基于统一灰色生成算子的三参数离散灰色预测模型及其应用  

A Three-parameter Discrete Grey Forecasting Model Based on Unified Grey Generation Operator and Its Application

作　　者：李惠 曾波[1] 苟小义 白云[1] LI Hui;ZENG Bo;GOU Xiao-yi;BAI Yun(School of Management Science and Engineering,Chongqing Technology and Business University,Chongqing 400067,China;College of Business Administration,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学管理科学与工程学院,重庆400067 [2]重庆工商大学工商管理学院,重庆400067

出　　处：《运筹与管理》2022年第7期119-123,共5页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(72071023,71771033,71801044);国家社科基金资助项目(19BSH064);重庆市基础研究与前沿探索专项项目(cstc2020jcyj-msxmX0297);重庆市教委科学技术研究重点项目(KJZD-K202000804)。

摘　　要：现有三参数离散灰色预测模型的累加阶数取值范围局限于正实数,导致模型建模能力和作用空间受限。为此,论文首先引入实数域统一灰色生成算子;然后,基于统一灰色生成算子构造了新型三参数离散灰色预测模型,实现了其阶数从正实数到全体实数的拓展与优化,从而使得新型模型具备挖掘时序数据积分特性与差异信息的双重功能;最后,将该新模型应用于某装甲装备维修经费的建模,结果显示其精度优于其它同类灰色模型。本研究成果对完善灰色算子基础理论及提高灰色预测模型建模能力具有重要价值。The accumulating order of the existing three-parameter discrete grey forecasting model are limited to positive real numbers,which leads to the limitation of modeling ability and action space of the model.In this study,a unified grey generation operator in real number field is introduced.Moreover,a novel three-parameter discrete grey forecasting model based on this unified grey generation operator is constructed,and the expansion and optimization of its order from non-zero positive real number to all real numbers are realized.Therefore,this novel model has the dual function of mining the integral characteristic and difference information of time series data.Finally,the new model is applied to the modeling of maintenance cost of an armored equipment,and the results show that its accuracy is better than other similar grey models.The research results are of great value for improving the basic theory of grey operators and increasing the modeling ability of grey forecasting models.

关 键 词：灰色理论 三参数离散灰色预测模型 实域分数阶算子 装甲装备维修经费预测 

分 类 号：N941.5[自然科学总论—系统科学]