Soal
Suatu kelurahan mendapatkan Bantuan Langsung Tunai dari pemerintah untuk masing masing kepala keluarga dengan syarat ketentuan sebagai berikut :
C1 : Jumlah Tanggungan
C2 : Pendapatan Kepala Keluarga
C3 : Luas Bangunan Rumah
C4 : Memiliki KK
Bobot W : [5,4,3,3]
Nama KK
|
C1
|
C2
|
C3
|
C4
|
Aldyan
|
2
|
2
|
3
|
1
|
Hendro
|
3
|
3
|
1
|
2
|
Joko
|
2
|
4
|
1
|
2
|
Doni
|
2
|
2
|
2
|
2
|
Dono
|
3
|
3
|
4
|
2
|
Kasino
|
2
|
2
|
2
|
2
|
Susento
|
1
|
4
|
5
|
1
|
Penyelesaian
:
X1 =√2²+3²+2²+2²+3²+2²+4²=5,916
R11=
2/5,916=0,3380
R21=
3/5,916=0,5070
R31=
2/5,916= 0,3380
R41=2/5,916
= 0,3380
R51=3/5,916=0,5070
R61=2/5,916=0,3380
R71=1/5,916=0,6190
X2=√2²+3²+4²+2²+3²+2²+4²=7,874
R12=
2/7,874=0,2540
R22=
3/7,874=0,3810
R32=
4/7,874=0,5080
R42=2/7,874=0,250
R52=3/7,874=0,3810
R62=2/7,874
=0,2540
R71=1/5,916=0,6190
X3=√3²+1²+1²+2²+4²+2²+5²=
7,745
R13=
3/7,745=0,3873
R23=
1/7,745=0,1291
R33=1/7,745=0,1291
R43=2/7,745=0,2582
R53=4/7,745=0,5164
R63=2/7,745=0,2582
R73=1/5,916=0,6190
X4=√1²+2²+2²+2²+2²+2²+1²= 4,690
R14=
1/4,690=0,1232
R24=
2/4,690=0,4264
R34= 2/4,690=0,4264
R44=
2/4,690=0,4264
R54=2/4,690=0,4264
R64=2/4,690=0,4264
R74=1/4,690=0,1232
Matrik Ternormalisasi terbobot Yij=W1.Rij
Y11= 5*0,3380 =1,96
Y11= 5*0,3380 =1,96
Y21=5*0,5070 =2,535
Y31=5*0,3380 =1,96
Y41 =5*0,3380 =1,96
Y51= 5*0,5070 =2,535
Y61= 5*0,3380 =1,96
Y71=5*0,6190=3,095
Y22=4*0,3810=1,524
Y32=4*0,5080=2,032
Y42 =4*0,2540=1,016
Y52= 4*0,3810=1,524
Y62= 4*0,2540=1,016
Y72=4*0,5080=2,032
Y13= 3*0,3873=1,1619
Y23=3*0,1291=0,3873
Y33=3*0,1291=0,3873
Y43 =3*0,2582=0,7746
Y53= 3*0,5164 =1,5492
Y63= 3*0,2584=0,7746
Y73=3*0,6455=1,9365
Y14= 3*0,2132=0,6396
Y24=3*0,4264=1,2792
Y34=3*0,4264=1,2792
Y44 =3*0,4264=1,2792
Y54= 3*0,4264=1,2792
Y64= 3*0,4264=1,2792
Y74=3*0,2132=0,6396
Solusi Ideal Positif
(A+)
Y1+ =Max
(1,69 ; 2,535 ; 1,69 ; 2,535 ; 1,69 ; 3,095)=3,095
Y2+ =Min (1,061
; 1,524 ; 2,032 ; 1,016 ; 1,524 ; 1,016 ; 2,032)= 1,016
Y3+ =Min (1,1619
; 0,3893 ; 0,3873 ; 0,7746 ; 1,5492 ; 0,7746 ; 1,9365)= 0,3873
Y4+ =Max (0,6396
; 1,2792 ; 1,2792 ; 1,2792 ; 1,2792 ; 1,2792 ; 0,6396) = 1,2792
Solusi Ideal Negatif
(A-)
Y1- =Min
(1,69 ; 2,535 ; 1,69 ; 2,535 ; 1,69 ; 3,095)=1,69
Y2- =Max (1,061
; 1,524 ; 2,032 ; 1,016 ; 1,524 ; 1,016 ; 2,032)= 2,032
Y3- =Max (1,1619
; 0,3893 ; 0,3873 ; 0,7746 ; 1,5492 ; 0,7746 ; 1,9365)= 1,9365
Y4- =Min (0,6396
; 1,2792 ; 1,2792 ; 1,2792 ; 1,2792 ; 1,2792 ; 0,6396) = 0,6396
Solusi Jarak Antara Nilai setiap Alternatif (Di+)
D1+ =√(1,69-3,095)2+(1,016-1,016)2+(1,1619-0,3873)2+(0,6396-1,2792)2
=2,983
D2+ =√(2,535-3,095)2+(1,524-1,016)2+(0,3873-0,3873)2+(1,279-1,2792)2
=0,5716
D3+ =√(1,69-3,095)2+(2,032-1,016)2+(0,3873-0,3873)2+(1,2792-1,2792)2
=3,004
D4+ =√(1,69-3,095)2+(1,016-1,016)2+(0,7746-0,3873)2+(1,2792-1,2792)2
= 2,124
D5+ =√(2,535-3,095)2+(1,524-1,016)2+(1,5492-0,3873)2+(1,2792-1,2792)2
=1,9216
D6+ =√(1,69-3,095)2+(1,016-1,016)2+(0,7746-0,3873)2+(1,2792-1,2792)2
=2,124
D7+ =√(3,095-3,095)2+(2,032-1,016)2+(1,9365-0,3873)2+(0,6396-1,2792)2
=3,8412
Solusi Jarak Antara Nilai setiap Alternatif (Di-)
D1- =√(1,69-1,69)2+(1,016-2,032)2+(1,1619-1,9365)2+(0,6396-0,6396)2
=1,6322
D2- =√(2,535-1,69)2+(1,524-2,032)2+(0,3873-1,9365)2+(1,2792-0,6396)2
= 3,803
D3- =√(1,69-1,69)2+(2,032-2,032)2+(0,3873-1,9365)2+(1,2792-0,6396)2
= 2,809
D4- =√(1,69-1,69)2+(1,016-2,032)2+(0,7746-1,9365)2+(1,2792-0,6396)2
= 2,013
D5- =√(2,535-1,69)2+(1,524-2,032)2+(1,5492-1,9365)2+(1,2792-0,6396)2
=1,531
D6- =√(1,69-1,69)2+(1,016-2,032)2+(0,7746-1,9365)2+(1,2792-0,6396)2
=2,7912
D7- =√(3,095-1,69)2+(2,032-2,032)2+(1,9365-1,9365)2+(0,6396-0,6396)2
=1,9740
Solusi Preperensi (Vi)
V1= 1,6322 / 2,983+1,6322
= 0,3536
V2= 3,803/ 0,5716+3,803=
0,8693
V3= 2,809/ 3,004+2,809 =
0,4832
V4= 2,013/ 2,124+2,013
= 0,4865
V5= 1,531/ 1,9216+1,531=
0,4434
V6= 2,7912/ 2,124+2,7912
=0,5576
V7= 1,9740/ 3,8412+1,9740
= 0,3394