... 3... 4 1.1... 4 1.1.1... 4 1.2... 5 1.3... 6 1.3.1... 6 1.3.2... 7 1.3.3... 7... 13 2.1 A...13 2.2 A...13 2.3 A...15 2.4...17 2.4.1 A...18 2.4.2...18 2.5...23... 25 3.1...25... 26 2
AHP 3
1.1 1.1.1 1-1 4
1.2 ( ) 5
1.3 1.3.1 The analytic hierarchy process AHP Thomas LSaaty1970 AHP 6
1.3.2 1.3.3 AHP 1 2 3 7
1-1 1 2 3 A B C A1/A2/ B1/B2/ C1/C2/ 1-2 8
1-9 n Y= {y1y2y3 yn} yi yjaij y I y j aij Saaty 1-9 1-2 aij 1 i j / 3 i j / 5 i j / 7 i j / 9 i j / 2468 1-9 1-9 Saaty 16 1~9 1-9 9
A =aijnn iaij0 iiaji = 1/ aij ij = 12 n ( aii=1i = 12 n ) aij1 i j, aji =1/aij 1 j i A=aij 1-9 5 A1A2A3A4A5 1/2 2 1 1-3 1-3 A1 A2 A3 A4 A5 A1 1 2 7 5 5 A2 1/2 1 4 3 3 A3 1/7 1/4 1 1/2 1/3 A4 1/5 1/3 2 1 1 A5 1/5 1/3 3 1 1 Excel Matlab 10
A n = 1 2 n) i=1 n y={y1y2y3 yn} z Y= {y1y2y3 yn} A max A=max Matlab A [VD]=eig(A) A 1= 5.019 = (0.48, 0.26, 0.05, 0.10, 0.11) Eecel 1-4 1-4 A1 A2 A3 A4 A5 A1 1 2 7 5 5 0.48 A2 1/2 1 4 3 3 0.26 A3 1/7 1/4 1 1/2 1/3 0.05 A4 1/5 1/3 2 1 1 0.10 A5 1/5 1/3 3 1 1 0.11 2 3+3/4 17 10+1/2 10+1/3 1 1 2 2 1 3 1 11
A aijajk=aik ( ijk = 12 n) 1: n A n 2: 1 1. n A=( aij ), (Consensus index) : CI=(1-n)/(n-1) CI = 0A CI 0A Saaty RT 1-5 N n 1 2 3 4 5 6 7 8 9 RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 CR=CI/RI0.1, A A 1 = 1 2 n) i=1 {y1y2y3 yn} = 1 2 n) i 12
2.1 A A 2000 4 50 A A A A A 2.2 A A A + 15% 20%25%40% 13
1 2 1) A A A 14
A A A A 2.3 A A 15
A 2-1 2-1 A A 2-2 A 16
A 1 2 2.4 A AHP 17
2.4.1 A A + 10 10 20 20 30 30 30 2.4.2 A 1 2 3 A 18
A 3 2-3 19
20 2-3 1 n n 1-9 3 1/2 1 1/4 1/2 2 2-1 A B1 C1 B4 B3 B2 C12 C1 C2 C2 C2 C3 C3 C3 C4 C4 C4
2-1 B1 B2 B3 B4 B1 1 3 1/2 1 B2 1/3 1 1/4 1/2 B3 2 4 1 2 B4 1 2 1/2 1 2 m m 3 2 1/2 1/9 1/6 3 2-2 C11 C13 C12 C11 1 1/2 1/9 C13 2 1 1/6 C12 9 6 1 2-3 C21 C22 C23 C21 1 1/2 1/5 C22 2 1 1/3 C23 5 3 1 21
2-4 C31 C33 C32 C31 1 3 5 C33 1/3 1 2 C32 1/5 1/2 1 2-5 C41 C42 C43 C41 1 1/6 1/2 C42 6 1 4 C43 2 1/4 1 A max A=max matlab7.0 5 4 2 1 1 11 Bi i Cij ij B1 0.2428 B2 0.0991 C11 0.0191 C13 0.0347 C12 0.1890 C21 0.0121 C22 0.0228 C23 0.0643 22
A B3 0.4387 B4 0.2194 C31 0.2844 C33 0.1008 C32 0.0535 C41 0.0233 C42 0.1538 C43 0.0423 CI=(1-n)/(n-1) CI = 0A CI 0A CR=CI/RI0.1, A RI 2 A CR 0.0077 B1 B2 B3 B4 CR 0.00880.00360.00360.0088 0.1 4 12 A A 2.5 23
Excel 24
3.1 25
[1] []E. N. [M] 1998 [2] [J] 2001 11 P38-39 [3] []Landy,F.J.,&Farr, JPerformance rating[m]psychological Bulletin1980 [4] [M] 2005 [5] [J] 1995 5 [6] Peter P. DruckerThe Management of Future[M]2004 4 [7] [M] 2001 [8] [M] 2007 [9] [M] 2003 [10] [M]1992 9 [11] [J]2002 [12] []Saaty A LThe analytic hierarchy process[m]mc Graw Hill Inc1980 [13] [M] 1988 [14] AHP MATLAB [J] ( )2006 4 [15] [] [M] 2006 26