灰色關(guān)聯(lián)度+層次分析法

1、#2層次分析法選擇旅游地目標(biāo)層準(zhǔn)則層方案層解:Cl、C2、C3.C4、C5分別表示景色、費(fèi)用、居住、飲食、旅途:Pl. P2. P3分別表示桂林、黃山、北戴河。（1）構(gòu)造成對(duì)比較矩陣:11/2433 21755A =1/4 1/7 11/2 1/3G =1/3 1/5 21 11/3 1/5 31 1_ 113_C3 =113C4 =1/3 1/3 1'12 f»1 1/3 1/8'1/2 1 2C-> =311/31/5 1/2 1831'13 4_1 1 1/4'1/3 11C5 =11 1/41/4 114 41（2）計(jì)算層次單排序的權(quán)向量

2、和一致性檢驗(yàn):成對(duì)比較矩陣A的最大特征值 入垃=5.073其對(duì)應(yīng)的歸一化特征向量為0.263 0.4750.055 0.0990.110ci =5.073-5= 0.0185-1CR = = 0.016 <0.11.12表明A通過一致性驗(yàn)證。對(duì)成對(duì)比較矩陣Cl、C2、C3、C4、C5求層次總排序的權(quán)向量，歸一化列于下表, 并進(jìn)行一致性檢驗(yàn)：k1234530.5950.0820.4290.6340.1660.264(3)3k0.2760.2360.4290.1920.1660.4760.1290.6820.1420.1740.6680.054,3)3.0063.00233.00930.09

3、8Ch0.0030.00100.00500.109由 CRk =CRk V0丄k = 1,2345Mk知Cl、C2. C3、C4> C5通過一致性檢驗(yàn)。（3）計(jì)算層次總排序權(quán)值和一致性檢驗(yàn):組合權(quán)向量0.2640.595 0.082 0.429 0.6340.166-0.4760.299一於=0.276 0.236 0.429 0.1920.1660.054=0.2450.129 0.682 0.142 0.1740.6680.0980.4550.109組合一致性檢驗(yàn)0.2640.476CI=0.003 0.001 0 0.005 o0.054= 0.001760.0980.109RI

4、=0.580.00176CR=0.016 += 0.019 < 0.10.58故層次總排斥通過一致性檢驗(yàn)，3 = 0.299 0.245 0.455可作為最后的決策依 據(jù)，各方案權(quán)重排序?yàn)镻3>Pi>P2,本題計(jì)算過程列表如下：權(quán)向量C對(duì)A0.2640.4760.0540.0980.109A m(2)CI(2)CR(2)5.0720.0180.016準(zhǔn)則CC1C2C3C4C5組合權(quán)向量P對(duì)U權(quán)向P10.5950.0820.4290.6340.1660.299最PP20.2760.2360.4290.1920.1660.245對(duì)CP30.1290.6820.1420.1740.

5、6680.455入 111(3)3.0063.00233.0093CR(3)CV3)0.0030.00100.0050RIk(3)0.580.580.580.580.580.019#3灰色關(guān)聯(lián)分析工業(yè)、農(nóng)業(yè)、運(yùn)輸業(yè)、商業(yè)各部門的行為數(shù)據(jù)如下:工業(yè)農(nóng)業(yè)運(yùn)輸業(yè)商業(yè)X=(458,43442.3,41.9)X? = (39.1,41.6,43.9,44.9)x3 = (3.433353.5)X4 =(6.7?6.8J5.4,4.7)參考序列為X,被比較序列為冷，X3, X4，試求關(guān)聯(lián)度。解：以X1為參考序列求關(guān)聯(lián)度。廣step：初始化，即將該序列所有數(shù)據(jù)分別除以第一個(gè)數(shù)據(jù)。得:X； = （1,0.94

6、76,0.9236,0.9148）X； = （l,09706JL0294J0294）X； = （1J.O639J.1228J.1483）X； = （1JL.0149,0.8060,0.7015）2ndStep：求序列差A(yù)3 =（0,0.0230,0.1058,0.1146）A2 =（0,0.1163,0.1992,0.2335 ）A4 =（0006730117602134）3ldStep：求兩極差m= niiii mill Ajk）= 0M = max max Ajk ）= 0.23354thStep：計(jì)算關(guān)聯(lián)系數(shù)取p=0.5,有:Zh（k）=0,11675Ax（k）+0.11675從而:712（2 ）=0.5009/12（3）= 0.3695Z12（4）= 0.3333/13（2）= 0.8355Z13（3）= 0.5245/13（4）= 0.5047714（2）= 0.6342Zu（3）= 0.4982Zu（4）= 035375th Step：求關(guān)聯(lián)度14