导　　师： 王传生

学科专业： L01

授予学位： 硕士

作　　者： ;

机构地区： 首都经济贸易大学

摘　　要： 多属性决策(或者称之为有限个方案的多目标决策)是现代决策科学的一个重要组成部分，其实质是利用己有的决策信息通过一定的方式对一组(有限个)备选方案进行排序并择优。由于客观世界的复杂性、不确定性以及人类思维的模糊性，在实际决策过程中，决策信息往往以区间数等不确定的形式给出，从而不确定性多属性决策理论、方法及应用是目前众多决策研究工作者关注的热点。本文在前面学者们研究的基础上对区间多属性决策主要做了以下几个方面的工作:
　　 对区间数多属性决策研究的相关文献进行了综述，总结了相关理论成果的可取之处与仍需要进一步研究的地方。在此基础上，提出了在区间数多属性决策问题的研究过程中应注意区间数信息量与计算量的平衡，如果过分强调区间数的特殊性与其带来的信息量，那么必然会带来决策模型计算的复杂化，不利于决策时机的把握。
　　 能描述各个待决策方案的差异程度是应用离差最大法的先决条件，为描述各个方案的差异程度，本文定义了决策矩阵的离差度函数。各个待评价方案差异越大，该函数也就越大，反之越小，较好的表示了各个待决策方案在所有指标下的差异程度，并且该函数具有计算量不大的优点。
　　 本文在求解各个指标的权重系数的过程中，将离差最大化法与熵理论结合起来，建立了一个双目标优化模型，并且利用拉格朗日算子给出了最优解，也就是各个指标的权重系数。从而给出了一种改进的基于离差最大化与熵理论的区间数多属性决策模型。该模型即考虑了区间数的特殊性，其计算又不是很复杂，较好的考虑了信息量与计算量之间的平衡。并且通过计算机程序实现了模型的计算过程。本文最后将该模型应用到项目融资风险评估中，用实证证明了该模型的有效性。 Multi-attribute decision making/(MADM/) is very important in modern decision making analysis, and its main task is, based on the gathered information, how to determine the priority vector of the alternatives. Because of the complexity and uncertainty involved in real-world decision problems and the inherent subjective nature of human judgment, during practical decision process, decision information is sometimes expressed as interval number. Further more, some studies on theories, methods and application of uncertain multi-attribute decision making have attracted much attention. In this thesis, some problems of interval number multi-attribute decision- making have been investigated. First of all, I do much wok in literature summary on interval number multi-attribute decision making theory to summarize the achievements and good points of the related theories. What's more, I find that there is something that we can do further study work. In this paper, I propose that we should pay more attention on the balance between the complex degree of computation and information content of interval number. If we pay too much attention on information content of interval number, we would lose the best opportunity that make a right decision. If we want to use the deviation maximization theory, we must resolve this problem that how to describe the difference between solutions to be appraised. In this paper, I define a new deviation-function to describe the difference between solutions to be appraised. If the deviation of solutions to be appraised is remarkable, the value of deviation-function that I define is large. Contrariously, the value of deviation-function is small. An other advantage of this deviation-function is it's calculated amount is quite simple. In this paper, I build a new decision-making model on deviation maximization theory and entropy to distribute right weight coefficient to right attribute. In this new decision-making model, I build a double target programming model. By Lagrange-operator, I calculate the best answers to that double target programming model. At last, I use this new decision-making model on deviation maximization theory and entropy in risk assessment in project -financing. The result proves that the new decision-making model is useful and simple.

关 键 词： 区间数多属性决策 熵理论 离差最大法 双目标优化模型 拉格朗日算子

分 类 号： [C934]

领　　域： [经济管理] [社会学]