Different ranking structures. Rankings may be a complete order, or a complete preorder, or a partial preorder. While each of these features may pose problems to specific ranking criteria, the main ranking structure can be perceived easily by decision makers. 

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... framework of multiobjective optimization is used to tackle the multicriteria ranking problem. The conceptual advantages of the multiobjective formulation are discussed and a new multiobjective evolutionary algorithm is introduced with the purpose of transforming a known valued outranking relation into an antisymmetric crisp outranking relation, on a set of classes of alternatives, where the elements of each class are indifferent each other, and with this as a background, we propose a recommendation for ranking problems of medium-sized set of alternatives. The performance of the algorithm is evaluated on a test problem. It was capable of producing a high-quality recommendation. Keywords : Multicriteria analysis; Valued outranking relations; Multiobjective evolutionary algorithms; Ranking procedure. A Multiple Criteria Decision Analysis provides two major approaches of constructing a global preference model from an actor involved in the decision process. The first one is the functional model, which has been widely used within the framework of multi-attribute utility theory (e.g. (Keeney and Raiffa, 1976; French, 1986; Triantaphyllou, 2000). The second one is the relational model, which has its most known representation in the form of a crisp or fuzzy outranking relation (e.g. (Roy, 1990)). The multiple criteria aggregation methods allow us to construct a recommendation from a set of alternatives based on the preferences of a decision maker. In the functional approach, the recommendation is immediately de- duced from the preferences aggregation process. When the aggregation model of preferences is based on the relational approach, a special treatment is required, but some non-rational violations of the explicit global model of preferences could happen. This paper is concerned with the relational approach to Multiple Criteria Decision Aid (MCDA). Methods related to this approach, including the well-known family of ELECTRE methods, are often presented as the combina- tion of two phases: aggregation (or construction) and ex- ploitation. For the multicriteria ranking problem, the second phase is usually carried out with a ranking method. Most respected text on MCDA (Vincke, 1992; Doumpos and Zopounidis, 2002 ; Figueira et al., 2005; Roy, 2006; Ehrgott et al., 2010; etc.) define the ranking problematic _ P .  informally, e.g. (Roy, 1996) defines the ranking problematic as: Definition (Roy, 1996). The ranking problematic P .  presents the problem in terms of ranking the actions of A, that is, of directing the investigation towards determining an order defined on a subset of A so as to be able to determine those actions that could be considered as “suff i- ciently satisfactory” based on a prefe rence model, while keeping in mind that A might evolve. This problematic leads to a recommendation or simple participation that either: suggest a partial or complete order formed by the classes containing actions considered equivalents. The use of informal definitions such as this reflects one of the prevailing and fundamental problems in MCDA: the difficulty of providing a single formal (but sufficiently broad) definition of the concept of a ranking. The concept of a ranking is a generalization of what decision makers perceive as a hierarchy of a set of alternatives in decreasing order of preferences, a decision maker intuition which is inherently difficult to capture by means of individual objective criteria. We illustrate this in Figure 1. On the other hand, most existing ranking methods for exploiting a known valued outranking relation attempt, ex- plicitly or otherwise, to optimize just one such criterion, and it is this confinement to a particular ranking property that explains the fundamental discrepancies observable between the recommendations produced by different algorithms on the same data, and will cause a ranking method to fail (as judged by means of external knowledge) in a context where the criterion employed is inap- propriate. In practice, this problem can be alleviated through the application and comparison of multiple ranking methods (see e.g. Guitouni and Martel (1998)). Initially, ranking algorithms were designed to capture the decision maker notion of a ranking, however, with the in- creased complexities of some kinds of decision problems, traditional ranking algorithms sometimes do not perform very well, especially in instances where there are a medium-sized set of alternatives and/or there are a lot of in- transitivities or incomparabilities between pairs of alternatives. But with the emergence of new mathematical techniques and with the enormous computer performance that exist nowadays, it is possible design new ranking algorithms for the application to the ranking of complex data sets not interpretable by decision makers. Applying new rules, further than only the traditional solutions and ideas, this kind of procedures should exploit the aggregation model of preferences of the decision maker and be able to provide a recommendation in form of a ranking. The aim of the proposed approach is twofold: first. We want to partition a medium-sized set of alternatives into k classes; second, based solely on the initially provided information, we want to elicit the antisymmetric crisp outranking relation between the determined classes. The particular advantage of the proposed approach is to integrate partition and relation between classes into the optimization process that the multiobjective evolutionary algorithm performs. The result of our method is thus given by a partition P k ( A ) of A into a set of classes C  { C 1 , C 2 ,..., C k } and a kxk crisp antisymmetric outranking relation S P k ( A ) on that partition. In the next section, the ranking problematic is presented. The single-objective ranking is explained in Section 3. Section 4 presents the multiobjective ranking, and with these as the background, we present a multiobjective evolutionary algorithm to a medium-sized ranking problem in Section 5. A test problem and the computational results are given in Section 6, and finally, in Section 7, several conclusions are ...