The weights of the deviation variables in the objective function
are wSYN as shown in Table 3. The objective function of the GP problem
is a combination of the heterogeneous units of measure. Thus,
the constraints should be normalized before solving the problem
so that the deviation variables in the objective function are adjusted
to the same unit of measure. We used Lingo to solve the
GP model. Because the purpose of the problem is to select the best
missile system, the optimal alternative in our case study was missile
system 5.
Because of the conflicts that typically accompany any selection
result, whatever it is, more information, such as the degree of preference
the optimal selection represents, is necessary. A selection
chosen as an overwhelming preference of the decision makers is
likely to gain wide support and follow-up measures will be accelerated
in the execution stage. On the other hand, a solution selected
by a slight margin may provoke controversy and questions
about the reliability and validity of the decision process.
Fig. 3 shows the values of the objective function with the selection
of each alternative, with x5 shown as the best choice with an
objective value of 1.705, and x3 is the least favorable choice with
an objective value of 12.394. For comparison, we constructed the
GP model with AHP alone (AHP–GP) and solved the same problem.
The AHP–GP model yielded a different decision result from the
AHP–PCA–GP model in that the optimal solution of the AHP–GP
model is x6 with an objective value of 2.295