湖南文理学院学报（自然科学版）
湖南文理學院學報（自然科學版）
호남문이학원학보（자연과학판）
JOURNAL OF HUNAN UNIVERSITY OF ARTS AND SCIENCE(SCIENCE AND TECHNOLOGY)
2013年
2期
61-66
,共6页
多变量%背景值%倒数累加生成%非等间距序列%逐步优化建模%MGM(1,n)模型%最小二乘法
多變量%揹景值%倒數纍加生成%非等間距序列%逐步優化建模%MGM(1,n)模型%最小二乘法
다변량%배경치%도수루가생성%비등간거서렬%축보우화건모%MGM(1,n)모형%최소이승법
multivariable%background value%accumulated generating operation of reciprocal number%nonequidista-nce sequence%a step by step optimum modeling%non-equidistance MGRM(1,n)%least square method
灰色系统理论是研究贫乏信息的科学理论,具有广泛的适应性。应用逐步优化的建模方法构造多变量非等间距优化灰色模型MGRM(1, n)的背景值,以相对误差均值最小为目标函数,以MGRM(1, n)响应初值修正量为设计变量,基于倒数累加生成建立了非等间距多变量优化灰色模型MGRM(1, n)。该模型不仅适合于等间距建模型,也适合于非等间距建模,拓广了灰色模型的应用范围。该模型精度高,使用简单。实例表明所建模型的实用性与可靠性。
灰色繫統理論是研究貧乏信息的科學理論,具有廣汎的適應性。應用逐步優化的建模方法構造多變量非等間距優化灰色模型MGRM(1, n)的揹景值,以相對誤差均值最小為目標函數,以MGRM(1, n)響應初值脩正量為設計變量,基于倒數纍加生成建立瞭非等間距多變量優化灰色模型MGRM(1, n)。該模型不僅適閤于等間距建模型,也適閤于非等間距建模,拓廣瞭灰色模型的應用範圍。該模型精度高,使用簡單。實例錶明所建模型的實用性與可靠性。
회색계통이론시연구빈핍신식적과학이론,구유엄범적괄응성。응용축보우화적건모방법구조다변량비등간거우화회색모형MGRM(1, n)적배경치,이상대오차균치최소위목표함수,이MGRM(1, n)향응초치수정량위설계변량,기우도수루가생성건립료비등간거다변량우화회색모형MGRM(1, n)。해모형불부괄합우등간거건모형,야괄합우비등간거건모,탁엄료회색모형적응용범위。해모형정도고,사용간단。실례표명소건모형적실용성여가고성。
Grey system is a theory which studies poor information specially, and it possesses wide suitability. Applying a step by step optimum modeling method, constructing background value of non-equidistance multi-variable optimizing Grey model MGRM(1, n), taking the mean relative error as objective function and taking the modified values of response function initial values as design variables, based on accumulated generating operation of reciprocal number non-equidistance multi-variable optimizing Grey model MGRM(1, n) was built. The proposed model can be used to build model in non-equal interval&equal interval time series, enlarges the scope of application, and, has high precision and easy to use. Example validates the practicability and reliability of the proposed model.
