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Representation and construction of self-dual aggregation operators [An article from: European Journal of Operational Research]
Book Details
Author(s)K.C. Maes, S. Saminger, B. De Baets
PublisherElsevier
ISBN / ASINB000PBZSDS
ISBN-13978B000PBZSD2
AvailabilityAvailable for download now
MarketplaceUnited States 🇺🇸
Description
This digital document is a journal article from European Journal of Operational Research, published by Elsevier in 2007. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.
Description:
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.
Description:
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.
