On the weak monotonicity of Gini means and other mixture functions

Beliakov, Gleb, Calvo, Tomasa and Wilkin, Tim 2015, On the weak monotonicity of Gini means and other mixture functions, Information Sciences, vol. 300, pp. 70-84, doi: 10.1016/j.ins.2014.12.030.

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Title On the weak monotonicity of Gini means and other mixture functions
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Calvo, Tomasa
Wilkin, TimORCID iD for Wilkin, Tim orcid.org/0000-0003-4059-1354
Journal name Information Sciences
Volume number 300
Start page 70
End page 84
Total pages 15
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2015-04-10
ISSN 0020-0255
Keyword(s) Science & Technology
Computer Science, Information Systems
Computer Science
Aggregation function
Penalty-based function
Gini mean
Mixture function
Summary 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 ϕ-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.
Language eng
DOI 10.1016/j.ins.2014.12.030
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, Elsevier
Persistent URL http://hdl.handle.net/10536/DRO/DU:30074246

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