Extending concordance and discordance relations to hierarchical sets of criteria in ELECTRE-III method

  • Authors:

  • Luis Del Vasto-Terrientes;Aida Valls;Roman Slowinski;Piotr Zielniewicz

  • Affiliations:

  • Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Catalonia, Spain;Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Catalonia, Spain;Institute of Computing Science, Poznan University of Technology, Poznan, Poland;Institute of Computing Science, Poznan University of Technology, Poznan, Poland

  • Venue:
  • MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
  • Year:
  • 2012

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Abstract

In many real-world multiple criteria decision problems, the family of criteria has a hierarchical structure presented in the form of a tree. The leaves of the tree correspond to elementary criteria on which a finite set of alternatives is directly evaluated. Evaluations of alternatives on elementary criteria are aggregated to form a sub-criterion at an upper level of the tree. Then, evaluations of alternatives on sub-criteria having the same predecessor in the hierarchy tree are aggregated again in a sub-criterion of a higher level, and so on, until the aggregation at the general goal criterion, which is the root of the tree, where the alternatives are finally ranked from the best to the worst. At each node of the tree, above the leaves, we are considering the aggregation of multiple criteria evaluations using the ELECTRE-III method, based on building and exploiting outranking relations for each pair of alternatives. As the result of ELECTRE-III is a partial preorder of alternatives, the sub-criteria are ordering the alternatives just partially. Therefore, in this paper we propose a new way of calculating concordance and discordance indices that take part in the definition of an outranking relation aggregating the (partially ordered) evaluations on sub-criteria. A robustness analysis has been performed to analyze the behavior of the proposed method in different settings.