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Title: A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case (English)
Author: Kouchakinejad, Fateme
Author: Šipošová, Alexandra
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 53
Issue: 1
Year: 2017
Pages: 129-136
Summary lang: English
Category: math
Summary: For an aggregation function $A$ we know that it is bounded by $A^*$ and $A_*$ which are its super-additive and sub-additive transformations, respectively. Also, it is known that if $A^*$ is directionally convex, then $A=A^*$ and $A_*$ is linear; similarly, if $A_*$ is directionally concave, then $A=A_*$ and $A^*$ is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively. (English)
Keyword: aggregation function
Keyword: overrunning and underrunning property
Keyword: sub-additive and super-additive transformation
MSC: 47H04
MSC: 47S40
idZBL: Zbl 06738598
idMR: MR3638560
DOI: 10.14736/kyb-2017-1-0129
Date available: 2017-04-03T10:51:10Z
Last updated: 2018-01-10
Stable URL:
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