Koen C. Maes, Susanne Saminger, Bernard De Baets,
"Representation and construction of self-dual aggregation operators"
, in European Journal of Operational Research, Vol. 177, Seite(n) 472-487, 2007, ISSN: 0377-2217
Original Titel:
Representation and construction of self-dual aggregation operators
Sprache des Titels:
Englisch
Original Kurzfassung:
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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