# Extremal symmetrization of aggregation functions

Ontology type: schema:ScholarlyArticle

### Article Info

DATE

2017-03-29

AUTHORS ABSTRACT

For aggregating observed unordered n values, based on an n-ary aggregation function A, two extremal symmetric aggregation functions A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^*$$\end{document} and A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_*$$\end{document} are introduced and discussed. In the case of weighted arithmetic means, the representation of A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^*$$\end{document} and A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_*$$\end{document} as particular OWA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{OWA}}}$$\end{document} operators is shown. Considering weighted aggregation function Aw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{A}}_{{\mathbf w} }}$$\end{document} with unordered weights and input values to be aggregated, another two symmetric aggregation functions (Aw)◊\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({{{A}}_{{\mathbf w} }})^\Diamond$$\end{document} and (Aw)◊\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({{{A}}_{{\mathbf w} }})_\Diamond$$\end{document} are introduced and discussed. A relation between our approach and the Hungarian algorithm known from the linear optimization domain is also shown. More... »

PAGES

535-548

### Journal

TITLE

Annals of Operations Research

ISSUE

1-2

VOLUME

269

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10479-017-2471-x

DOI

http://dx.doi.org/10.1007/s10479-017-2471-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1084024797

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