Extremal symmetrization of aggregation functions

Radko Mesiar (), Andrea Stupňanová () and Ronald R. Yager ()
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Radko Mesiar: Slovak University of Technology
Andrea Stupňanová: Slovak University of Technology
Ronald R. Yager: Slovak University of Technology

Annals of Operations Research, 2018, vol. 269, issue 1, No 25, 535-548

Abstract: Abstract For aggregating observed unordered n values, based on an n-ary aggregation function A, two extremal symmetric aggregation functions $$A^*$$ A ∗ and $$A_*$$ A ∗ are introduced and discussed. In the case of weighted arithmetic means, the representation of $$A^*$$ A ∗ and $$A_*$$ A ∗ as particular $${{\mathrm{OWA}}}$$ OWA operators is shown. Considering weighted aggregation function $${{{A}}_{{\mathbf w} }}$$ A w with unordered weights and input values to be aggregated, another two symmetric aggregation functions $$({{{A}}_{{\mathbf w} }})^\Diamond $$ ( A w ) ◊ and $$({{{A}}_{{\mathbf w} }})_\Diamond $$ ( A w ) ◊ are introduced and discussed. A relation between our approach and the Hungarian algorithm known from the linear optimization domain is also shown.

Keywords: Aggregation function; Choquet integral; Hungarian algorithm; OWA operator; Weighted arithmetic mean (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10479-017-2471-x

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