Yaoguo Dang

Unbiased Grey Verhulst Model and Its Application

Abstract As to the inherent simulant error of grey Verhulst model, this article presents unbiased grey Verhulst model. Recursive solutions are given under two initial conditions of the unbiased model. The results show the complete coincidence of the prediction and simulation to the original data of S-shaped curve generated form has achieved. The unbiased grey Verhulst model presented in this article has not only completely eliminated the inherent simulant error of the traditional model, but also avoided the jumping errors from the differential equation to differential equation in traditional grey modeling. Case analysis shows that the simulation and prediction accuracy in traditional modeling has been significantly improved by unbiased grey Verhulst model.

The optimized GPM(1,1) for forecasting small sample oscillating series

This paper puts forward a modeling approach for oscillating series based on an optimized grey power model with first-order one-variable (abbreviated as GPM(1,1). An optimization method is used to determine the initial value in GPM(1,1) model, and furthermore, the parameters in the model are optimized by utilizing a non-linear programming model. The results show that the modeling approach proposed in this paper can reflect the fluctuation of original data and be solved handily using a computer. The range of application of Grey Model is further extended to forecast oscillating series. The effectiveness of the optimized GPM(1,1) model is demonstrated by an actual case study.

Comprehensive optimized GM（1,1 ） model and application for short term forecasting of Chinese energy consumption and production

In order to improve prediction accuracy of the grey prediction model and forecast China energy consumption and production in a short term, this paper proposes a novel comprehensively optimized GM(1,1) model, also named COGM(1,1),based on the grey modeling mechanism. First, the relationship of the background value formula and its whitenization equation is analyzed and a new method optimizing background values is proposed to eliminate systemic errors in the modeling process.Second, the solving process of the new model is derived. For parameter estimation, a set of auxiliary parameters are used to change grey equation’s form. Then, original parameters are restored by an equations system. After solving the whitenization equation, initial value in time response function is established by least errors criteria. Finally, a numerical case and comparison with other grey prediction models are made to testify the new model’s effectiveness, and the computational results show that the COGM(1,1) model has a better property and achieves higher precision. The new model is used to forecast China energy consumption and production, and the ability of energy self-sufficiency is further analyzed. Results indicate that gaps between consumption and production in future are predicted to decline.

Study on Novel Property of Some Grey Relational Analysis Models

The purpose of this paper is to further study the properties of algorithms for grey relational analysis. Based on analyzing of some existing algorithms for grey relational analysis and their properties, this paper firstly creates the novel definitions of affine transformation isotonicity of grey relational models. Secondly, we investigated this novel property of some models for grey relational analysis. Finally, the study result shows that the algorithms for general relational analysis, grey pointed relational analysis, grey T-mode relational analysis and grey rate relational analysis is satisfying the novel property. This result may enrich the theoretical system of grey relational analysis.

Research on characteristics of grey non-equidistant Verhulst model

In this paper multiple transformation method was made for the data series of grey non-equidistant Verhulst model. The least square estimate method was used to get parameters series of multiple transformations. The changes on parameters characteristics of the model under multiple transformations were analyzed, and the affect of multiple transformations to the value of simulation, prediction precision and the relative error of the model were discussed in details. The numerical results show that the simulative and predicative results of the model are consistent, while the magnitude of the data is reduced.

Hybrid multi-attribute decision model of grey target

To handle the uncertain multiple attribute decision problem that the decision index value is hard to define accurately, this paper studies on the hybrid multi-attribute decision model of grey target when the index values are real number, interval number and triangular fuzzy number which exist together. According to the basic connotations of grey target decision and uncertain decision information, this paper defines the hybrid ellipsoid grey target based on which it also constructs the hybrid decision model of grey target, and discusses the weights assignment problems under the circumstances where there is completely no weight information on index or there is only partial weight information. The result shows that the model established in this paper can better resolve the multi-attribute decision problem with hybrid information and finally this paper proves the practicality and effectiveness of this model through a case study.

Grey distance incidence degree and its properties

According to the basic theory of grey system correlation space, a type of new grey incidence degree model is constructed by starting from the perspective of n dimensional linear space. This paper makes a research about some properties of the incidence degree and compares this incidence degree with Dengs. Results indicate that this incidence degree has the same properties with Dengs; and it also has some unique advantages. It can reflect the relevance better between system factors in the view of distance space, further enrich and perfect the theoretical system of grey incidence analysis.

A grey multi-stage dynamic multiple attribute decision making method

To tackle a class of grey multi-index decision problems with completely unknown attribute weighted values and interval grey number, a dynamic multi-stage decision-making method is proposed based on the grey system theory. Firstly, we presented a method for comparison of two grey numbers and identification of the attribute weighted values. Secondly, the experts expressed attribute values in internal grey numbers by multiple stages. Finally the obtained attribute weights and values are aggregated to solve the multiple-stages evaluation problem.

The intelligent optimization of GM(1,1) power model and its application in the forecast of traffic accident

In order to improve prediction accuracy of traffic accidents, an optimization GM (1, 1) power model is put forward based on the characteristics of S-type and a single traffic accident peak. Specifically, an intelligent optimization method is proposed to optimist the parameter α using PSO algorithm and the optimization formula of background value in GM (1, 1) power model is given based on the integral mean value theorem as well as the intelligent optimization algorithm of background value is proposed. The number of traffic fatalities during the period 1996–2009 is fitted and predicted using the optimization GM (1, 1) power model, whose results show that the optimization GM (1, 1) power model has higher fitting and prediction accuracy than the grey Verhaulst model.

The multi-attribute weighing decision model of grey target based on savage decision criteria

This paper studies on the multi-attribute weighing decision model of grey target based on theories of decision-making analysis. Concerning of Savage decision criteria under the circumstance of uncertain decision, grey interval number series have been put forward to extend definition of real number series as well as a ranking method has been given according to the distance from Grey target. In this case, a decision model of multi-indicator and weighing grey target is developed based on grey target decision theory. Such method provides a new approach of multi-indicator interval grey number decision. Finally, the effectiveness of the method has been verified by a real example.