基于粒子群算法的变权累加生成的GM(1,1)模型

根据灰色系统的新信息优先原理可知新信息对认知的作用大于旧信息的作用,而传统的累加生成没有体现原始数据中新信息的重要性.针对这一问题引入了变权累加生成的方法,并对变权累加生成在单调性、灰指数规律、凸性等方面的性质进行了研究,得到变权累加生成序列具有单调递增性,具有较强的指数规律,并具有下凸性,这些性质是高精度建模的保证,然后建立了基于变权累加生成的GM(1,1)模型,并运用粒子群算法确定了变权累加生成的权重.通过具体的算例计算表明,变权累加生成的GM(1,1)模型能够提高模型的模拟和预测精度.

GM(1,1) Model Based on Variable Weight Accumulated Generating Operation and Particle Swarm Optimization

Based on the priority principle of new information in grey system theory,the new information counts much in information cognition to the old.As the traditional GM(1,1) model does not reflect the importance of the new information,this paper presented the concept of weighting accumulated generating operation and made a research on its properties including monotonic property,grey exponent law and convexity.The research shows that weighting accumulated generating sequence displays a strong law of grey exponent,the characteristics of monotonic increment and downwards convexity.So a new GM(1,1) model is established based on weighting accumulated generating operation.The example indicates that the new method can improve the precision of simulation and prediction greatly compared with the traditional one and thereby shows its efficiency.