QUIZ SISTEM PENDUKUNG KEPUTUSAN

 

SOAL QUIZ!!!

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 =W_ij x R_ij DIMANA [W = 3   4   5   4]

 

Y_{11 =} 3(0.4160) = 1.2481        Y₁₂=4(0.3665) = 1.4660      Y₁₃=5(0.3906) =1.9528      Y₁₄=4(0.4264) = 1.7056

Y_{21 =} 3(0.4160) = 1.2481        Y₂₂=4(0.3665) =1.4660       Y₂₃=5(0.2604) =1.3019       Y₂₄=4(0.4264) = 1.7056

Y_{31 =} 3(0.5547) = 1.6641        Y₃₂=4(0.4887) = 1.9547      Y₃₃=5(0.1302) =0.6509       Y₃₄=4(0.2132) = 0.8528

Y_{41 =} 3(0.1387) =0.4160         Y₄₂=4(0.4887) = 1.9547      Y₄₃=5(0.2604) =  1.3019     Y₄₄=4(0.2132) = 0.8528

Y_{51 =} 3(0.2774) =0.8321         Y₅₂=4(0.3665) =1.4660       Y₅₃=5(0.5208) = 2.6038      Y₅₄=4(0.4264) = 1.7056

Y_{61 =} 3(0.2774) = 0.8321        Y₆₂=4(0.2443) =0.9774       Y₆₃=5(0.5208) =2.6038       Y₆₄=4(0.4264) = 1.7056

Y_{71 =}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 Y_J⁺  DAN Y_J^–

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 D_I⁺  DAN D_I^–

 

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 V_i

 

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

Jadi, 5 mahasiswa yang berhak untuk mendapatkan beasiswa adalah Joko, Widodo, Simamora, Susilawati, dan Hendro.