多属性决策中指标权重确定方法的研究-数学专业论文.docxVIP

ii ii 摘 要 对于一个多方案的多属性决策问题, 由于其问题的复杂性, 往往表现为多属性 的综合评价. 综合评价是决策的前提, 正确的决策来源于对各方案的科学的综合评 价. 本文主要讨论了多属性综合评价过程中评价指标的权重的确定问题. 一般来 说, 构成多属性综合评价的要素有: 评价者或决策者; 被评价对象或方案; 指标集; 权重系数和综合评价模型等. 其中, 各指标权重的确定是核心问题. 关于权重的确 定, 一般分为主观赋权法和客观赋权法两大类, 这两类方法各有利弊. 为了消除主 观赋权法和客观赋权法各自的不足, 人们又提出了集成主、客观权重的组合赋权 方法. 目前, 集成权重方法的研究已成为多属性决策问题的研究热点, 取得了不少 的研究成果. 本文的结构如下: 第一节简要介绍了多属性决策的模式和评价指标的建立、筛选以及评价指标 的规范化方法. 第二节介绍了主、客观赋权法的含义和特征, 以及一些常用的主、客观赋权 法的方法和特点. 第三节介绍了运用一种主观权重和一种客观权重集成指标最终权重的研究成 果. 第四节将第三节中的运用一种主观权重和一种客观权重集成最终权重的模型 推广到已知p(p ≥ 1)种主观权重和q(q ≥ 1)种客观权重集成最终权重的情形; 并对 已有的一些集成指标最终权重的模型做了改进, 改进后的模型使得各指标权重的 确定更加方便、简洁; 同时, 建立了新的基于最优化理论和Jaynes最大恼原理的 集成指标最终权重的模型; 最后, 通过算例验证了作者所提出的这些方法的有效性. 关键词:多属性决策; 指标; 权重; 集成方法; 模型 iii iii Abstract A decision-making problem that has many schemes always shows multi-attribute aggregated evaluation as it is complexity. The aggregated evaluation is the premise of decision-making. The proper decision-making comes from the scientific aggregated evalu- ation. In this paper, we mainly discuss the determinant problem of evaluated indices in the procedure of multiple indices aggregated evaluation. Usually, the elements that con- struct the multi-attribute aggregated evaluation are: evaluator(decision maker), evaluated objects(schemes), index set, coefficient of weights and the model of aggregated evaluation. The determinant problem of weights of indices is the crucial one of all. The methods to determine weights are usually divided into two categories: the subjective approach and the objective one. The two approaches to determine weights have both merits and defects, respectively. In order to avoid the disadvantages themselves, the integrated approach of it has been a fashion in this field and results have been acquired. The organization of this paper is follows: In Section 1, we introduce the models of the multiple attribute decision-making, the methods of establishment, selection, as well as standard of indices briefly. In Section 2, we introduce the meaning and char