Minggu, 08 Juni 2014

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
LANGKAH 2: CARI NILAI RATING KINERJA POSITIF PADA SETIAP KRITERIA

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
LANGKAH 4: HITUNG NILAI Y =Wij x Rij DIMANA [W = 3   4   5   4]

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
LANGKAH 6: MENCARI NILAI YJ+  DAN YJ-
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


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