A Distance-Based Collective Preorder Integrating the Relative Importance of the Group's Members

In this paper, we propose an aggregation procedure, which includes two steps. In the first one, the group's members elaborate individually a preorder (total or partial) on the alternatives set. These preorders can be obtained, for example, by applying a multicriterion aggregation procedure such as ELECTRE III, PROMETHEE I or II. In the second step, these individual preorders (total or partial) are aggregated into a collective preorder (total or partial). For this purpose, we first built a distance measure between pairs of binary relations in order to quantify the divergence between two preorders. Then we determine, for each pair of alternatives, the relative importance coefficients of the group's members by using a method based on subjective and objective components. These coefficients and the distance measure are finally exploited by an iterative algorithm in order to elaborate a collective preorder synthesizing the individual preorders.