变权综合理论与多目标决策

【作者】 李月秋；

【导师】 刘文奇；

【作者基本信息】 昆明理工大学 ， 系统理论， 2008， 硕士

【摘要】 常权综合仅仅考虑到各类指标在决策中的相对重要性,而忽略了对状态均衡程度的偏好,这种“以不变”(常权)应万变(指标值)的做法具有一定的片面性,为了解决此类问题,我国的汪培庄教授最早提出了变权的思想,并给出一个变权经验公式,李洪兴教授在系统研究因素空间理论时由经验公式出发对变权综合进行了深入的分析,给出了变权、状态变权向量和均衡函数的公理化定义,随后刘文奇教授根据变权综合与效用分析这两大决策理论之间的联系提出了折衷型变权模式,揭示了均衡函数为综合效用的推广形式和单因素效用的类型与均衡函数类型之间的关系,通过折衷型效用函数获得折衷变权,从而扩展了变权方法。李德清教授提出了多层次变权分析、等效关系及变权综合时状态变权向量的确定等一系列理论。本文在上述成果的基础上完成了以下几个方面的工作：首先介绍了因素空间理论的一些基本概念,接着是文章的主体部分,讨论了均衡函数的代数性质,指出在一定前提下,均衡函数集的加法、乘法运算构成半群,然后按等效关系进行等价类划分,验证了取自不同等价类中的均衡函数可根据代数运算得到与原有均衡函数均不等效的均衡函数,并给出了计算机可以实现的具体算法,同时,为了解决在决策中可以根据人的均衡要求有效地选择变权模型,而引入带参数的均衡函数。因为均衡函数的梯度向量是状态变权向量,所以用类似的方法讨论了状态变权向量的代数性质,得出状态变权向量集对于Hadamard运算也构成半群,按等效性分类,取自不同等价类中的状态变权向量,经过代数运算,可以获得与原状态变权向量均不等效的状态变权向量,同时,也给出了计算机可以实现的具体算法,并利用几何平均值和信息熵构造了两类新的状态变权向量。由于变权综合与多目标决策相结合,可以为许多实际问题提供更加合理的解决方法,因此在文章中给出了基于变权理论的可行方案集优劣顺序的排列方法,接下来用实例验证了该方法的科学性和有效性。最后,文章提出了对未来变权理论的研究设想。更多还原

【Abstract】 Professor WANG Pei-zhuang proposed most early variable weights thought, and gives one empirical formula of variable weights in order to solve the kind of problem that constant weight synthesis merely considers each kind of indicator in the decision-making relation importance, but has neglected to the condition balanced degree by personal preference, which "remain unchanged" (constant weight) should be changing (indicator value) practice has a certain one-sidedness. Professor LI Hong-xing gives axiomatic definition of variable weights, state variable weights vector and balance function through systematic research factor space theory and thorough analysis variable weights synthesis. Later Professor LIU Wen-qi proposed compromise of the variable weights pattern according to these two big decision theories relation between the utility analysis and variable weights synthesis, concluded balance function is extended form of synthesis utility and between the single factor utility type and balance function relation, obtained through the compromised utility function compromised variable weights, thus expended method of variable weights. Professor LI De-qing proposed a series of theories, for example hierarchy variable weight, the equivalent relations, state variable weights vector s determination when variable weights synthesis and so on.This article has completed the following several aspect work in the above achievement s foundation. First this article introduces some basic concepts of factor space theory. The main conclusion of the article is that discussed the algebraic properties of balance function, points out under certain premise, balance function collection can constitute semi-group by addition and multiple operation, then carries on the equal kind of division according to the equivalent relation, and verifies that between the new balance function which picks out different equal kinds by addition, multiply, power operation and original balance function are not the equivalent, and has given the concrete algorithm which the computer can do, at the same time, introduces the balance function with parameter in order to solve that variable weight s model can be effective choose, according to balance request of decision-making. Because the gradient vector of balance function is state variable weights vector, this article discusses the algebraic properties of state variable weights vector s with the similar method, obtains the state variable weights vector s collection can also constitute the semi-group by Hadamard multiple operator, then carries on the equal kind of division according to the equivalent relation, and verifies the between the new state variable weights vectors which picks out different equal kinds by Hadamard multiple operation and original state variable weight vectors are not equivalent, and has given the concrete algorithm which the computer can do and give two kind of new state variable weight vectors, based on geometry mean value and the information entropy. Variable weights synthesis and multi-objective decision-makings unify that may provide the more reasonable solution for many actual problems, therefore this article has given arrangement method of the feasible plan collection, then has confirmed this method scientific nature and the validity with the example. Finally, the article proposes the research tentative plan of variable weights theory.更多还原