Jawaban Soal No. 2

Tabel Alternatif

Alternatif	Kriteria
	C1	C2	C3	C4
Aldyan	2	2	3	1
Hendro	3	4	1	2
Joko	2	5	1	2
Doni	2	3	2	2
Dono	3	4	4	2
Kasino	2	3	2	2
Susanto	1	5	5	1

Bobot W=[4,5,4,3]

Penyelesaian:
X1=√2²+3²+2²+2²+3²+2²+1²= 5,9160

R11=2/5,9160= 0,3380 R51= 3/5,9160= 0,5070

R21= 3/5,9160= 0,5070 R61= 2/5,9160= 0,3380

R31= 2/5,9160= 0,3380 R71= 1/5,9160= 0,1690

R41= 2/5,9160= 0,3380

X2=√2²+4²+5²+3²+4²+3²+5²= 10,198

R12= 2/10,198= 0,1961 R52= 4/10,198= 0,3922

R22= 4/10,198= 0,3922 R62= 3/10,198= 0,2941

R32= 5/10,198= 0,4902 R72= 5/10,198= 0,4902

R42= 3/10,198= 0,2941

X3= √3²+1²+1²+2²+4²+2²+5²= 7,7459

R13= 3/7,7459= 0,3873 R43= 2/7,7459= 0,2582 R73= 5/7,7459 = 0,6455

R23= 1/7,7459= 0,1291 R53= 4/7,7459= 0,5164

R33= 1/7,7459= 0,1291 R63= 2/7,7459= 0,2582

X4=√1²+2²+2²+2²+2²+2²+1²= 4,6904

R14= 1/4,6904= 0,2132 R44= 2/4,6904= 0,4264 R74= 1/4,6904= 0,2132

R24= 2/4,6904= 0,4264 R54= 2/4,6904= 0,4264

R34= 2/4,6904= 0,4264 R64= 2/4,6904= 0,4264

Matrix R0,3380 0,1961 0,3873 0,2132
0,5070 0,3922 0,1291 0,4264
0,3380 0,4902 0,1291 0,4264
0,3380 0,2941 0,2582 0,4264
0,5070 0,3922 0,5164 0,4264
0,3380 0,2941 0,2582 0,4264
0,1690 0,4902 0,6455 0,2132


Y11= W1 R11= 4 X 0,3380 = 1,352 Y13= W1 R13= 4 X 0,3873 = 1,5492
Y21= W2 R21= 4 X 0,5070 = 2,028 Y23= W2 R23= 4 X 0,1291 = 0,5164
Y31= W3 R31= 4 X 0,3380 = 1,352 Y33= W3 R33= 4 X 0,1291 = 0,5164
Y41= W4 R41= 4 X 0,3380 = 1,352 Y43= W4 R43= 4 X 0,2582 = 1,0328
Y51= W5 R51= 4 X 0,5070 = 2,028 Y53= W5 R53= 4 X 0,5164 = 2,0656
Y61= W6 R61= 4 X 0,3380 = 1,352 Y63= W6 R63= 4 X 0,2582 = 1,0328
Y71= W7 R71= 4 X 0,1690 = 0,676 Y73= W7 R73= 4 X 0,6455 = 2,582

Y12= W1 R12= 5 X 0,1961 = 0,9805 Y14= W1 R14= 3 X 0,2132 = 0,6396
Y22= W2 R22= 5 X 0,3922 = 1,961 Y24= W2 R24= 3 X 0,4264 = 1,2792
Y32= W3 R32= 5 X 0,4902 = 2,451 Y34= W3 R34= 3 X 0,4264 = 1,2792
Y42= W4 R42= 5 X 0,2941 = 1,4705 Y44= W4 R44= 3 X 0,4264 = 1,2792
Y52= W5 R52= 5 X 0,3922 = 1,961 Y54= W5 R54= 3 X 0,4264 = 1,2792
Y62= W6 R62= 5 X 0,2941 = 1,4705 Y64= W6 R64= 3 X 0,4264 = 1,2792
Y72= W7 R72= 5 X 0,4902 = 2,451 Y74= W7 R74= 3 X 0,2132 = 0,6396


Matrix Y1,352 0,9805 1,5492 0,6396
2,028 1,961 0,5164 1,2792
1,352 2,451 0,5164 1,2792
1,352 1,4705 1,0328 1,2792
2,028 1,961 2,0656 1,2792
1,352 1,4705 1,0328 1,2792
0,676 2,451 2,582 0,6396



Y1+=max{1,352;2,028;1,352;1,352;2,028;1,352;0,676}= 2,028
Y2+=min{0,9805;1,961;2,451;1,4705;1,961;1,4705;2,451}= 0,9805
Y3+=min{1,5492;0,5164;0,5164;1,0328;2,0656;1,0328;2,582}= 0,5164
Y4+=max{0,6396; 1,2792; 1,2792; 1,2792; 1,2792; 1,2792; 0,6396}= 1,2792

A+= {2,028;0,9805;0,5164;1,2792}

Y1¯=min{1,352; 2,028; 1,352; 1,352; 2,028; 1,352; 0,676}= 0,676
Y2¯=max{0,9805; 1,961; 2,451; 1,4705; 1,961; 1,4705; 2,451}= 2,451
Y3¯=max{1,5492; 0,5164; 0,5164; 1,0328; 2,0656;1,0328; 2,582}= 2,582
Y4¯=min{0,6396; 1,2792; 1,2792; 1,2792; 1,2792; 1,2792; 0,6396}= 0,6396

