Axiomatic foundation of the analytic hierarchy process
Management Science
Biorder families, valued relations and preference modelling
Journal of Mathematical Psychology
On ordered weighted averaging aggregation operators in multicriteria decisionmaking
IEEE Transactions on Systems, Man and Cybernetics
Characterization of some aggregation functions stable for positive linear transformations
Fuzzy Sets and Systems
Aggregation operators: properties, classes and construction methods
Aggregation operators
Aggregation with generalized mixture operators using weighting functions
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Commutativity and self-duality: Two tales of one equation
International Journal of Approximate Reasoning
IEEE Transactions on Fuzzy Systems
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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, seems to give some indication on the dispersion of the variables. In order to illustrate the method proposed, we apply it to two important classes of continuous aggregation operators with the properties of idempotency, symmetry, and stability for translations: the OWA operators and the exponential quasiarithmetic means.