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On the weak monotonicity of Gini means and other mixture functions
journal contribution
posted on 2015-04-10, 00:00 authored by Gleb BeliakovGleb Beliakov, T Calvo, Tim WilkinTim WilkinWeak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing their ϕϕ-transforms, and we established weak monotonicity of several classes of averaging functions, in particular Gini means and mixture operators. Mixture operators with Gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters. This study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers.
History
Journal
Information SciencesVolume
300Pagination
70 - 84Publisher
ElsevierLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0020-0255Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2015, ElsevierUsage metrics
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