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1毕业生志愿层次结构模型摘要本文主要针对青年毕业生志愿选择建立层次结构模型。首先根据实际情况列举若干准则,以毕业选择为目标层;以考研,留学,创业,打工四个选择去向为方案层;以社会贡献,期望收入,发展空间,家庭情况,生活环境5个准则为准则层建立层次结构。再构造成对比较矩阵矩阵,从层次结构模型的第2层准则层开始,对于从属于上一层每个因素的同一层诸因素,用成对比较法和1—9比较尺度构造成对比较阵,直到最下层,分别得到5个准则对于目标层的矩阵,方案层对社会贡献的矩阵,方案层对期望收入的矩阵,方案层对发展空间矩阵,方案层对家庭情况矩阵,方案层对生活环境矩阵。接着对于每一个成对比较阵计算最大特征根及对应特征向量,利用一致性指标、随机一致性指标和一致性比率做一致性检验,得到上述六个矩阵的权向量(见文中表二),最后利用求得权向量计算各方案对目标的权向量,比较创业、打工和留学在目标中的组合权重,最后得出志愿选择权重次序为:留学创业考研打工。此模型还可以利用选择旅游地,评选优秀学生生活实际问题。关键词层次结构模型;成对比较矩阵;一致性检验;权向量2一、问题重述大学生毕业即将都面临着去向的选择,是继续深造还是找工作的问题,继续深造的同学可以选择考研或者留学,找工作的同学可以选择打工或者自主创业,所以为大学毕业的青年建立一个选择志愿的层次结。二、模型建立与求解①建立层次结构模型首先,列出准则建立层次结构,最上层为目标层,即毕业选择志愿,最下方为方案层,有考研,留学,创业,打工4个供选择的志愿,中间层为准则层,有社会贡献,期望收入,发展空间,家庭情况,生活环境5个准则,各层次间的联系用相连的直线表示,如图1;图1青年毕业生选择志愿层次结构图②构造成对比较阵比较某一层n个元素c1,c2,…,cn对上层一个因素的影响,5个准则对目标的重要性,每次取两个因素ci和cj,用aij表示ci和cj对目标的影响之比,全部比较结果可用成对比较矩阵表示,则5个准则对于目标层的矩阵为:成对比较矩阵:11/21/41/51/7211/21/31/54211/21/453211/375431A毕业选择志愿C1社会贡献C2期望收入C3发展空间C4家庭情况C5生活环境P1考研P2创业P3打工P4留学目标层准则层方案层3方案层对社会贡献的矩阵:111/51/23513821/3161/31/81/61B方案层对期望收入的矩阵:211/521/351531/21/511/531/351B方案层对发展空间的矩阵:311/531/351731/31/711/531/351B方案层对家庭情况的矩阵:411/351/53171/31/51/711/85381B方案层对生活环境的矩阵:51331/51/3111/81/3111/85881B③计算特征向量并作一致性检验对于每一个成对比较阵计算最大特征根及对应特征向量,利用一致性指标、随机一致性指标和一致性比率做一致性检验。若检验通过,归一化后的特征向量即为权向量:若不通过,需重新构追成对比较阵。成对比较矩阵A的最大特征值:max=5.0995归一化特征向量:T0.0475,0.0837,0.1453,0.2301,0.4934e进行一致性检验,过程如下:(1)一致性检验指标CI为:max0.02491nCIn4(2)查找相应的平均随机一致性指标RI如下表:表1平均随机一致性指标RI数值从表中数据可得0.90RI,则0.02220.1CICRRI通过了一致性检验,所以权向量就是最大特征值的归一化特征向量,即:T0.0475,0.0837,0.1453,0.2301,0.4934对方案层与准则层之间的成对比较矩阵12345BBBBB、、、、进行特征值及特征向量的计算并且进行一致性检验的结果如表2:表2求解成对比较阵1B、2B、3B、4B、5B的相关数据成对比较阵最大特征值对应归一化特征向量CICR1B4.0686T(0.1270,0.5779,0.2445,0.0506)0.02290.02542B4.1315T(0.1087,0.5476,0.0698,0.2379)0.04380.04873B4.1170T(0.1175,0.5650,0.0553,0.2622)0.03900.04334B4.2011T(0.1286,0.2704,0.0419,0.5591)0.06700.07445B4.0498T(0.1839,0.0710,0.0710,0.6741)0.01660.0184因0.01CR故矩阵均通过了一致性检验。所以,每个矩阵的权向量为:T1=(0.1270,0.5779,0.2445,0.0506)T2=(0.1087,0.5476,0.0698,0.2379)T3=(0.1175,0.5650,0.0553,0.2622)T4=(0.1286,0.2704,0.0419,0.5591)T5=(0.1839,0.0710,0.0710,0.6741)④计算组合权向量并做组合一致性检验矩阵阶数n1234567RI值0.000.000.580.901.121.241.32矩阵阶数n891011121314RI值1.411.451.491.511.541.561.575利用12345,,,,和计算各方案对目标的权向量,即组合权向量,记作ˆ,比如对于方案层中的考研,它在准则层中的权重用12345,,,,的第一个分量表示,即:1ˆ=0.1270,0.1087,0.1175,0.1286,0.1839则考研在目标中的组合权向量为和1ˆ相应项的两两乘积之和,即:0.04750.1270+0.08370.1087+0.14530.1175+0.23010.1286+0.49340.1839=0.1525同样可以算出,创业、打工和留学在目标中的组合权重