【作者】 万玉成；

【导师】 盛昭瀚；

【作者基本信息】 东南大学 ， 管理科学与工程， 2004， 博士

【摘要】 本文根据不确定性信息的不同表现将不确定性分为随机性、模糊性、灰性和未确知性四种不确定性。其中,前三种不确定性已为人们所熟悉并进行了广泛地研究,后一种不确定性是一种新的不确定性,正在引起人们越来越多的关注,对它的研究和应用已取得了一些有价值的成果。但未确知性在预测与决策问题中的应用研究还很少,因此,本文将研究未确知性在预测与决策问题中的应用。本文除前言、未确知数学基础和结论外,共包括如下三部分内容: 第一部分:未确知预测的基本方法与组合预测方法(第二章和第三章)。第二章利用未确知数学方法给出了三种基本预测方法。首先给出了输出信息为未确知信息的回归预测法及其参数估计与应用实例,然后给出了基于未确知测度的分类预测法与应用实例,最后给出了基于未确知测度的聚类预测法与应用实例。第三章利用组合预测模型综合处理实际预测问题中含有的多种不确定性信息,给出了三种新的广义加权平均组合预测模型,并对其参数估计方法进行了研究,数值例子表明了方法的有效性。第二部分:未确知决策方法与未确知优化方法(第四章和第五章)。第四章首先给出了判断值为未确知数的层次分析法,给出了未确知判断矩阵的构造方法及其一致性检验方法和权系数求解方法以及数值例子; 然后给出了未确知测度评价方法和几种客观赋权法并对客观赋权法进行了比较。第五章首先给出了未来收益为未确知数的投资组合优化模型,给出了利用群决策相对熵集结模型求解未确知风险投资组合优化模型的方法与应用实例; 然后给出了含等式约束的系数为未确知数的线性规划模型及其求解方法与应用实例。第三部分:未确知预测与未确知决策的应用(第六章和第七章)。第六章给出了未确知预测在航材消耗预测中的应用,建立了三种基于灰色预测与未确知聚类预测的航材消耗广义加权平均组合预测模型,得到了满意的结果。第七章给出了未确知决策在风险投资决策中的应用,首先利用未确知层次分析法对风险投资项目进行选择,然后在对风险投资非系统风险因素进行系统分析的基础上利用未确知测度评价对风险投资非系统风险进行评价,并在评价的基础上建立了风险的未确知控制模型,并对实际问题获得了成功地应用。更多还原

【Abstract】 The uncertainty of objective is divided into four kinds in this paper. There are randomness, fuzziness, greyness and unascertainty. Among them the former three kinds of uncertainty have been researched widely and the fourth kind uncertainty has received significant attention in recent years. And a number of valuable results and applications of unascertainty have been obtained. But little work has been carried out for the applications of unascertainty in forecasting and decision making. This paper will research the applications of unascertainty in forecasting and decision making. Except the foreword, basic knowledge of unascertained mathematics and conclusion, this paper includes the following three parts: Part One is the basic methods of unascertained forecasting and combining forecasting (Chapter 2 and Chapter 3). In Chapter 2, the unascertained linear regression model with unascertained regression parameter is presented and its parameter estimation method is given firstly. The unascertained classfiy regression forecasting is given secondly. And the unascertained clustering forecasting is given finally. In Chapter 3, we use the combining forecasting model to deal with the different kinds of uncertainty information of the forecasting problem. Three kinds of generalized weighted mean combining forecasting models and their parameter estimation methods are proposed. And their efficiencies are demonstrated by examples. Part Two is the methods of unascertained decision making and unascertained optimization (Chapter 4 and Chapter 5). In Chapter 4, the analytic hierarchy process based on the unascertained three-valued judgments is presented and its method to check the consistency degree of the pairwise comparisons judgment matrix and the calculation method of weighting coefficients are given. Then, the unascertained measure evaluating method is given and several objective methods of determining the weights are given. In Chapter 5, a new decision model of investment combination on venture capital by using the unascertained mathematics is given for the future income of venture capital is unascertained. The coefficients of the general partners on risk and income are given by using the relative entropy aggregation model of group decision making. And the method of weighting coefficients of venture capital investment combination is given. Then, the all coefficient unascertained linear programming with equations is discussed and its solution method is given. And an application example is given. Part Three are the applications of unascertained forecasting and unascertained decision making (Chapter 6 and Chapter 7). In Chapter 6, the application of unascertained forecasting in air material consumption is given. Three kinds of generalized weighted mean combining forecasting models of air material consumption based on grey system and unascertained clustering forecasting are proposed and their efficiencies are demonstrated by examples. In Chapter 7, the application of unascertained decision making in venture capital is given. Firstly, the unascertained analytic hierachy process is used to choose the venture capital items. Then, an index system for evaluating the non-systematic risks of venture capital investments is established on the basis of analysing the factors affecting the non-systematic risks of venture capital investments. And the unascertained measure method for evaluating the risks of venture capital investments is presented by applying the unascertained measure theory. Finally, the model for controlling the risks of venture capital investments is established on the basis of the results of the unascertained measure evaluation of venture capital investments. An example of practical application is given to show the effectiveness of this method.更多还原