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

where v e qq ′ ;k and ve qij;k
C.-S. Yu / Computers & Operations Research 29 (2002) 1969–2001 1991
(ve qij;k−1 log aeqij;k−1 − ye qij;k−1 )
m−1 �
+ (se qij;k − se qij;k−1 ) log ae ⎫�
⎬
qij;k−1 ⎭
k=1
log ae m−2 �
qij + de qij;k ¿ log aeqij;m−2 k=1
0 6 d e qij;k 6 log ae qij;k − log ae qij;k−1
(s e qij;m−1);
for s e qij;k ¡se qij;k−1 ;
ye qij;k−1 ¿ log aeqij +(ve qij;k−1 − 1)M
ye for s
qij;k−1 ¿ 0
e qij;k ¿se qij;k−1 ;
vq;vqi;ae qq ′;ae e e
qij; qq ′; qij;de qq ′;deqij;k ;ye qq ′ ;k ;ye qij;k ¿ 0;
(q; q ′ ) ∈{(q; q ′ ) | 1 6 q¡q ′ 6 m}; (i; j) ∈{(i; j) | 1 6 i¡j6 n};
are 0–1 variables and M is a big value.
6. Solution algorithm and numerical examples
Based on the previous discussion, a solution algorithm is described as follows.
6.1. Solution algorithm
Step 1: Express each fuzzy comparison by using Corollaries 1, 2 or 3.
Step 2: Formulate the problem by applying the proposed GP-AHP method.
Step 3: Compute M 0 , M 1 , and values with Theorem 1.
Step 4: Derive the vector V by employing any popular linear programming package like LINDO
or EXCEL to solve the programmed model.
Step 5: Generate the priority vector W by normalizing the vector V .
Now consider the following three-level structured AHP problem initially provided by Laarhoven
et al. [8].
Example 4. Assume that a professorship position is vacant in the Operations Research Department
of a certain university. After several competitive screening interviews, only three serious
candidates remain, referred to herein as A, B, and C. To identify which applicant is best quali
ed for the job, the committee has been installed to provide advice. The committee has three
members and they assess the candidates by four decision criteria: (1) mathematical creativity
(q1); (2) creativity in implementations (q2); (3) administrative capabilities (q3); (4) maturity
or personal integrity (q4).
Therefore, the committee derives evaluations of the candidates following the above criteria.
Through a pair-by-pair comparison, the relative importance of the decision criteria is constructed