Example: Fighter Aircraft Problem – Permutation Method
Fighter
Aircraft Problem
Assume that
the cardinal weight of the criteria be w = (0.2,0.1,0.1,0.1,0.2,0.3). There
are 4! = 24 alternatives to be tested:
Let's test
the hypothesis (i.e. the ordering P_{4}). The
matrix C_{4} is then:

1 
3 
4 
2 
1 
0 
0.5 
0.6 
0.7 
3 
0.5 
0 
0.8 
0.7 
4 
0.7 
0.2 
0 
0.7 
2 
0.3 
0.6 
0.3 
0 
For example,
the variant A_{1} is than better than A3 under criteria f1 and f6.
The element c_{31}
we got comparing variants A_{3} and A_{1}.Variant A_{3}
is better under criterion f2 (v2=0.1), f3 (v3=0.1), f_{4} (v_{4}=0.1)
and f5 (v5=0.2). The sum of weights is:
Note that the
criterion f_{4} price is minimal !
Then the
evaluating criterion of P_{4} is:
,
where is the
sum of uppertriangular elements of matrix C_{4 }and is the sum of lowertriangular elements.
The similar C
matrices could be computed for all 24 permutations. Since the R for permutation (A3,A4,A1,A2) gives the highest
value, this order is the best.