some particular aspects concerning electre method applications

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P gh = Table no.8. Equivalence matrix (P gh = ) A 1 A 2 A 3 A 4 A 5 A 1 X 0 0 0 0,1 A 2 0 X 0 0 0 A 3 0 0 X 0 0,2 A 4 0 0 0 X 0 A 5 0,1 0 0,2 0 X For example, the classification for the threshold values: c= 0,5; d = 0,5 is presented in the table no.9. Table no.9. ELECTRE II A(0,5; 0,5) A 1 A 2 A 3 A 4 A 5 Classif. A 1 X Yes Yes No No I A 2 No X Yes No No II A 3 Yes No X Yes No I A 4 No No Yes X Yes I A 5 No No No No X III The mild classification can be achieved for the pair c=0,5; d=0,6. This contains, more, overtaking relationships: A 3 P A 1 ; A 5 P A 3 . The tough overtaking drive us to un inserting result, because three alternatives are equally. The second classification decides for alternative A 3 , which realizes the overtaking of A 1 . ELECTRE IV: It compares the indicators’ value c gh and c hg , respective d gh and d hg , alternative which are satisfying the both comparing, being better than other. Thus, we can constat : c 12 >c 21 ; d 12 >d 21 , as a consequence we can’t satisfy the both relations for each relations between the alternatives; c 13 =c 31 ; d 13 >d 31 , alternative A 3 are satisfying at limits the conditions, so it overtakes the A 1 alternative; c 15 < c 51 ; d 15 =d 51 = 1,0 in this case not even one of the alternatives can be declared eligible. The overtaking matrix is show in the table no.10. Table no.10. ELECTRE IV ELECTRE IV A 1 A 2 A 3 A 4 A 5 Classif. A 1 X No No Yes No II A 2 No X Yes No No II A 3 Yes No X No No II A 4 No No Yes X Yes I A 5 No Yes No No X II 6
So, the optimal alternative is A 4 , being the only one which are overtaking two alternatives. The others have each one overtaking. Modified ELECTRE: It subtractions the discordance indicators matrix from the concordance indicators matrix: c gh – d gh .The resulted are presented in the table no.11. Table no.11. Modified ELECTRE c gh – d gh A 1 A 2 A 3 A 4 A 5 Class A 1 X 0,1 0 -0,2 -0,5 III A 2 -0,01 X 0 -0,5 -0,2 IV A 3 0,03 -0,1 X 0 0 I A 4 -0,3 -0,5 0,1 X 0,1 V A 5 -0,4 -0,17 0,07 -0,1 X II The alternative A 3 stands out in top . The other three alternatives have the values very close. Ascertainment: Generally speaking, the decisions making methods don’t offer the same results (only in a less measure). In the table no.12 are centralized the classements obtained by applying the previous methods. Method A i ELECTRE I ELECTRE II Table nr.12. The alternatives classification ELECTRE IV Modified ELECTRE Total Final classification A 1 2 1 2 3 8 II A 2 3 2 2 4 11 V A 3 1 1 2 1 5 I A 4 2 1 1 5 9 III A 5 3 3 2 2 10 IV In the last columns of the table we made a sum of the partial classification, respective last order, applying the rule of the simple sum method of the ranges. The idea is the alternative which is more close to the first place is the best alternative. But this conclusion is not compulsory. As there is a method of dictator, in which the decision maker can choose a single criteria from many others, same it is possible to choose by a single criteria or a single decision method group and is not necessarily to choose all the methods 7
Page 1 and 2: SOME PARTICULAR ASPECTS CONCERNING
Page 3 and 4: Issue Method Overtaking relationshi
Page 5: Table no. 5. Discordance Matrix (d

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