ELECTRE-III-H: An outranking-based decision aiding method for hierarchically structured criteria

Abstract

This paper proposes a method for ranking a set of alternatives evaluated using multiple and conflicting criteria that are organised in a hierarchical structure. The hierarchy permits the decision maker to identify different intermediate sub-problems of interest. In that way, the analysis of the criteria is done according to the subsets defined in the hierarchy, and following the precedence relations in a bottom-up approach. To deal with this type of hierarchical structures, an extension of the ELECTRE-III method, called ELECTRE-III-H, is presented. As all methods of ELECTRE family, this one also relies on building a binary outranking relation on the set of alternatives on the basis of concordance and discordance tests. The exploitation of this outranking relation generates a partial pre-order, establishing an indifference, preference or incomparability relation for each pair of alternatives. The idea of a bottom-up application of the classical ELECTRE-III method to sub-problems involving subsets of criteria at the intermediate levels of the hierarchy is infeasible because the evaluations of alternatives by criteria aggregating some sub-criteria have the form of partial pre-orders, and not complete pre-orders. Thus, we propose a new procedure for building outranking relations from a set of partial pre-orders, as well as a mechanism for propagating these pre-orders upwards in the hierarchy. With this method, the decision maker is able to analyse the problem in a decomposed way and gain information from the outputs obtained at intermediate levels. In addition, ELECTRE-III-H gives the decision maker the possibility to define a local preference model at each node of the hierarchy, according to his objectives and sub-problem characteristics. We show an application of this method to rank websites of tourist destination brands evaluated using a hierarchy with 4 levels.