【作者】 崔杰；

【导师】 党耀国；

【作者基本信息】 南京航空航天大学 ， 管理科学与工程， 2010， 博士

【摘要】 灰色系统理论是一种解决一类贫信息不确定性问题的有效方法,如今在农业、工业、国防、科技、教育、经济、管理等诸多领域已得到了广泛应用。随着研究的不断深入,该理论方法日趋完善,但依然存在许多亟须解决的问题。本文针对灰色不确定性建模的理论与方法展开一系列基础理论研究,其中包括缓冲算子的构建研究;灰色预测模型的构建研究,以及该模型的参数特性研究;现有关联度模型的优化,以及灰色关联分析模型的构建与性质研究;求解指标权重方法的优化研究,以及灰色决策模型构建研究等。本文的主要内容有:(1)缓冲算子的构建研究。根据新信息优先原理,在现有缓冲算子研究成果基础上,构建了若干个弱化缓冲算子和强化缓冲算子,并通过实例分析将本文构建的缓冲算子与已有缓冲算子的数据缓冲效果进行了对比分析。(2)灰色预测模型的构建与优化研究。根据灰色预测模型的建模机理,分析了经典GM(1,1)模型存在的缺陷,构建了一种灰色NGM(1,1,k)模型,并对该模型的初始值和背景值构造方法进行了优化,同时提出了非等间距灰色NGM(1,1,k)模型,并给出了该模型的建模方法与步骤。(3)灰色预测模型的参数特性研究。针对灰色建模时的原始数据预处理问题,研究了原始数据经过数乘变换后的灰色NGM(1,1,k)模型参数特性。针对原始数据的微小摄动对建模结果的影响程度问题,利用矩阵条件数对灰色NGM(1,1,k)模型的病态性问题进行了深入的分析,研究结果为该模型在实际中的有效应用提供了理论依据。(4)灰色关联分析模型的构建与性质研究。针对现有邓氏关联度模型存在的缺陷,提出了点关联系数稳定度的概念,并对该关联度模型进行了优化。另外,针对灰色关联度模型的性质,提出了关联度仿射性和仿射变换保序性的新概念,构建了一种灰色相似关联度模型,并对该模型的性质进行了研究。(5)灰色决策模型的构建研究。针对现有指标权重求解方法存在的缺陷,提出了一种求解指标权重的优化方法;根据新信息充分利用原则,构建了一种灰色多阶段动态决策模型,并通过算例对该模型的有效性进行了分析和验证。更多还原

【Abstract】 Grey system theory is an effective approach for solving a kind of problems with poor information uncertainty. It has been widely applied in agriculture, industry, national defense, science and technology, education, economy, management and other fields. With the deepening research, this theory has been continuously improved, but it still has many unsolved theoretical problems. With regard to the theories and methods for grey uncertain systems modeling, this paper conducts a series of basic theory research, including constructing new buffer operator, proposing an novel grey forecasting model, studying the characteristic parameters of the novel grey forecasting model, optimizing the existing grey relational model, creating a novel grey relational analysis model, optimizing approach for solving the index weight, and presenting a novel grey decision-making model, etc. The main contentss are as follows:The first innovation is to establish some novel buffer operators. According to the principle of new information, based on the existing researches on buffer operator, several novel weakening buffer operators and some novel strengthening buffer operators were built, and the compare novel buffer operators with the existing buffer operators in performance that buffer modeling data effect were carried out through a numerical example.The second innovation is to build a novel grey forecasting model, and study the parameter optimization of this model. According to the modeling mechanism of grey prediction model, we analyzed the defects of classical GM (1, 1) model, proposed a novel grey NGM (1, 1, k) model based on approximate non-homogeneous discrete exponential function, presented the optimizing approaches for the initial value and the background value of this grey model, put forward the non-equidistant NGM (1, 1, k) model, and gave its modeling steps.The third innovation is to study the novel grey NGM (1, 1, k) model. With regard to the preprocessing of original grey modeling data, we studied the parameters characteristics of the novel grey NGM (1, 1, k) model under multiple transform. We also analyzed the morbidity of NGM (1, 1, k) model under the original modeling data occur small perturbation, by using matrix conditions as research tool. The research results provide theory basis for the model in the actual application.The forth innovation is to propose a novel grey relational analysis model and its characters. With regard to some defects of the general relational analysis model, we put forward a novel definition of the stability of point correlative coefficient, and used it to optimize general relational analysis model. In addition, we built a novel grey similar relational analysis model, and proposed the novel concepts of affine and affine transform isotonicity of grey relational analysis model. Finally, we studied the two properties of the some grey relational analysis model.The fifth innovation is to establish a novel grey decision-making model. With regard to the defects of the existing method for solving index weight, we put forward an optimized method for solving index weight, According to the principle of fully using new information, we proposed a grey multi-stage dynamic decision-making model, and analyzed the validity of the model through an example.更多还原