An idea for ordinal sorting based on ELECTRE without category limits

This work proposes a simple and logical principle for ordinal sorting problems based on an outranking relation (namely ELECTRE’s) on the set of the alternatives to be sorted. This principle can be stated as “if an alternative outranks (is as good as) a second one, then it must belong to the same category or to a better category”. We operationalize this principle through a procedure based on asking a Decision Maker to provide sorting examples, which are then used to constrain the range of categories where other alternatives may be sorted. We show how the same idea may be used in an aggregation/disaggregation approach, considering the weights and the cutting level of ELECTRE are not fixed a priori, but are constrained only by the examples provided. In this context, we establish a “convex-shape property” stating that the range of possible categories for an alternative is always an interval of categories. Finally, we propose and illustrate with some examples a process based on the computation of the minimum cutting level associated to each sorting possibility. A discussion contrasting this approach with ELECTRE TRI is included in the conclusions.

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