灰色系统研究进展(2004—2014)

Advances in Grey System Research(2004—2014)

从灰数及其运算、灰色序列算子与灰色预测模型、灰色关联分析与灰色聚类评估模型、灰色决策模型、灰色组合模型和灰色控制几个方面介绍了灰色系统理论2004—2014年的研究进展及部分应用成果。梳理了基于"核"和灰度的灰数运算法则、一般灰数的概念、灰度合成公理及缓冲算子的一般形式,总结了4种GM(1,1)基本模型,即均值GM(1,1)模型(EGM)、离散GM(1,1)模型(DGM)、均值差分GM(1,1)模型(EDGM)、原始差分GM(1,1)模型(ODGM),及其适用的序列类型。介绍了灰色相似关联度、灰色接近关联度、三维灰色绝对关联度,以及基于中心点和端点混合三角白化权函数的灰色聚类评估模型、多目标加权智能灰靶决策模型、两阶段综合测度决策模型、灰色博弈模型、灰色投入产出模型,并且阐述了分布型、中立型和中立-分布型灰色随机时滞系统的指数鲁棒稳定性等新概念、新模型、新方法。同时提出了有待进一步研究解决的问题。

Abstract：The progress in grey system research from 2004 to 2014 is summarized. Some important new conceptions, new models and new methods are presented, such as algorithm rules of grey numbers based on the ＂kernel＂ and the degree of greyness of grey numbers, the concept of general grey number, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operator of grey sequence operator; four basic models of GM（1,1）, namely the even grey model （EGM）, the original difference grey model（ODGM）, the even difference grey model（EDGM）, the dis- crete grey model（DGM） , and their suitable type of each basic model; the similarity degree of grey inci- dence, the closeness degree of grey incidence and the three-dimensional absolute degree of grey inci- dence; the grey cluster model based on center-point and end-point mixed triangular whitenization weight functions~ the multi-attribute intelligent grey target decision model, the two-stage decision model with grey synthetic measure, the grey game model, and the grey input-output model; the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral dis- tributed-delay type of grey control, etc. Moreover, the problems which remain for further studying and solving are proposed.