Kybernetika 53 no. 1, 129-136, 2017

A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case

Fateme Kouchakinejad and Alexandra ŠipošováDOI: 10.14736/kyb-2017-1-0129

Abstract:

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.

Keywords:

aggregation function, overrunning and underrunning property, sub-additive and super-additive transformation

Classification:

47H04, 47S40

paper.pdf

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