Representation and construction of self-dual aggregation operators

Representation and construction of self-dual aggregation operators

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Article ID: iaor20084652
Country: Netherlands
Volume: 177
Issue: 1
Start Page Number: 472
End Page Number: 487
Publication Date: Feb 2007
Journal: European Journal of Operational Research
Authors: , ,
Keywords: duality
Abstract:

Two different characterizations of self-dual aggregation operators are available in the literature: one based on C(x,y) = x/(x + 1 − y) and one based on the arithmetic mean. Both approaches construct a self-dual aggregation operator by combining an aggregation operator with its dual. In this paper, we fit these approaches into a more general framework and characterize N-invariant aggregation operators, with N an involutive negator. Various binary aggregation operators, fulfilling some kind of symmetry w.r.t. N and with a sufficiently large range, can be used to combine an aggregation operator and its dual into an N-invariant aggregation operator. Moreover, using aggregation operators to construct N-invariant aggregation operators seems rather restrictive. It suffices to consider n-ary operators fulfilling some weaker conditions. Special attention is drawn to the equivalence classes that arise as several of these n-ary operators can yield the same N-invariant aggregation operator.

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