灰色累加算子与灰色累减算子的统一及其应用  

Unification of grey accumulation operator and the inverse operator and its application

作　　者：曾波[1] 余乐安[2] 刘思峰[3] 孟伟[1] 李惠 周猛 ZENG Bo;YU Lean;LIU Sifeng;MENG Wei;LI Hui;ZHOU Meng(School of Management Science and Engineering,Chongqing Technology and Business University,Chongqing 400067,China;College of Economics and Management,Beijing University of Chemical Technology,Beijing 100029,China;College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,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]北京化工大学经济管理学院,北京100029 [3]南京航空航天大学经济与管理学院,南京211106

出　　处：《系统工程理论与实践》2021年第10期2710-2720,共11页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71771033,72071023);重庆市基础研究与前沿探索项目(cstc2019jcyj-msxmX0003)。

摘　　要：当前灰色算子阶数取值范围(R^(+))的局限性导致其难以实现对序列差异信息的有效挖掘.本文在传统Gamma函数基础引入参数δ,构建了一种阶数面向实数域R的新型灰色算子,实现了传统灰色累加算子和累减算子的统一.进一步研究表明,阶数通过其极性的正负来判定灰色算子的类型:当阶数r> 0,灰色算子对序列做累加生成;当r <0,灰色算子对序列做累减生成;当r=0,灰色算子对序列不做任何运算.通过三个典型序列验证了新型灰色算子的有效性.最后,基于新型灰色算子构建雷达故障预测的RDGM(1,1)模型,其模型综合精度高达99.5%,实现了对雷达故障发生时点的精准预测.本研究成果解决了阶数取值非负性所导致的灰色算子运算类型单一性的不足,对提高灰色预测模型性能具有积极意义.The limited value range(R^(+)) of the order of grey operator makes it difficult to mine the sequence difference information effectively.In this study,the parameter δ is introduced into Gamma function and a new grey operator oriented to real number field R is constructed,which realizes the unification of the traditional grey accumulation operator and the inverse grey accumulation operator.Further research shows that the order determines the type of grey operator by its sign,positive or negative.When r> 0,the grey operator makes accumulation generation to the sequence,when r <0,the grey operator generates the sequence by subtraction,and when r=0,the grey operator does no operation on the sequence.The validity of the new grey operator is verified by three typical sequences.Finally,the RDGM(1,1) model of Radar fault prediction is constructed based on the new grey operator,and its comprehensive accuracy is as high as 99.5%,which realizes the accurate prediction of the time point of Radar fault occurrence.The results of this study provide a solution to the single type of grey operator operation caused by non-negativity of the order value,which can improve the performance of grey prediction models.

关 键 词：灰色理论 灰色生成算子 实数域 灰色预测模型 雷达故障预测 

分 类 号：N941.5[自然科学总论—系统科学]