A GP-AHP method for solving group decision-making fuzzy AHP ...

C.-S. Yu / Computers & Operations Research 29 (2002) 1969–2001 1993
Table 4
The pairwise comparison of candidates under criterion 3
q =3 AB C
A 1 ã e q12 ã e q13
B 1=ã e q12 1 ã e q23
C 1=ã e q13 1=ã e q23 1
Table 5
The pairwise comparison of candidates under criterion 4
q =4 AB C
A 1 — ã e q13
B — 1 ã e q23
C 1=ã e q13 1=ã e q23 1
ã 2 3;13 =ã 3 3;13 =( 5
2
; 3; 7
ã 1 4;23 =ã 2 4;23 =ã 3 4;23 =( 3
2
2 ), ã13;23 =ã 2 3;23 =ã 3 3;23 =( 2
3
; 2; 5
2 ).
Fig. 7. Afuzzy value log a 1 12.
; 1; 3
2 ), ã14;13 =ã 2 4;13 =( 3
2
; 2; 5
2 ), ã34;13 =( 2
5
; 1
2
2 ; 3 ), and
Based on the solution algorithm, the required six steps are:
Step 1: For a triangular fuzzy value log a1 12 as displayed in Fig. 7, by employing Corollary 1,
is expressed as follows:
log a 1 12
log a 1 12 = { (log a 1 12) − 11:35782 log 1+11:35782 d 1 12 +5:67891 log(2=3)}=(−5:67891)
= −0:17609013 (log a 1 12) − 2 d 1 12 +0:176091259; (6.1)
where log a1 12 − log 1+d112 ¿ 0, a112 ;d112 ¿ 0.