PENYELESAIAN:
LANGKAH 1: BUAT TABEL KEPUTUSAN
ALTERNATIF | C1 | C2 | C3 | C4 |
a1 | 3 | 3 | 3 | 2 |
a2 | 3 | 3 | 2 | 2 |
a3 | 4 | 4 | 1 | 1 |
a4 | 1 | 4 | 2 | 1 |
a5 | 2 | 3 | 4 | 2 |
a6 | 2 | 2 | 4 | 2 |
a7 | 3 | 2 | 3 | 2 |
X1 = √32+32+42+12+22+22+32
= √9+9+16+1+4+4+9
= √52
= 7.2111
R11 = 3 / 7.2111
= 0.4160
R21 = 3 / 7.2111
= 0.4160
R31 = 4 / 7.2111
= 0.5547
R41 = 1 / 7.2111
= 0.1387
R51 = 2 / 7.2111
= 0.2774
R61 = 2 / 7.2111
= 0.2774
R71 = 3 / 7.2111
= 0.4160
X2 = √32+32+42+42+32+22+22
= √9+9+16+16+9+4+4
= √67
= 8.1854
R12 = 3 / 8.1854
= 0.3665
R22 = 3 / 8.1854
= 0.3665
R32 = 4 / 8.1854
= 0.4887
R42 = 4 / 8.1854
= 0.4887
R52 = 3 / 8.1854
= 0.3665
R62 = 2 / 8.1854
= 0.2443
R72 = 2 / 8.1854
= 0.2443
X3 = √32+22+12+22+42+42+32
= √9+4+1+4+16+16+9
= √59
= 7.6811
R13 = 3 / 7.6811
= 0.3906
R23 = 2 / 7.6811
= 0.2604
R33 = 1 / 7.6811
= 0.1302
R43 = 2 / 7.6811
= 0.2604
R53 = 4 / 7.6811
= 0.5208
R63 = 4 / 7.6811
= 0.5208
R73 = 3 / 7.6811
= 0.3906
X4 = √22+22+12+12+22+22+22
= √4+4+1+1+4+4+4
= √22
= 4.6904
R14 = 2 / 4.6904
= 0.4264
R24 = 2 / 4.6904
= 0.4264
R34 = 1 / 4.6904
= 0.2132
R44 = 1 / 4.6904
= 0.2132
R54 = 2 / 4.6904
= 0.4264
R64 = 2 / 4.6904
= 0.4264
R74 = 2 / 4.6904
= 0.4264
LANGKAH 3: BUAT TABEL KEPUTUSAN TERNORMALISASI
ALTERNATIF | C1 | C2 | C3 | C4 |
a1 | 0.4160 | 0.3665 | 0.3906 | 0.4264 |
a2 | 0.4160 | 0.3665 | 0.2604 | 0.4264 |
a3 | 0.5547 | 0.4887 | 0.1302 | 0.2132 |
a4 | 0.1387 | 0.4887 | 0.2604 | 0.2132 |
a5 | 0.2774 | 0.3665 | 0.5208 | 0.4264 |
a6 | 0.2774 | 0.2443 | 0.5208 | 0.4264 |
a7 | 0.4160 | 0.2443 | 0.3906 | 0.4264 |
Y11 = 3(0.4160) = 1.2481 Y12=4(0.3665) = 1.4660 Y13=5(0.3906) =1.9528 Y14=4(0.4264) = 1.7056
Y21 = 3(0.4160) = 1.2481 Y22=4(0.3665) =1.4660 Y23=5(0.2604) =1.3019 Y24=4(0.4264) = 1.7056
Y31 = 3(0.5547) = 1.6641 Y32=4(0.4887) = 1.9547 Y33=5(0.1302) =0.6509 Y34=4(0.2132) = 0.8528
Y41 = 3(0.1387) =0.4160 Y42=4(0.4887) = 1.9547 Y43=5(0.2604) = 1.3019 Y44=4(0.2132) = 0.8528
Y51 = 3(0.2774) =0.8321 Y52=4(0.3665) =1.4660 Y53=5(0.5208) = 2.6038 Y54=4(0.4264) = 1.7056
Y61 = 3(0.2774) = 0.8321 Y62=4(0.2443) =0.9774 Y63=5(0.5208) =2.6038 Y64=4(0.4264) = 1.7056
Y71 =3(0.4160) = 1.2481 Y72=4(0.2443) =0.9774 Y73=5(0.3906) =1.9528 Y74=4(0.4264) = 1.7056
LANGKAH 5: BUAT TABEL Y (TABEL KEPUTUSAN TERNORMALISASI TERBOBOT)
ALTERNATIF | C1 | C2 | C3 | C4 |
a1 | 1.2481 | 1.4660 | 1.9528 | 1.7056 |
a2 | 1.2481 | 1.4660 | 1.3019 | 1.7056 |
a3 | 1.6641 | 1.9547 | 0.6509 | 0.8528 |
a4 | 0.4160 | 1.9547 | 1.3019 | 0.8528 |
a5 | 0.8321 | 1.4660 | 2.6038 | 1.7056 |
a6 | 0.8321 | 0.9774 | 2.6038 | 1.7056 |
