灰色GM(1,1)分数阶累积模型及其稳定性  

GM(1,1) model based on fractional order accumulating method and its stability

作　　者：吴利丰[1] 刘思峰[1] 刘健[2] 

机构地区：[1]南京航空航天大学经济与管理学院,南京210016 [2]南京理工大学经济管理学院,南京210094

出　　处：《控制与决策》2014年第5期919-924,共6页Control and Decision

基　　金：国家社科基金重点项目(12AZD102);国家自然科学基金项目(71171113;71173106;71171116);教育部人文社会科学研究项目(12YJC630082);江苏省基础研究计划-–青年基金项目(BK20130786);国家级教学团队基金项目(10td128);南京航空航天大学研究生创新基地开放基金项目(kfjj130128);中央高校基本科研业务费专项资金项目;南京理工大学科研启动基金项目(AE88370)

摘　　要：基于矩阵扰动理论,研究利用累积法估计GM(1,1)模型参数时解的稳定性问题.研究结果表明:累积的阶数越高,解的扰动界越大;在扰动值相等的情况下,新数据相比于老数据,解的扰动界较小;新数据对解的影响较小,这与新信息优先原理相矛盾.对此,提出分数阶累积法,当阶数小于1时,这种矛盾有所缓解,解的扰动界也较小.最后通过具体实例验证了分数阶累积法的实用性与可靠性.Based on the matrix perturbation theory, the stability problem of the solution to accumulating GM（1,1） is studied. The research results show that the larger the order of accumulating is, the larger the perturbation bound is, and the perturbation bound is smaller when the newer data is perturbed under the equal perturbation. The traditional grey integer order accumulate method leads to the solution to model, which is contradictory with the principle of new information priority, thus the fractional order accumulating method is proposed. The contradiction is relieved and the perturbation bound is becoming smaller when the order is less than 1. A real example demonstrates the practicability and reliability of the proposed method.

关 键 词：灰色系统理论 GM(1 1)模型 累积法 分数阶 

分 类 号：N941.5[自然科学总论—系统科学]