基于MATLAB的AHP实现

湖南人文科技学院毕业论文（设计）第1页目录中英文摘要...........................................................................................................................21．层次分析法·······················································································31．1概述..........................................................................................................................31．2AHP的基本原理和步骤[6]......................................................................................31.2.1递阶层次结构原理·······································································31.2.2标度原理···················································································41.2.3排序原理···················································································41.3AHP的层次总排序及其一致性检验.......................................................................61.3.1层次总排序··············································································61.3.2AHP的一致性检验···································································72．MATLAB的基本内容··········································································72.1MATLAB矩阵..........................................................................................................82.1.1MATLAB矩阵的建立·································································82.1.2矩阵的特征值与特征向量····························································82.2MATLAB的M文件...............................................................................................93．基于MATLAB的AHP实现·································································103．1AHP的MATLAB的计算流程框图....................................................................103．2平均随机一致性指标的MATLAB实现.............................................................103．3AHP各环节的MATLAB实现...........................................................................123.3.1特征向量及其归一化的MATLAB实现············································123.3.2一致性检验及单排序的MATLAB实现············································133.3.3一致性检验及总排序的MATLAB实现············································143.3.4选择最优排序············································································154．基于MATLAB的AHP应用·································································164．1挑选合适工作问题..............................................................................................165．结束语·····························································································26参考文献·······························································································27致谢·····································································································28湖南人文科技学院毕业论文（设计）第2页基于MATLAB的AHP实现摘要：在实际统计分析工作中，常会遇到多指标的综合评价和多目标决策的问题。许多人利用层次分析法将复杂的问题分解为若干层次和若干因素，在各因素之间进行简单的比较和计算，就可以得出不同方案的权重，为最佳方案的选择提供依据且使问题简单化。但是，受计算条件的限制，不能及时给出结果，从而影响现场决策。MATLAB是当今最优秀的科技应用软件之一，利用MATLAB对层次分析法的判断、分析和计算过程进行处理后，为决策者提供方便友好的对话界面。只要决策者在MATLAB软件中输入自己的层次结构方案和两两对比的判断矩阵后能迅速得出相应的结果，为解决实际问题提供一个快捷的方法。从而提高人们的决策效率，同时也为科技工作者使用层次分析法提供一种新思路。关键词：AHP；层次分析法；MATLAB应用MATLAB-basedimplementationoftheAHPAbstract:Inpractice,statisticalanalysiswork,weoftenencountermulti-indexcomprehensiveevaluationandmulti-objectivedecision-making.ManypeopleuseAHPtothecomplexproblemintoanumberoflevelsandanumberoffactors,amongvariousfactors,asimplecomparisonandcalculationcanbedrawnontheweightofdifferentoptions,inordertoprovideabasisforselectionofthebestprogramsmaketheproblemsimpleof.However,duetothecalculationconditions,theresultscannotbegiveninatimelymanner,thusaffectingtheon-sitedecision-making.MATLABisthemostoutstandingapplicationofscienceandtechnology,usingMATLABtodeterminetherightlevelofanalysis,analysisandcomputationprocessing,inordertoprovidedecisionmakerswithconvenientuser-friendlydialoginterface.Whenthedecision-makersinMATLABsoftware,entertheirownhierarchyoftheprogramandjudgmentmatrixtodeterminequicklyafterthecorrespondingresultsobtained,inordertosolvepracticalproblemstoprovideaquickmethod.Therebyenhancingtheefficiencyofpeople'sdecision-making,butalsoforthescientificandtechnologicalworkerstouseAHPtoprovideanewidea.Keywords:AHP；MATLABApplications湖南人文科技学院毕业论文（设计）第3页1．层次分析法1．1概述在市场竞争日益激烈的今天，企业或个人经常面临复杂的决策问题，不仅需要快速作出决策，而且需要解决决策问题中多种不确定性所带来的困难。决策分析问题中的重要组成部分是多属性决策，虽然多属性决策问题的背景不同，但它们通常具有下列共同特点:[1](1)属性之间通常是相互冲突和不可公度的(属性量纲不同)；(2)在属性集中，可能同时存在定性属性和定量属性；(3)属性经常构成一个层次结构；(4)决策信息有时是不完全的，决策者只能提供决策参数的不完全信息；决策者的判断可能是不确定的，即没有100%的把握做出主观判断。美国著名运筹学家T.L.Saaty教授于70年代中期创立了一种实用的多准则决策法——层次分析法（TheAnalyticHierarchyProcess，简称AHP）[2]。是一种实用的多准则决策方法，是处理那些完全用定量方法来解决复杂问题的有效手段，也是定量分析和定性分析相结合的决策方法。更是在多目标、多准则的条件下，对多种方案进行选择与判断的一种简洁而有力的工具。众多的工作表明，AHP的应用范围十分广泛，其应用已涉及到能源政策和资源规划，企业管理与生产决策，管理信息系统[3]，经济分析和计划，政治和冲突分析[4]，行为和社会学[5],科技发展和评价，军事指挥，农业气候区划，大气和水环境质量评价，湖泊富营养化评价等领域，可以预料，随着对AHP理论的深入研究，它的应用范围必将进一步拓广。正因为如此，人们自然地要求了解和掌握AHP的应用技巧。本文旨在基于层次分析法的基础上，在MATLAB中编制对层次分析法的判断、分析和计算过程的程序，决策者只要输入层次结构方案和判断矩阵，就能迅速得出相应的结果，为决策者解决问题提供一种快速的、具有较强实用价值的方法。1．2AHP的基本原理和步骤[6]AHP的内容和决策方法是由它的基本原理确定的。AHP的原理包括递阶层次结构原理、标度原理、排序原理。[7]1.2.1递阶层次结构原理一个复杂的问题可分解为它的目标、约束准则和方案等因素,按照不同属性把这些因素分组形成互不相交的层次,上一层的因素对相邻下一层次的全部或部分因素