a7 | 1.2481 | 0.9774 | 1.9528 | 1.7056 |
Y1 + = MAX{1.2481; 1.2481; 1.6641; 0.4160; 0.8321; 0.8321; 1.2481}= 1.6641
Y2 + = MAX{1.4660; 1.4660; 1.9547; 1.9547; 1.4660; 0.9774; 0.9774}= 1.9547
Y3 + = MIN {1.9528; 1.3019; 0.6509; 1.3019; 2.6038; 2.6038; 1.9528}= 0.6509
Y4 + = MAX{1.7056; 1.7056; 0.8528; 0.8528; 1.7056; 1.7056; 1.7056}= 1.7056
A+ = (1.6641 ; 1.9547 ; 0.6509; 1.7056)
Y1 - = MAX{1.2481; 1.2481; 1.6641; 0.4160; 0.8321; 0.8321; 1.2481}= 0.4160
Y2 - = MAX{1.4660; 1.4660; 1.9547; 1.9547; 1.4660; 0.9774; 0.9774}= 0.9774
Y3 - = MIN {1.9528; 1.3019; 0.6509; 1.3019; 2.6038; 2.6038; 1.9528}= 2.6038
Y4 - = MAX{1.7056; 1.7056; 0.8528; 0.8528; 1.7056; 1.7056; 1.7056}= 0.8528
A- = (0.4160 ; 0.9774 ; 2.6038 ; 0.8528)
LANGKAH 7: MENCARI NILAI DI+ DAN DI-
D1+ = √((1.2481-1.6641)2 + (1.4660-1.9547)2 + (1.9528-0.6509)2 + (1.7056-1.7056)2)
= √2.1068
= 1.4515
D2+ = √((1.2481-1.6641)2 + (1.4660-1.9547)2 + (1.3019-0.6509)2 + (1.7056-1.7056)2)
= √0.8356
= 0.9141
D3+ = √((1.6641-1.6641)2 + (1.9547-1.9547)2 + (0.6509-0.6509)2 + (0.8528-1.7056)2)
= √0.7273
= 0.8528
D4+ = √((0.4160-1.6641)2 + (1.9547-1.9547)2 + (1.3019-0.6509)2 + (0.8528-1.7056)2)
= √2.7087
= 1.6458
D5+ = √((0.8321-1.6641)2 + (1.4660-1.9547)2 + (2.6038-0.6509)2 + (1.7056-1.7056)2)
= √4.7447
= 2.1782
D6+ = √((0.8321-1.6641)2 + (0.9774-1.9547)2 + (2.6038-0.6509)2 + (1.7056-1.7056)2)
= √5.4611
=2.3369
D7+ = √((1.2481-1.6641)2 + (0.9774-1.9547)2 + (1.9528-0.6509)2 + (1.7056-1.7056)2)
= √2.8232
= 1.6802
D1- = √((1.2481-0.4160)2 + (1.4660-0.9774)2 + (1.9528-2.6038)2 + (1.7056-0.8528)2)
= √2.0821
= 1.4430
D2- = √((1.2481-0.4160)2 + (1.4660-0.9774)2 + (1.3019-2.6038)2 + (1.7056-0.8528)2)
= √3.3533
= 1.8312
D3- = √((1.6641-0.4160)2 + (1.9547-0.9774)2 + (0.6509-2.6038)2 + (0.8528-0.8528)2)
= √6.3265
= 2.5152
D4- = √((0.4160-0.4160)2 + (1.9547-0.9774)2 + (1.3019-2.6038)2 + (0.8528-0.8528)2)
= √2.6501
= 1.6279
D5- = √((0.8321-0.4160)2 + (1.4660-0.9774)2 + (2.6038-2.6038)2 + (1.7056-0.8528)2)
= √1.1392
= 1.0673
D6- = √((0.8321-0.4160)2 + (0.9774-0.9774)2 + (2.6038-2.6038)2 + (1.7056-0.8528)2)
= √0.9003
=0.9489
D7- = √((1.2481-0.4160)2 + (0.9774-0.9774)2 + (1.9528-2.6038)2 + (1.7056-0.8528)2)
= √1.8433
= 1.3577
LANGKAH 8: MENCARI NILAI Vi
V1 = D1- / (D1- + D1+) = 0.4985
V2 = D2- / (D2- + D2+) = 0.6670
V3 = D3- / (D3- + D3+) = 0.7468
V4 = D4- / (D4- + D4+) = 0.4973
V5 = D5- / (D5- + D5+) = 0.3289
V6 = D6- / (D6- + D6+) = 0.2888
V7 = D7- / (D7- + D7+) = 0.4469
Joko, Widodo, Simamora, Susilawati, dan Hendro.. adalah 5 mahasiswa yang berhak untuk mendapatkan beasiswa