

Predicting Hardness of Four Groundwater Monitoring Stations in Kaohsiung City of Taiwan Using Seven Types of GM (1, 1) Model

In this study, seven types of first-order and one-variable grey differential equation model (abbreviated as GM (1, 1) model) were used to predict the hardness of four groundwater monitoring stations in Kaohsiung City of Taiwan. The mean absolute percentage error (MAPE) was used to evaluate the predicting performance. The results indicated the minimum MAPE of 4.71 %, 3.15 %, 2.66 %, and 16.63 % could be achieved when predicting hardness of Fonsi, Datung, Shaukang, and Chihsien stations, respectively. According to the results, it revealed that GM (1, 1) was an efficiently early warning tool for providing groundwater quality information to the competent authority.

Ground Target Tracking Using Aerial Images

The tracking of ground targets using aerial images was studied. A improved Kalman filter was derived for the tracking of ground targets. The novel feature of this improved filter were that the grey prediction equations and the road information have been incorporated to improve the accuracy of state estimates.The GM(1,1) (Grey Model) was introduced into Kalman prediction equations.The next value was forecasted by using few forward estimated values with a grey differential equation,which was baesd on the correction of mesurement covariance matrix. The tracking of the targets shows a satisfactory result.

The Optimized White Differential Equation of GM(1,1) Based on the Original Grey Differential Equation

This paper starting from the original grey differential equations, through finding the relationship between the raw data and the derivative of its , constructed a new white differential equation which equal to the original grey differential equation, at the same time, getting the new GM(1,1)model which closer to the changes of data. Through the modeling and prediction of the standard index series, this model not only adapts to low growth index series, but also adapts to high-growth index series, and the simulation accuracy and prediction accuracy are high.

Influence of Grey System Parameter Identification Method on Prediction of Bearing Capacity of Piles

An unequal interval grey model GM (1,1) was established according to the variation characteristics of sequence data about the bearing capacity of overlength piles, and a difference equations was usually adopted to replace the grey differential equation for determining the system parameters of the model; however, great errors would occur when the model thus established was used to predict the bearing capacity of overlength piles, that is, the prediction results would be overestimated or underestimated. In order to improve the prediction accuracy of the model, we established an error objective function based on optimization theory in this study, employed the method of nonlinear least squares to identify the system parameters in the grey differential equation for the bearing capacity of overlength piles, and built an optimization-based grey optimization model. The model system built with optimization method was used to predict the bearing capacity of overlength piles, and the predicted values fit the test values well. In addition, the model system had a higher accuracy, compared with the grey difference model built with difference method; therefore, the model system built with optimization method could provide reference for prediction of the bearing capacity of overlength piles.