Abstract
For aggregating observed unordered n values, based on an n-ary aggregation function A, two extremal symmetric aggregation functions \(A^*\) and \(A_*\) are introduced and discussed. In the case of weighted arithmetic means, the representation of \(A^*\) and \(A_*\) as particular \({{\mathrm{OWA}}}\) operators is shown. Considering weighted aggregation function \({{{A}}_{{\mathbf w} }}\) with unordered weights and input values to be aggregated, another two symmetric aggregation functions \(({{{A}}_{{\mathbf w} }})^\Diamond \) and \(({{{A}}_{{\mathbf w} }})_\Diamond \) are introduced and discussed. A relation between our approach and the Hungarian algorithm known from the linear optimization domain is also shown.
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Acknowledgements
The support of the Grants APVV-14-0013 and VEGA 1/0682/16 is kindly announced.We express our gratitude to Dr. Carlos Lopez-Molina for rivet our attention to the Hungarian algorithm. We are also grateful to anonymous reviewers and editors for their valuable comments helping us to improve the original version of this paper.
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Mesiar, R., Stupňanová, A. & Yager, R.R. Extremal symmetrization of aggregation functions. Ann Oper Res 269, 535–548 (2018). https://doi.org/10.1007/s10479-017-2471-x
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DOI: https://doi.org/10.1007/s10479-017-2471-x