A¯= {0,676;2,451;2,582; 0,6396}

D1+= √(1,352-2,028)²+(0,9805-0,9805)²+(1,5492-0,5164)²+(0,6396-1,2792)²
= √(-0,676)^2 )+(0)^2+〖(1,0328)^2+(〖-0,6396)^2
= √0,4569+0+1,0666+0,4090
=√1,9325
=1,3901

D2+=√(2,028-2,028)^2 )+(1,961-0,9805)^2+(0,5164-0,5164)^2+(1,2792-1,2792)^2
= √(0)^2 )+(0,9805)^2+(0)^2+(0)^2
= √0+0,9613+0+0
= √0,9613
= 0,9805

D3+=√((1,352-2,028)^2 )+(2,451-0,9805)^2+(0,5164-0,5164)^2+(1,2792-1,2792)^2
= √(-0,676)^2 )+(1,4705)^2+(0)^2+(0)^2
= √0,4569+2,1623+0+0
= √2,6192
= 1,6183

D4+=√(1,352-2,028)^2 )+(1,4705-0,9805)^2+(1,0328-0,5164)^2+(1,2792-1,2792)^2
= √((-0,676)^2 )+(0,49)^2+(0,5164)^2+(0)^2
= √0,4569+0,2401+0,2666+0
= √0,9636
= 0,9816

D5+=√((2,028-2,028)^2 )+(1,961-0,9805)^2+(2,0656-0,5164)^2+(1,2792-1,2792)^2
= √(0)〗^2 )+(0,9805)^2+(1,5492)^2+(0)^2
= √0+0,9613+2,4000+0
= √3,3613
= 1,8333

D6+=√(1,352-2,028)^2 )+(1,4705-0,9805)^2+(1,0328-0,5164)^2+(1,2792-1,2792)^2
= √(-0,676)^2 )+(0,49)^2+(0,5164)^2+(0)^2
= √0,4569+0,2401+0,2666+0
= √0,9636
= 0,9816

D7+=√(0,676-2,028)^2 )+(2,451-0,9805)^2+(2,582-0,5164)^2+(0,6396-1,2792)^2
= √(-1,352)^2 )+(1,4705)^2+(2,0656)^2+(-0,6396)^2
= √1,8279+2,1623+4,2667+0,4090
= √8,6659
= 2,9437

D1¯=√(1,352-0,676)^2 )+(0,9805-2,451)^2+(1,5492-2,582)^2+(0,6396-0,6396)^2
= √(0,676)^2 )+(-1,4705)^2+(-1,0328)^2+(0)^2
= √0,4569+2,1623+1,0666+0
=√3,6858
=1,9198

D2¯=√(2,028-0,676)^2 )+(1,961-2,451)^2+(0,5164-2,582)^2+(1,2792-0,6396)^2
= √((1,352)^2 )+(-0,49)^2+(-2,0656)^2+(0,6396)^2
= √1,8279+0,2401+4,2667+0,4090
= √6,7437
=2,5968

D3¯=√(1,352-0,676)^2 )+(2,451-2,451)^2+(0,5164-2,582)^2+(1,2792-0,6396)^2
= √(0,676)^2 )+(0)^2+(-2,0656)^2+(0,6396)^2
= √0,4569+0+4,2667+0,4090
= √5,1326
= 2,2655

D4¯=√(1,352-0,676)^2 )+(1,4705-2,451)^2+(1,0328-2,582)^2+(1,2792-0,6396)^2
= √(0,676)〗^2 )+(-0,9805)^2+(-1,5492)^2+(0,6396)^2
= √0,4569+0,9613+2,4000+0,4090
= √4,2272
= 2,0560


D5¯=√(2,028-0,676)^2 )+(1,961-2,451)^2+〖(2,0656-2,582)^2+(1,2792-0,6396)^2
= √(1,352)^2 )+(-0,49)^2+(-0,5164)^2+(0,6396)^2
= √1,8279+0,2401+0,2666+0,4090
= √2,7436
= 1,6563

D6¯=√(1,352-0,676)^2 )+(1,4705-2,451)^2+(1,0328-2,582)^2+(1,2792-0,6396)^2
= √(0,676)^2 )+(-0,9805)^2+(-1,5492)^2+(0,6396)^2
= √0,4569+0,9613+2,4000+0,4090
= √4,2272
= 2,0560

D7¯=√(0,676-0,676)^2 )+(2,451-2,451)^2+(2,582-2,582)^2+(0,6396-0,6396)^2
= √(0)^2 )+(0)^2+(0)^2+(0)^2
= √0+0+0+0
= √0
= 0

V1 = (D1-)/(D1-+D1+ ) V2 = (D2-)/(D2-+D2+ ) V3 = (D3-)/(D3-+D3+ )
      = 1,9198/(1,9198+1,3901)      = 2,5968/(2,5968+0,9805)       = 2,2655/(2,2655+1,6183)
      = 1,9198/3,3099       = 2,5968/3,5773      = 2,2655/3,8838
      = 0,5800            = 0,7259                     = 0,5833

V4 = (D4-)/(D4-+D4+ )         V5 = (D5-)/(D5-+D5+ ) V6 = (D6-)/(D6-+D6+ )
      = 2,0560/(2,0560+0,9816)      = 1,6563/(1,6563+1,8333)       = 2,0560/(2,0560+0,9816)
      = 2,0560/3,0376       = 1,6563/3,4896               = 2,0560/3,0376
      = 0,6768            = 0,4746                       = 0,6768

V7 = (D7-)/(D7-+D7+ )
      = 0/(0+2,9437)
      = 0/2,9437
      = 0