Example: The Fighter Aircraft Problem ELECTRE

Fighter Aircraft Problem
 
Criteria f1 f2 f3 f4 f5 f6
weights 0.2 0.1 0.1 0.1 0.2 0.3

1. Normalised Decision Matrix
 
0.4671 0.3662 0.5056 0.5063 0.4811 0.6708
0.5839 0.6591 0.4550 0.5983 0.2887 0.3727
0.4204 0.4882 0.5380 0.4143 0.6736 0.521117
0.5139 0.4392 0.5056 0.4603 0.4811 0.3727

2. Weighted normalised Decision Matrix
 
0.0934 0.0366 0.0506 0.0962 0.0962 0.2012
0.1168 0.0659 0.0455 0.0598 0.0577 0.1118
0.0841 0.0488 0.0531 0.0414 0.1347 0.1565
0.1028 0.0439 0.0506 0.0460 0.0962 0.1118

3. Concordance and Discordance Sets
(Remember f4 is minimal criterion.)
 
C 12 3 4 5 6 D 12 1 2
C 13 1 6 D 13 2 3 4 5
C 14 3 5 6 D 14 1 2 4
C 21 1 2  D 21 3 4 5 6
C 23 1 2 D 23 3 4 5 6
C 24 1 2 6 D 24 3 4 5
C 31 2 3 4 5 D 31 1 6
C 32 3 4 5 6 D 32 1 2
C 34 2 3 4 5 6 D 34 1
C 41 1 2 3 4 5 D 41 6
C 42 3 4 5 6 D 42 1 2
C 43 1 D 43 2 3 4 5 6

4. Concordance Matrix:
 
- 0.7 0.5 0.6
0.3 - 0.3 0.6
0.5 0.7 - 0.8
0.7 0.7 0.2 -

5. Discordance Matrix
 
- 1 0 1
0 - 0 1
0 1 - 1
1 1 0 -

6. Concordance Dominance Matrix
 
- 1 0 1
0 - 0 1
0 1 - 1
1 1 0 -

7. Discordance Dominance Matrix
 
- 1 0 1
0 - 0 0
0 1 - 1
0 1 0 -

8. Aggregate Dominance Matrix E:
 
- 1 0 1
0 - 0 0
0 1 - 1
0 1 0 -

9. Eliminating Less Favourable Alternatives

Hence the first and third column have no 1 element, A2 and A4 are dominated by A1 and A3. We say, A2 and A4 have been eliminated by ELECTRE method.