Outranking Relations Case Study

1.2.1.6.4 The ELECTRE method:-

The ELECTRE (for Elimination and Choice Translating Reality; method was first introduced in 1966. The basic concept of the ELECTRE method is to deal with “outranking relations” by using pairwise comparisons among alternatives under each one of the criteria separately. The outranking relationship of the two alternatives Ai and Aj describes that even when the i-th alternative does not determine the j-th alternative quantitatively, then the decision maker may still take the risk of regarding Ai as almost better than Aj. Alternatives are said to be dominated, if there is another alternative which excels them in one or more criteria and equals in the remaining criteria. The ELECTRE method begins with pairwise comparisons
Using physical or monetary values, denoted as gi(Ai) and gj(Aj) of the alternatives Ai and Aj respectively, and by introducing threshold levels for the different gi(Ai) and gj(Aj), the decision maker may declare that he/she is indifferent between the alternatives under consideration, that he/she has a weak or strict preference for one of the two, or that he/she is unable to express any of these preference relations. Therefore a set of binary relations of alternatives, the so-called outranking relations may be complete or incomplete. Next the decision maker is requested to assign weights or importance factors in order to express their relative importance. Through the consecutive assessments of the outranking relations of the alternatives, the ELECTRE method elicits the so-called concordance index defined as the amount of evidence to support the conclusion that alternative Aj outranks or dominates, alternatives Ai, as well as the discordance index the counter-part of the concordance index. Finally, the ELECTRE method yields a system of binary outranking relations between the alternatives. Because this system is not necessarily complete, the ELECTRE method is sometimes unable to
The basic concept of this method is that the selected alternative should have the shortest distance from the ideal solution and the farthest distance from the negative-ideal solution in some geometrical sense. The TOPSIS method assumes that each criterion has a tendency of monotonically increasing or decreasing utility. Therefore, it is easy to define the ideal and negative-ideal solutions. The Euclidean distance approach was proposed to evaluate the relative closeness of the alternatives to the ideal solution. Thus, the preference order of the alternatives can be derived by a series of comparisons of these relative distances. The TOPSIS method first converts the various criteria dimensions into non-dimensional criteria as was the case with the ELECTRE method. As a remark, it should be stated that in the ELECTRE and TOPSIS methods the Euclidean distance represent some plausible assumptions. Other alternative distance measures could be used as well, in which case it is possible for one to get different answers for the same problem. However, it is reasonable to assume here that for the benefit criteria, the decision maker wants to have a maximum value among the alternatives. For the cost criteria, the decision maker wants to have a minimum value among