The integration of valued outranking relations in ELECTRE methods for ranking problem

The ELECTRE family of decision aid methods are well-known approaches in the field of multiple criteria decision aiding (MCDA). Different ELECTRE methods can be used for choice problem, ranking problem and sorting problem respectively. These methods are characterized by outranking relations and exploitation procedures. Different definitions of the outranking relations result in the difference of the exploitation procedures. It makes the DM difficult to choose a appropriate method to deal with the decision problem. On the other hand, the essence of the original ELECTRE is to evaluate the outranking relation of two alternatives from two different aspects, i.e. the concordance and the discordance. So, it is expected that the two aspects are independent. However, in classic ELECTRE methods, the correlation between two parameters still exist. More importantly, the uncertainty and imprecision are always exist in real-life situations. But the definition of the outranking relation in ELECTRE-I and ELECTRE-II methods can’t handle the phenomena very well. The ELECTRE-III method uses the concept of pseudo-criterion to handle these uncertain or imprecise phenomena. But the definition of the outranking relation is still incomplete. This paper aims at integrating the valued outranking relation on the basis of ELECTRE-I, ELECTREII and ELECTRE-III methods for ranking problem. The new outranking relation incudes most information of these three methods and the three methods can be treated as three special situations of the new relation. By introducing the discordance index and the preponderance index as well as the non-linear form of the concordance index and the discordance index, the new outranking relation is more complete and more suitable to simulate the non-linear and uncertain real-life situations. An illustrative example has been given to prove the rationality of this method for ranking problem.