为:0.2526、0.0702和0.5217,于是权组合向量为:Tˆ=0.1525,0.2526,0.0702,0.5217故志愿选择权重次序为:留学创业考研打工6附录:程序:[11/21/41/51/7;211/21/31/5;4211/21/4;53211/3;75431]ans=1.00000.50000.25000.20000.14292.00001.00000.50000.33330.20004.00002.00001.00000.50000.25005.00003.00002.00001.00000.33337.00005.00004.00003.00001.0000[V,D]=eig(ans)V=0.0831-0.0126-0.0793i-0.0126+0.0793i0.2673-0.10230.1464-0.0530-0.0434i-0.0530+0.0434i-0.80180.09480.2542-0.1766+0.1183i-0.1766-0.1183i0.53450.31360.40260.0436+0.3169i0.0436-0.3169i0.0000-0.59710.86310.91730.9173-0.00000.7251D=5.099500000-0.0125+0.7110i007000-0.0125-0.7110i00000-0.000000000-0.0746b1=[11/51/23;5138;21/316;1/31/81/61]b1=1.00000.20000.50003.00005.00001.00003.00008.00002.00000.33331.00006.00000.33330.12500.16671.0000[V,D]=eig(b1)V=0.1977-0.5803-0.0694+0.0714i-0.0694-0.0714i0.89990.00000.94700.94700.38070.8124-0.1310+0.2621i-0.1310-0.2621i0.07880.0580-0.0299-0.0805i-0.0299+0.0805iD=4.06860000-0.00000000-0.0343+0.5273i08000-0.0343-0.5273ib1=[11/521/3;5153;1/21/511/5;31/351]b1=1.00000.20002.00000.33335.00001.00005.00003.00000.50000.20001.00000.20003.00000.33335.00001.0000[V,D]=eig(ans)V=0.1738-0.53740.0903-0.0276i0.0903+0.0276i0.8750-0.4224-0.9164-0.91640.11160.20490.0365+0.1069i0.0365-0.1069i0.43780.70060.1081-0.3561i0.1081+0.3561iD=4.13150000-0.03990000-0.0458+0.7330i0000-0.0458-0.7330ib3=[11/531/3;5173;1/31/711/5;31/351]9b3=1.00000.20003.00000.33335.00001.00007.00003.00000.33330.14291.00000.20003.00000.33335.00001.0000[V,D]=eig(b3)V=0.1847-0.1730+0.0292i-0.1730-0.0292i-0.24090.88800.90610.9061-0.82670.0869-0.0103-0.0913i-0.0103+0.0913i0.08860.41210.0091+0.3738i0.0091-0.3738i0.5006D=4.11700000-0.0037+0.6934i0000-0.0037-0.6934i0000-0.1095b4=[11/351/5;3171/3;1/51/711/8;5381]b4=1.00000.33335.00000.20003.00001.00007.00000.33330.20000.14291.00000.1250105.00003.00008.00001.0000[V,D]=eig(b4)V=-0.2023-0.2003+0.0721i-0.2003-0.0721i0.2754-0.42550.0591+0.3562i0.0591-0.3562i-0.6048-0.0660-0.0124-0.0751i-0.0124+0.0751i-0.0534-0.87960.90470.90470.7454D=4.20110000-0.0209+0.9153i0000-0.0209-0.9153i0000-0.1594b5=[1331/5;1/3111/8;1/3111/8;5881]b5=1.00003.00003.00000.20000.33331.00001.00000.12500.33331.00001.00000.12505.00008.00008.00001.0000[v,d]=eig(b5)v=110.26050.0849-0.2356i0.0849+0.2356i0.00000.10060.0353+0.0466i0.0353-0.0466i-0.70710.10060.0353+0.0466i0.0353-0.0466i0.70710.9549-0.9646-0.96460.0000d=4.04980000-0.0249+0.4484i0000-0.0249-0.4484i00000
本文标题:毕业生志愿层次结构模型
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