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購車問題的數學模型
購車問題的數學模型
摘要
本文針對不同人群購車的考慮因素，以及市場上幾款典型用車的各項性能指標，使用層次分析法（AHP）建立數學模型分析各種汽車的市場前景。層次分析法是對1些較為復雜、較為模糊的問題作出決策的簡易方法，它特別適用于那些難于完全定量分析的問題。模型分為3個層次：目標層（購車），準則層（汽車性能指標）和方案層（汽車購買選擇）。目標層是分析問題的預定目標，也就是購車。準則層包含了為實現目標所涉及的中間環節，根據不同人群在購車時所考慮因素，建立正互反矩陣，計算出權重向量，得出不同人群購車時的偏重因素。方案層包括了為實現目標可供選擇的各種措施或決策方案，也是通過計算權重向量，得出各種汽車在同1指標中的優劣。最后將準則層和方案層進行整合，即可得出不同人群可供選擇的車型。把模型得出的結論和搜集的資料進行對比，可以發現兩者的結論基本1致，說明該模型和實際比較貼近，結果比較合理。
關鍵詞：購車問題；決策；層次分析；1致性；權重向量。
Abstract
The article is concerning consideration automobiles and various function targets of above typical cars , I established Maths model to analyze market prospects of different cars by use of AHP . It fives easy solutions to some complex and unclear problems , and is suitable for those 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 is a predetermined one for problem analysis , which is automobile purchase . The principle includes middle segments involved for the realization of goals . According to adequate consideration of different consumer needs , setting up matrix , counting vectors ,I get the preferred elements of them to purchase a car . The plan includes kinds of suggestions for choices . Then advantages and disadvantages of the car are concluded under the models are finished for buyers to choose . Through the comparison between the conclusion from the model and material collected if the result is mostly the same , that means the model is close to reality and the the result is reasonable .
Key words : purchasing , decisopn , consistency , matrix
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