The self-dual core and the anti-self-dual remainder of an aggregation operator

In most decisional models based on pairwise comparison between alternatives, the reciprocity of the individual preference representations expresses a natural assumption of rationality. In those models self-dual aggregation operators play a central role, in so far as they preserve the reciprocity of the preference representations in the aggregation mechanism from individual to collective preferences. In this paper we propose a simple method by which one can associate a self-dual aggregation operator to any aggregation operator on the unit interval. The resulting aggregation operator is said to be the self-dual core of the original one, and inherits most of its properties. Our method constitutes thus a new characterization of self-duality, with some technical advantages relatively to the traditional symmetric sums method due to Silvert. In our framework, moreover, every aggregation operator can be written as a sum of a self-dual core and an anti-self-dual remainder which, in some cases,...

• Type: Journal
• Year: 2008
• Where: FSS
• Authors: José Luis García-Lapresta, Ricardo A. Marques Pereira
• Keywords: Aggregation Operators, FSS 2008, Preference Representations, Self-dual Aggregation Operator