Abstract
Accurate estimations can provide a solid basis for decision-making and policy-making that have experienced some kind of complication and uncertainty. Accordingly, a multivariable grey convolution model (GMC (1, n)) having correct solutions is put forward to deal with such complicated and uncertain issues, instead of the incorrect multivariable grey model (GM (1, n)). However, the conventional approach to computing background values of the GMC (1, n) model is inaccurate, and this model’s forecasting accuracy cannot be expected. Thereby, the drawback analysis of the GMC (1, n) model is conducted with mathematical reasoning, which can explain why this model is inaccurate in some applications. In order to eliminate the drawbacks, a new optimized GMC (1, n), shorted for OGMC (1, n), is proposed, whose background values are calculated based on Simpson’ rule that is able to efficiently approximate the integration of a function. Furthermore, its extended version that uses the Gaussian rule to discretize the convolution integral, abbreviated as OGMCG (1, n), is proposed to further enhance the model’s forecasting ability. In general, these two optimized models have such advantages as simplified structure, consistent forecasting performance, and satisfactory efficiency. Three empirical studies are carried out for verifying the above advantages of the optimized model, compared with the conventional GMC (1, n), GMCG (1, n), GM (1, n), and DGM (1, n) models. Results show that the new background values can effectively be calculated based on Simpson’s rule, and the optimized models significantly outperform other competing models in most cases.
Highlights
Grey system theory has gained extensive attentions from worldwide researchers and has been successfully used in many fields with favorable outcomes since it was designed by Deng in 1982 [1,2,3]. is theory is capable of addressing issues characterized by uncertainty, insufficient information, and limited data points, thereby providing strong technical support for uncertain analysis [4, 5]
Accurate future estimations play an essential role for decision-makers in framing and implementing sensible plans and policies. us, a grey prediction model with convolution integral, shorted for GMC(1, n), is introduced alongside with its improved variants GMCG(1, n). ese two models have been applied to solve various prediction issues by many researchers because of their correct solutions to the whitening function
Inaccurate methods to calculate the background values may incur large deviations of the parameter estimations, which are essential for accurate future projections. erefore, mathematical analyses of the gap between the actual and estimated background values are discussed in detail
Summary
Grey system theory has gained extensive attentions from worldwide researchers and has been successfully used in many fields with favorable outcomes since it was designed by Deng in 1982 [1,2,3]. is theory is capable of addressing issues characterized by uncertainty, insufficient information, and limited data points, thereby providing strong technical support for uncertain analysis [4, 5]. Ough the previous improvements in background values with the support of those heuristic intelligent techniques lead to the improvements of forecasting ability, they result in the low-level, -repeated, and complicated computations of grey models. General consensus gotten from the literature was that accurate background values are regarded as a crucial requirement to ensure the reliability and practicability of the GMC(1, n) model [23, 24], and the forecasting precision is heavily dependent on their correct computations Supporting this argument, one of the major contributions in this paper stems from the mathematical derivation of the actual background values, finding its differences from the estimated one in the conventional GMC(1, n) model. E nomenclature utilized in this paper is presented below and detailed explanations related to the formulas employed in each technique are given
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