Exploitation procedure based on eigenvector revisited: the concept of weighted preference flows in multicriteria outranking analysis

The outranking analysis has been frequently used to deal with the complex decisions involving qualitative criteria and imprecise data. So far, various versions of ELECTRE have been proposed for ranking alternatives in the outranking analysis. Among others, ELECTRE III has been widely used. A distillation procedure using a qualification index is proposed to rank alternatives from the fuzzy outranking relation. A weakness of ELECTRE III, however, is to involve the arbitrariness in the selection of the discrimination threshold function for the distillation procedure. On the other hand, various variants of PROMETHEE has also been proposed for the outranking analysis. PROMETHEE intends to be simple and easy to understand. A deficiency of PROMETHEE is that it does not take discordance into account when the outranking relation matrix is constructed. This note revisits an exploitation procedure based on eigenvector using the "weighted" preference in-and out-flows. of each alternative in the outranking analysis. The basic idea is that it should be better to outrank a "strong" alternative than a "weak" one and, conversely, it is less serious to be outranked by a "strong" alternative than by a "weak" one in a PROMETHEE context. It has a completely different interpretation with the AHP (Analytic Hierarchy Process) since the components of the fuzzy (valued) outranking relation matrix are neither ratios nor reciprocal as in the AHP