分类号 密级
本 科 毕 业 论 文
题 目 决策论与效用理论的学习及应用
英文题目 Learning and Application of Decision theory and Utility Theory
2013年 5月
摘 要
在现代社会中，随着社会生产力的巨大增长和科学技术的迅速进步，各种经济部门和组织的规模越来越大，它们之间的社会联系越来越广泛和复杂，竞争也越来越激烈。个人、企业、部门、地区乃至国家，经常面临许多需要作出决策的问题。决策者能否作出正确的决策是至关重要的。预期目标的实现，来源于正确的决策。本文简要介绍了决策的过程、要素和分类，初步了解决策论及效用理论的基础知识。内容包括：1，对不确定性决策进行决策的悲观主义准则、乐观主义准则、等可能性准则、最小机会损失准则和折中主义准则；2，对风险决策进行决策的最大期望收益决策准则、最小机会损失决策准则等；3，贝叶斯公式及其应用，决策树的分析举例；4，效用函数及其确定方法，效用曲线及其确定方法；5，效用值决策准则，多目标决策中的加权效用值准则，最大期望效用值准则。
关键词：不确定型决策； 风险型决策； 决策树； 贝叶斯公式； 效用曲线
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ABSTRACT
In modern society，with the tremendous growth of the social productive forces and the rapid progress of science and technology，the scale of various economic sectors and organizations is becoming larger and larger。The social connections between them are more and more extensive and complex，the competitions are more and more intense。Individuals, enterprises, sectors, regions and even countries often face many problems need to make decisions。Whether the decision-makers can make the right decisions is crucial。Achieving the desired objectives, from the right decisions。This article briefly describes the decision-making process，elements and classification；A preliminary understanding of the basics of the decision theory and utility theory。Includes ：（1）Making decision of uncertain decision in pessimism criteria，optimism criteria，equally likely possibility criteria，the minimum loss of opportunity criteria and eclecticism criteria。（2）Making decision of risk decision in maximum expected profit decision criteria，the minimum loss of opportunity decision-making criteria and so on。（3）Bayes formula and its applications，the analysis and examples of decision tree。（4）Utility function and the methods to ascertain it，utility curves and the methods to ascertain them。（5）The utility value of decision criteria，weighted utility value criteria in multi-objective decision，the maximum expected utility value criteria 。
Keywords：Decision making under uncertainty；Decision making under risk；Decision tree；Bayes formula；Utility curve。
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目 录
前 言....................................................................... 1 1 决策的程序、要素和分类 ..................................................... 2 1.1 决策程序 ............................................................... 2 1.2 决策问题的要素 ......................................................... 2 1.2.1 要素 .............................................................. 2 1.2.2 决策矩阵 .......................................................... 2 1.3 决策的分类 ............................................................. 3 2 不确定型决策 ............................................................... 4 2.1 等可能性准则（Laplace准则） ........................................... 4 2.2 悲观主义（max min）准则 ................................................ 4 2.3 乐观主义（max max）准则 ................................................ 5 2.4 折衷主义准则（乐观系数准则） ........................................... 5 2.5 最小机会损失准则（后悔值准则） ......................................... 5 2.6 应用 ................................................................... 5 3 风险型决策 ................................................................. 8 3.1 决策准则 ............................................................... 8 3.1.1 最大期望收益决策准则（expected monetary value ,EMV） .............. 9 3.1.2 最小机会损失决策准则（expected opportunity loss，EOL） ............ 9 3.1.3 EMV与EOL决策准则的关系 .......................................... 9 3.2 主观概率 .............................................................. 10 3.3 修正概率的方法——贝叶斯公式的应用 .................................... 10 3.4 应用——决策树 ........................................................ 10 3.4.1 决策树 ........................................................... 11 3.4.2 决策树决策分析举例 ............................................... 12 3.4.3 决策树的优缺点 ................................................... 14
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4 灵敏度分析和风险分析 ...................................................... 15 4.1 灵敏度分析 ............................................................ 15 4.1.1 灵敏度分析的意义 ................................................. 15 4.1.2 转折概率 ......................................................... 16 4.2 风险分析 .............................................................. 16 4.2.1 风险分析的意义 ................................................... 16 4.2.2 风险程度的度量 ................................................... 16 5 效用理论在决策中的应用 .................................................... 18 5.1 效用值 ................................................................ 18 5.2 效用函数和效用曲线的确定 .............................................. 18 5.2.1 效用函数的确定 ................................................... 18 5.2.2 效用曲线的确定 ................................................... 19 5.2.3 效用曲线的类型 ................................................... 19 5.3 效用值决策准则 ........................................................ 20 5.4 效用和风险的关系 ...................................................... 20 5.4.1 中立型效用函数 ................................................... 20 5.4.2 保守型效用函数 ................................................... 21 5.4.3 冒险型效用函数 ................................................... 21 5.5 在规范模型中的应用 .................................................... 22 结 论...................................................................... 24 致 谢...................................................... 错误！未定义书签。 参考文献 .................................................................... 25
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