Abstract
In the empirical researches, the discrete GM (1,1) model is not always fitted well, and sometimes the forecasting error is large. In order to solve this issue, this study proposes a dynamic discrete GM (1,1) model based on the grey prediction theory and the GM (1,1) model. In this paper, we use the equal division technology to fit the concavity and convexity of the cumulative sequence and then construct two dynamic average values. Based on the dynamic average values, we further develop two dynamic discrete GM (1,1) models and provide the gradual heuristics method to draw the initial equal division number and the dichotomy approach to optimize the equal division number. Finally, based on an empirical analysis of the number of conflict events in the urbanization process in China, we verify that the dynamic discrete GM (1,1) model has higher fitting and prediction accuracy than the GM (1,1) model and the discrete GM (1,1) model, and its prediction result is beneficial to the government for prevention and solution of the urbanization conflict events.
Highlights
After years of development [1, 2], the grey system theory has formed a relatively complete system theory
If the once accumulated sequence has the characteristic of the concave function, based on the equal division technology, the dynamic average value can be presented as tn(1) (k + 1)
This paper uses the fitting of the dynamic discrete GM (1,1) models to predict the number of the urbanization conflict events in China and analyzes social problems that presently exist in China
Summary
After years of development [1, 2], the grey system theory has formed a relatively complete system theory. If the once accumulated sequence has the characteristic of the concave function, based on the equal division technology, the dynamic average value can be presented as tn(1) (k + 1). If we substitute x(0)(k + 1) = x(1)(k + 1) − x(1)(k) and tn(1)(k + 1) = [(n − 1)x(1)(k) + (n + 1)x(1)(k + 1)]/2n into the average value form of the GM (1,1) model, we can get the convex dynamic discrete GM (1,1) model including the equal division number n as follows: x(1) (k + 1) − x(1) (k). The above dynamic discrete GM (1,1) models are developed by introducing the improved average value They have original properties of the discrete GM (1,1) model and have the following special characteristics. When n → ∞, (17) and (18) can be transformed to the restored function of the discrete GM (1,1) model (see (7))
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