Weak monotonicity of Lehmer and Gini means

Beliakov, Gleb and Spirkova, Jana 2016, Weak monotonicity of Lehmer and Gini means, Fuzzy sets and systems, vol. 299, pp. 26-40, doi: 10.1016/j.fss.2015.11.006.

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Title Weak monotonicity of Lehmer and Gini means
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Spirkova, Jana
Journal name Fuzzy sets and systems
Volume number 299
Start page 26
End page 40
Total pages 15
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2016-09-15
ISSN 0165-0114
Keyword(s) mixture function
weak monotonicity
Lehmer mean
Gini mean
Summary We analyze directional monotonicity of several mixture functions in the direction (1,1...,1), called weak monotonicity. Our particular focus is on power weighting functions and the special cases of Lehmer and Gini means. We establish limits on the number of arguments of these means for which they are weakly monotone. These bounds significantly improve the earlier results and hence increase the range of applicability of Gini and Lehmer means. We also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions.
Language eng
DOI 10.1016/j.fss.2015.11.006
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical 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:30081992

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