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1、 购车问题的数学模型摘要本文针对不同人群购车的考虑因素，以及市场上几款典型用车的各项性能指标，使用层次分析法（AHP）建立数学模型分析各种汽车的市场前景。层次分析法是对 1些较为复杂、较为模糊的问题作出决策的简易方法，它特别适用于那些难于完全定量分析的问题。模型分为3个层次：目标层（购车），准则层（汽车性能指标）和方案层（汽车购买选择）。目标层是分析问题的预定目标，也就是购车。准则层包含了为实现目标所涉及的中间环节，根据不同人群在购车时所考虑因素，建立正互反矩阵，计算出权重向量，得出不同人群购车时的偏重因素。方案层包括了为实现目标可供选择的各种措施或决策方案，也是通过计算权重向量，得出各种汽车
2、在同 1 指标中的优劣。最后将准则层和方案层进行整合，即可得出不同人群可供选择的车型。把模型得出的结论和搜集的资料进行对比，可以发现两者的结论基本1致，说明该模型和实际比较贴近，结果比较合理。关键词：购车问题；决策；层次分析；1致性；权重向量。AbstractThe article is concerning consideration automobilesand various function targets of above typical cars , Iestablished Maths model to analyze market prospects ofdifferent c
3、ars by use of AHP . It fives easy solutions tosome complex and unclear problems , and is suitable forthose problems not solved by quantitative analysis in particular . This model consists of three gradations :Aim(purchasing the car) , principle(capability target)and plan(choosing the car) . The aim
4、is a predeterminedone for problem analysis , which is automobile purchase .The principle includes middle segments involved for therealization of goals . According to adequateconsideration of different consumer needs , setting upmatrix , counting vectors ,I get the preferred elementsof them to purcha
5、se a car . The plan includes kinds ofsuggestions for choices . Then advantages anddisadvantages of the car are concluded under the modelsare finished for buyers to choose . Through thecomparison between the conclusion from the model andmaterial collected if the result is mostly the same ,that means
6、the model is close to reality and the theresult is reasonable .Key words : purchasing , decisopn , consistency , matrix购车问题的数学模型摘要本文针对不同人群购车的考虑因素，以及市场上几款典型用车的各项性能指标，使用层次分析法（AHP）建立数学模型分析各种汽车的市场前景。层次分析法是对1些较为复杂、较为模糊的问题作出决策的简易方法，它特别适用于那些难于完全定量分析的问题。模型分为3个层次：目标层（购车），准则层（汽车性能指标）和方案层（汽车购买选择）。目标层是分析问题的预定目标
7、，也就是购车。准则层包含了为实现目标所涉及的中间环节， 根据不同人群在购车时所考虑因素，建立正互反矩阵，计算出权重向量，得出不同人群购车时的偏重因素。方案层包括了为实现目标可供选择的各种措施或决策方案，也是通过计算权重向量，得出各种汽车在同1指标中的优劣。最后将准则层和方案层进行整合，即可得出不同人群可供选择的车型。把模型得出的结论和搜集的资料进行对比，可以发现两者的结论基本1致，说明该模型和实际比较贴近，结果比较合理。关键词：购车问题；决策；层次分析；1致性；权重向量。AbstractThe article is concerning considerationautomobiles and
8、 various function targets of above typicalcars , I established Maths model to analyze marketprospects of different cars by use of AHP . It fives easysolutions to some complex and unclear problems , and issuitable for those problems not solved by quantitativeanalysis in particular . This model consis
9、ts of threegradations : Aim(purchasing the car) ,principle(capability target) and plan(choosing the car) .The aim is a predetermined one for problem analysis ,which is automobile purchase . The principle includesmiddle segments involved for the realization of goals .According to adequate considerati
10、on of different consumerneeds , setting up matrix , counting vectors ,I get thepreferred elements of them to purchase a car . The planincludes kinds of suggestions for choices . Thenadvantages and disadvantages of the car are concludedunder the models are finished for buyers to choose . Throughthecomparisonbetweentheconclusionfromthemodelandmaterialcollectediftheresultismostlythesame,thatmeansthemodelisclosetorealityandthetheresultisreasonable.Keywords:purchasing,decisopn,consistency,matrix