加权累加生成的GM(1,1)模型及其应用  

GM(1,1) Model Based on Weighting Accumulated Generating Operation and Its Application

作　　者：钱吴永[1] 党耀国[1] 王叶梅[1] 

机构地区：[1]南京航空航天大学经济与管理学院,江苏南京210016

出　　处：《数学的实践与认识》2009年第15期47-51,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目(70473037);江苏省软科学重点项目资助项目(BK2006025)

摘　　要：根据灰色系统理论中的新信息优先原理知新信息对认知的作用大于老信息的作用,而传统的累加生成没有体现原始数据中新信息的重要性.针对这一问题提出了加权累加生成的概念,并对加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,得到加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,然后建立了基于加权累加生成的GM(1,1)模型.通过具体算例的计算表明,加权累加生成的GM(1,1)模型的模拟和预测精度比传统的GM(1,1)模型模拟和预测精度高,从而说明了该法的有效性.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.

关 键 词：灰色系统 加权累加生成 GM(1 1)模型 信息 

分 类 号：N941.5[自然科学总论—系统科学]