some particular aspects concerning electre method applications

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1.The first original proposition (ELECTRE IV) In [4] the authors have proposed the next hierarchical relationship: If: c hg . ≥ c hg d gh ≤ d hg ↔ A g is better than A h . ( A g P A h ) where : c gh - the concordance indicator between the A g and A h alternatives; d gh - the discordance indicator between the A g and A h alternatives; This method has an inconvenience: even if both the alternatives (A g and A h ) have a major flaw, one of them will be accepted anyway, which is contrary to the principle of the original method, that doesn’t agree with accepting an alternative with a major flaw. Comparing our solution with the ELECTRE II method solution we can see that the hierarchical relationship we proposed: c gh ≥ c hg is identical with the ELECTRE II relationship: P + gh/ P - gh ≥ 1 where: P + gh – is the amount of better criteria in favor of the A g alternative as comparing with the A h alternative. P - gh – is the amount of better criteria in favor of the A h alternative as comparing with the A g alternative. Our suggestion, which we can name the ELECTRE IV, is based on the following: the second relationship: d gh ≤ d hg can be completed by a third relationship, like d gh ≤ d, thus getting rid of the inconvenience; d is a discordance threshold, whose value is imposed by the decision maker (over 0,5 in our opinion). 2. The second original proposition ELECTRE II method has proposed a concept of tough and mild hierarchy, which we can generalize, using the “hierarchical rank” – meaning the order in which we’ve done the hierarchy. How could we show this using a calculus? A suggestion might be the following: (ELECTRE V). In the hierarchical graph we can add an arrow every time the concordance or discordance threshold respectively changes. This may lead to the selection of the alternative for which we obtain a “better hierarchical difference” as comparing to the alternatives for which we get “mild hierarchical differences”. 2
Issue Method Overtaking relationships 1. ELECTRE I If : c gh ≥ c; d gh ≤ d ↔ A g P A h 2. ELECTRE II If : c gh ≥ c; d gh ≤ d ↔ A g P A h P + gh /P - gh ≥ 1; 3. ELECTRE III 4. ELECTRE IV (original alternative) 5. ELECTRE V (original alternative) 6. Modified ELECTRE 7. Rate –set ELECTRE If : c gh ≥ c; d gh ≤ d ↔ A g P A h P gh + /P gh - ≥ 1; If c gh ≥ c hg ; d gh ≤ d hg ; d ≤ 1 ↔ A g P A h If : c gh ≥ c; d gh ≤ d ↔ A g P A h If: c gh – d gh ≥ c – d ↔ A g P A h The discordance indicator: d gh = ∑ j (u hj – u gj ) · k j where : k j – the importance level of C J criteria Table no.1. ELECTRE Methods Decision algorithm Aforementioned algorithm It uses two pairs of threshold values: one pair for tough overtaking and one pair for mild overtaking. We consider the both directly an indirectly hierarchies. The tough classification is completed by the mild classification.. It proposes the concept named insensbility for the discordance indicators less then threshold value. It makes directly and indirectly classification for the alternatives. The threshold values disappear, the comparing it makes between the values from matrix. The result is getting by the ELECTRE II method. Each overtaking relationship is marked every time when are modified the threshold values. Hereby, the alternative which have bigger values of concordance indicators or/and less values of discordance indicators will obtain more overtaking relationships than all of others. It subtractions the discordances matrix from the concordances matrix and the line which have more positives values indicates the optimal alternative. This way, an alternative with lots of small disadvantages can be defeated by another one with only one big disadvantage. We illustrate our suggested solutions with the following numericalal example. In the following application there are presented some of the methods. 3
Page 1: SOME PARTICULAR ASPECTS CONCERNING
Page 5 and 6: Table no. 5. Discordance Matrix (d
Page 7 and 8: So, the optimal alternative is A 4

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