Outranking Methods

A classical problem in the field of Multiple Criteria Decision Making (mcdm) is to build a preference relation on a set of multi-attributed alternatives on the basis of preferences expresses on each attribute and “inter-attribute” information such as weights. Based on this preference relation (or, more generally, on various relations obtained following a robustness analysis) a recommendation is elaborated (e.g. exhibiting of a subset likely to contain the “best” alternatives). A common way [20] to do so is to attach a number v(x) to each alternative x ∈ X and to declare that x is at least as good as y if and only if v(x) ≥ v(y). The number v(x) depends on the evaluations x1, x2, ...xn of x on the n attributes and we have v(x) = V (x1, x2, ..., xn). The most common form for V is an additive value function in which V (x1, x2, ..., xn) = ∑n i=1 kivi(xi); in that case the task of the analyst reduces down to assessing the partial value functions vi and the scaling constants ki. The preference relation that is built using this value function approach is a weak order, i.e. a complete and transitive binary relation. Using such information it is not difficult, in general, to elaborate a recommendation. The definition if the aggregation function V may not always be simple however. Making all alternatives comparable in a “nice transitive way” requires much information and, in particular, a detailed analysis of trade-offs between attributes. Outranking Methods (OMs) were first developed in France in the late sixties following difficulties experienced with the value function approach in dealing with practical problems. They are closely associated with the name of Bernard Roy who developed the well-known family of electre Methods. A large part of the literature on OMs was written in French which has been prejudicial to their international diffusion; good accounts in English are [18, 37, 44, 51, 54] while detailed references in French include [24, 31, 39, 45, 46].