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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 Wilkin
Weak 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 Sciences

Volume

300

Pagination

70-84

Location

Amsterdam, The Netherlands

ISSN

0020-0255

Language

eng

Publication classification

C Journal article, C1 Refereed article in a scholarly journal

Copyright notice

2015, Elsevier

Publisher

Elsevier